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Talk:PNAS Response to Letter

2008-11-03T23:19:43Z

DavyJones: /* Point 5 Rejected */ A reasoned argument is not a rant.

Notice: misrepresentations are not going to be allowed on this page. Substantive comments only, please.

Note: earlier posts are archived [[Talk:PNAS_Response_to_Letter/Archive1|here]]. --[[User:BillA|BillA]] 17:05, 20 September 2008 (EDT)

== Point 5 Confirmed ==

I would like to contribute to this discussion because I have taught statistics to graduate biology students for 16 years.

The combination of data from several experiments is a specialist and sometimes difficult area of statistical theory but a simple example shows why Aschafly’s concern about combining the results of three different experiments is not justified and why this aspect of his criticism of Lenski’s recent paper in PNAS is not valid.

Suppose we want to conduct a test of whether or not men are taller than women on average. For the sake of the example, I generated random heights of people from a population in which men had an average height of 175cm (5’10’) and women of 165cm (5’6”). The standard deviations of height in both sexes were 7cm. I think these numbers are approximately correct for people in the UK but the details aren’t important.

Suppose we take 5 samples of 2 men and 2 women. Here are the numbers I generated:

{| class="wikitable"
|-
! Man1 !! Man2 !! Woman1 !! Woman2 !! Men mean !! Women mean !! Mean difference !! t !! P
|-
| 176 || 179 || 157 || 148 || 177.5 || 152.5 || 25 || 5.27 || 0.017
|-
| 180 || 176 || 160 || 164 || 178 || 162 || 16 || 5.66 || 0.015
|-
| 176 || 175 || 167 || 165 || 175.5 || 166 || 9.5 || 8.50 || 0.0068
|-
| 169 || 171 || 168 || 173 || 170 || 170.5 || -0.5 || -0.19 || 0.57
|-
| 179 || 175 || 166 || 178 || 177 || 172 || 5 || 0.79 || 0.26
|-
|}

P in the last column is the t-test probability for a one-side test of women being shorter than men. (Formally, it’s the probability of getting a value of t greater than that calculated from the data if women are in fact taller than men on average.)

Should the fact that, in the fourth sample, the average height of the women is taller than that of the men make us doubt that men are in fact taller on average? Should we be concerned about the last sample, in which the difference in height of the two sexes is rather small, though in the expected direction? No, in both cases. When we combine the data on all 10 men and all 10 women, we get this:

{| class="wikitable"
|-
! Men mean !! Women mean !! Mean difference !! t !! ''P''
|-
| 175.6 || 164.6 || 11 || 3.85 || 0.00058
|-
|}

Clearly, combining the data from several similar experiments strengthens the conclusions considerably, as shown by the fact that ''P'' is much smaller for the combined data than for any individual sample.

Although the combination of data from several experiments is a specialised area of statistics, I see nothing particularly incorrect about the approach used by Lenski and his colleagues. The general point is that it is valid to combine the results of different experiments if it is scientifically meaningful to do so. (For example: A. Combining the results of five samples of the heights of men and women is clearly valid. B. Combining three samples of heights of men and women with two samples of lengths of male and female squid clearly isn’t.) Generally speaking, the outcome of a combined analysis of several small experiments which all point in the same direction (or at least in a similar direction) will be more significant than that of any one of those experiments, as is shown in the larger table above.

I hope this clarifies the extensive discussion on this point and puts Aschafly’s mind at rest on this subject. [[User:KennyMac|KennyMac]] 08:20, 18 September 2008 (EDT)

:That's very nicely put, thanks. You should work on some of the stats pages here. Of course, technically any sample is ultimately just a combination of ''n'' samples of size 1. [[User:MikeR|MikeR]] 13:28, 18 September 2008 (EDT)

:I'll take a look at this Friday. It's not immediately obvious what the point is to your analysis above.--[[User:Aschlafly|Aschlafly]] 23:46, 18 September 2008 (EDT)
::"''The general point is that it is valid to combine the results of different experiments if it is scientifically meaningful to do so"''--[[User:KingOfNothing|KingOfNothing]] 00:57, 19 September 2008 (EDT)

:::This makes no sense as an argument. It may be true in this simple case that you can do one large or several small samples and get similar results - which is quite obvious and wouldn't need such a detailed rant. However, you provide no mathematical proof, just one example. [[User:Etc|Etc]] 01:08, 19 September 2008 (EDT)
:''"It's not immediately obvious what the point is to your analysis above"''. No surprise, Aschlafly, really. Maybe you should take your own advice: ''"I suggest you try harder with an open mind"''. --[[User:CrossC|CrossC]] 02:46, 19 September 2008 (EDT)

It is with great sadness that I note that the author of this - the only significant statistical explanation and discussion in this entire fiasco- has [http://www.conservapedia.com/index.php?title=Special%3ALog&type=block&user=DeanS&page=User%3AKennyMac just been blocked] for five years. Even his email is blocked, so he can't even appeal the action. I don't see such manouvers as having contributed to the much vaunted "open mind" of which various people here speak. [[User:BenHur|BenHur]] 10:27, 19 September 2008 (EDT)

'''REPLY''': I have now reviewed the above analysis, and it supports Point 5 rather than the PNAS paper. Point 5 stated, "The Third Experiment was erroneously combined with the other two experiments based on outcome rather than sample size, thereby yielding a false claim of overall statistical significance." The analysis above does nothing more than reinforce Point 5 by combining experiments based on sample size.

In Pavlovian manner, some Lenski types nod their head here in agreement at the above analysis, apparently unaware that it reinforces Point 5.

When combining results from samples that are vastly different in sample size, it is necessary to factor in the different sample sizes. Apparently the PNAS paper failed to do that, which helps explain why it refuses to provide a meaningful response to Point 5.--[[User:Aschlafly|Aschlafly]] 19:24, 19 September 2008 (EDT)

(rants below were deleted for being non-substantive in violation of this page's rules.)--[[User:Aschlafly|Aschlafly]] 19:24, 19 September 2008 (EDT)

:::I understand point 5 now, or at least I think I do. What we have as a "sample" is either:

::::1. Individual cultures (Schlafly)
::::2. Cultures that developed cit+. (Lenski)

:::Schlafly contends that the sample should be all the cultures and that Lenski has, improperly, filtered the sample by excluding the vast majority of it (i.e. all those cultures that did not become cit+). Am I right in thinking this is the argument? --[[User:Toffeeman|Toffeeman]] 19:57, 19 September 2008 (EDT)

:::: No, we're talking about how Lenski combined a large study (which did not really support Lenski's hypothesis) with small studies (which Lenski claims does support his hypothesis). The studies were not combined in a logical manner with proper weighting given to the much bigger size of the large study.--[[User:Aschlafly|Aschlafly]] 23:15, 19 September 2008 (EDT)
:::::Aschlafly, have you read the paper on z-transforms which explains the statistical technique used? You can download a .pdf copy of the paper for free [http://www3.interscience.wiley.com/journal/118663174/abstract here]. --[[User:BillA|BillA]] 06:30, 20 September 2008 (EDT)

:::::: You say "statistical technique used," but you should have said "statistical technique ''cited''." In fact, a close reading of the Z-transform paper provides more support for Point 5: combined studies must be weighted based on sample size:

::::::: "When there is variation in the sample size across studies, there can be a noticeable difference in the power of the two methods, with the weighted Z-approach being superior in all cases. As such, we should always prefer the weighted Z to the unweighted Z-approach when the independent studies test the same hypothesis."[http://www3.interscience.wiley.com/journal/118663174/abstract see p. 1371].

:::::: In other words, the cited paper actually ''supports'' Point 5.--[[User:Aschlafly|Aschlafly]] 09:34, 20 September 2008 (EDT)

(unindent)Lenski used the weighted method. See note 49 to the paper and the text around the combination. Of course there is the question of on what basis Lenski weighted the results. Lenski weighted the results on the basis of the Cit+ numbers and we may think it would have been better to weight on the basis of the number of replicates. I have below the calculations (not mine) of combined P-values based on 1) no weighting, 2) weighting on the basis of Cit+ and 3) weighting on the basis of replicates. The weighted Z-transformed = SUM(Weight x Z-score for each run)/SQRT(SUM(Weight^2 for each run))

{| class="wikitable"
|-
! Expt# !! p-value !! z-score !! #Cit+ muts !! #replicates
|-
| 1 || 0.0085 || 2.387 || 4 || 72
|-
| 2 || 0.0007 || 3.195 || 5 || 340
|-
| 3 || 0.0823 || 1.390 || 8 || 2800
|-
|}

Applying the formula described above..

{| class="wikitable"
|-
! Weighting !! Z transformed !! p
|-
| Equal || 4.025 || <0.001
|-
|By total Cit+|| 3.576 || <0.001
|-
|By total replicates|| 1.825 || 0.034
|-
|}

So weighting on the basis of the number of replicates considerably increases the P-value. It remains, however, well within the range of statistical significance (0<P<0.05). If we hold that Lenski should have weighted on the basis of replicates then he should have rejected the null hypothesis and reached exactly the same conclusions that he did. The entire paper would have been exactly the same except the sentence “the result is extremely significant (P<0.0001) whether or not….” Would read “the result is significant (P<0.04) whether or not”. Point 5 establishes one number and an “extremely”. Point 5, therefore, has no weight (excuse the pun).
--[[User:Toffeeman|Toffeeman]] 15:18, 20 September 2008 (EDT)

: Sorry, Toffeeman, a falsehood is still a falsehood. Based on your own posting, if Lenski had applied the Whitlock Z-transform paper in a logical manner, the results would not have been nearly as striking as Lenski claimed (his paper said the results were "extremely significant"). Moreover, I found Lenski's description of his application of the Whitlock paper to be particularly misleading. Lenski's use of "whether or not"<ref>"We also used the Z-transformation method (49) to combine the probabilities from our three experiments, and '''the result is extremely significant (P < 0.0001) whether or not''' the experiments are weighted by the number of independent Cit+ mutants observed in each one." (Lenski paper at 7902).</ref> obscures the basic error that he did not apply Whitlock's paper in the straightforward, correct manner. I think the wording in the Lenski paper deliberately obscures this falsehood from the reader.

: People have free will to embrace and defend falsehoods. I don't expect them to change quickly or admit they were wrong. But you'll find me defending and promoting the truth.

: Point 5 remains valid and the falsehood remains uncorrected by PNAS or Lenski. Four other points in higher priority remain uncorrected by them also.--[[User:Aschlafly|Aschlafly]] 16:47, 20 September 2008 (EDT)

::'''''"a falsehood is still a falsehood"'''''. Precisely, the null hypothesis should be considered false and the conclusions of the paper stand.

::Oh? Do you mean ''Lenski's falsehood''? And what falsehood is that? Lenski said that he had calculated the P-value without weighting and that had come out at <0.0001. That is true, not false. Lenski said he had calculated the P-value weighting on the basis of the Cit+ replicates and that had come out at <0.0001. That is true, not false. There is no falsehood. Lenski did not mention the results of weighting on the basis of replicate numbers. He thus made no claim about weighting on the basis of replicate numbers. If he made no claim he cannot have made a false claim.

::How do the words Lenski uses "mislead". If you read them as written what conclusion do you come to? You are lead to the conclusion that the mutation was not "rare-but-equal", instead it was contingent. That is the right conclusion. If Lenski had presented the data in a different manner (perhaps by including the results of weighting on the basis of replicate numbers) what conclusion do you come to? You are again lead to the conclusion that the mutation was not "rare-but-equal", instead it was contingent. That is the right conclusion. To mislead you must be lead to a conclusion that is incorrect. By Lenski's paper you are not lead to a conclusion that is incorrect. Thus is cannot be said to be "misleading".

::I shall not comment on your second paragraph, the temptation to ''"Tu Quoque"'' would be too great.

--[[User:Toffeeman|Toffeeman]] 17:13, 20 September 2008 (EDT)

::: The falsehood consists of pretending to apply the Whitlock Z-transform in a straightforward, logical and correct manner. I think the Lenski paper is intentionally misleading by using the "whether or not" wording, when both alternatives are nonsensical. Point 5 has been proven above to be correct in identify an error in the Lenski paper.

::: "Toffeeman", your blocking history suggests you have been less than straightforward yourself. Go elsewhere if you seek to be deceitful. You're not fooling anyone here.--[[User:Aschlafly|Aschlafly]] 17:54, 20 September 2008 (EDT)

::::Lenski did apply the Z-transformation correctly, both weighted and unweighted. The data points extracted from each replay are the ''generation numbers of those replicates that gave rise to Cit+ mutants''. Thus Replay 1 produced four data points: 30,500 31,500 32,500 32,500. Replay 2 produced five data points: 32,000 32,000 32,000 32,000 32,500. Replay 3 produced eight data points: 20,000 20,000 27,000 27,000 31,000 31,500 32,000 32,000. Thus the N for replay 1 is 4; replay 2 is 5 and replay 3 is 8. The fact that replay 3 used 38 times as many replicates as replay 1 does not mean that it should be weighted 38 times as much; it only produced twice as much data, not 38 times as much.

::::Suppose I want to find out what the average age of a murderer is in three cities. In L.A. I interview 72 random people and find that 4 of them were convicted of murder; I record the ages of the four. In Seattle I interview 340 people and find that 5 of them are convicted murderers; likewise in Singapore I interview 2800 and find 8 murderers. In the end, I have 4,5, and 8 data points from the three cities; the number of people I had to interview to obtain those data points doesn't factor into the analysis of what the average age of the murderers is.--[[User:Brossa|Brossa]] 00:06, 21 September 2008 (EDT)

::::: In your first paragraph you simply repeat the error underlying Lenski's paper. You, like the paper, incorrectly apply Whitlock's Z-transform.

::::: The quality and reliability of data is proportional to sample size, and when different studies are combined they need to be weighted accordingly. The results from a very large sample size would not be weighted equally with the results from a small sample size, as you and Lenski have done. That's basic logic, though I'm not optimistic that you or Lenski will admit it. Open-minded people who respect logic have no difficulty elevating logic over personal whim.-[[User:Aschlafly|Aschlafly]] 11:30, 21 September 2008 (EDT)

::::::Andy if you read Whitlock's paper you would see it say, and I quote, "Ideally each study is weighted proportional to the inverse of its error variance, that is, by the '''reciprocal of its squared standard error'''." It says nothing about weighting according to sample size, which is what you seem to be insisting should be done.
::::::Also Whitlock acknowledges in the paper that there is no preference for weighted versus equal weighting, so the fact that both equal weighting and weighting by the standard error give a statistically significant result shows that the 3 experiments combined support rejection of the null hypothesis. [[User:DanB|DanB]] 20:39, 21 September 2008 (EDT)

:::::::ASchlafly, you state that I incorrectly apply "Whitlock's Z-transform" (actually the test belongs to Mosteller & Bush<ref>Mosteller, F. & Bush, R.R. 1954. Selected quantitative techniques. In: ''Handbook of Social Psychology,'' Vol. 1 (G. Lindzey, ed.)</ref> and/or Liptak<ref>Liptak, T. 1958. On the combination of tests. ''Magyar Tud. Akad. Mat. Kutato Int. Kozl.'' '''3''': 171-197</ref>). Whitlock describes weighting by the reciprocal of the squared standard error. The standard error of the mean is proportional to 1/sqrt(N), so the reciprocal of the squared standard error is proportional to N. Thus larger studies ''are'' given more weight. I maintain that the sample sizes N of the three replays are 4, 5, and 8 respectively. Weighting based on those three N does not weight all three replays equally as you claim: it gives replay 2 25% more weight and replay 3 100% more weight than replay 1. Rather than simply repeating that I am wrong, will you please state what ''you'' think the sample sizes of the three replay experiments are, and, in your opinion, what the ''correct'' application of the Z-transformation would be?--[[User:Brossa|Brossa]] 18:00, 22 September 2008 (EDT)

:::::::: The Lenski paper states how it weighted the experiments, and that weighting is incorrect. Admit it. Moreover, the incorrect weighting in the Lenski paper was not likely an inadvertent error, as it inflated the significance of the results. I found the wording used by the Lenski paper to describe its (incorrect) weighting to be artfully misleading.

:::::::: Provide me with federal funding as Lenski received, and I'll write a paper for you. But I don't have to write an alternative paper to point out glaring errors in Lenski's paper.--[[User:Aschlafly|Aschlafly]] 08:35, 23 September 2008 (EDT)

::::::::: I've been following this discussion for a while and I have to agree with ASchlafly. It hardly seems fair that he should have to, in his spare time, replicate an experiment done by a professional just to "earn" the right to criticize it. I am unfamiliar with statistics, but if some complicated transform goes against common sense, common sense should prevail. After all, there are lies, damned lies, and statistics... [[User:AndyM|AndyM]] 10:57, 23 September 2008 (EDT)

(unindent)I'm not asking anyone to write a paper or replicate an experiment. I'm asking ASchlafly to support his statement "The results from a very large sample size would not be weighted equally with the results from a small sample size, '''as you and Lenski have done'''"(bolding mine). I have stated publicly, subject to challenge by others, that the sample sizes (n) of the three replays are four, five, and eight respectively. Furthermore, using n of 4, 5, and 8 in the weighted Z-method DOES NOT weight all the replay experiments equally - it weights replay 3 twice as much as replay 1 and 8/5 as much as replay 2. Tell you what: I'll drop all my questions about Monte Carlo and the Z-transform, and simply ask ASchlafly one question: '''what is the sample size, n, of the second replay experiment?''' He need not even do any calculations - a statement in words that will allow someone else to do the calculation will suffice. This is not a complicated question to answer; the paper states how many replicate cultures there were (340), how many cells there were in each replicate (3.9x10^8), how many replicates gave rise to Cit+ cells (5), and which generations those Cit+ replicates came from (4 from 32,000 and one from 32,500). I will even give ''my'' answer: '''five'''. Furthermore, I will say ''why'' I believe that, using the murderer/age analogy: performing the 340 replicates is the same as interviewing 340 people in order to find out if any of them are convicted murderers. Finding that five replicates gave rise to Cit+ mutants is the same as the survey finding that 5 of those 340 people were convicted murderers. Finding that the Cit+ mutants arose from 4 replicates from generation 32,000 and 1 from generation 32,500 is the same as finding the ages of the murderers. The five data points in the Lenski study allow one to calculate the 'mean generation of clones yielding Cit+': 32,100. This is the same as finding the mean age of the five murderers. If I want to compare this hypothetical murderer age study to some other study of the mean age of murderers, I would weight the studies based on how many murderers were in each study, not on how many non-murderers were included in the initial survey.

Surely ASchlafly can say ''what'' he thinks the n of the second replay is, even if he won't say ''why'' he thinks it. Is it five? 340? The number of replicates times the number of cells per replicate? Something else? No analysis need be performed on the resulting number.--[[User:Brossa|Brossa]] 15:54, 23 September 2008 (EDT)

:OK - would you care to put in writing that after ASchlafly gives you his response, you won't start obfuscating the issue with Monte Carlo and Z-transform issues? You understand: it is typical of liberals to, after being proven wrong, to start pretending that they were talking about an entirely different issue altogether. '''After ASchlafly states the sample size of the second replay experiment you will consider yourself answered.''' Correct?

:Brossa, your rant is misplaced. One cannot salvage an error in logic by questioning which of superior alternatives should be used instead. The sample size of an experiment is the number that comprises the underlying sample used in the experiment, not the number of a certain outcome from the experiment. Maybe you can debate yourself over what the correct underlying sample size is, but it is plainly not the number of a certain outcome from the experiment.--[[User:Aschlafly|Aschlafly]] 19:28, 23 September 2008 (EDT)

Maybe the Journal of Nature can be your next letter submission source. ''International Weekly Journal of Science'' -- [[Image:50 star flag.png|14px]] [[User:Jpatt|jp]] 21:17, 22 September 2008 (EDT)

==Point 5 Rejected==

Referring to ASchlafly's latest revert: OK, so let's forget about my specialist knowledge of the subject. It really doesn't matter. In science, what matters is what is said, not who says it. Remember that the most outstanding scientific discoveries of the 20th century were made by a patent clerk; the facts that he had no academic position at the time and a rather moderate educational record were irrelevant.

So, I repeat: if you don't agree with me, present a reasoned argument against my points and don't just delete my comments (it's not wiki etiquette to delete other people's comments on a Talk page unless they're abusive or obscence). At least you haven't been so feeble as to block me to prevent me from contributing to this page, as you've done to other contributors. So I now repeat once again my cut-and-paste from Longstop's contribution a couple of weeks ago - as I said, if you don't agree with it, present a rational argument against it.

:The main point he [Kennymac] makes is quite correct, that combining experiments will tend to give a more significant result (i.e. a lower P-value) than any single experiment on its own.

:The point that ASchlafly makes (headed '''REPLY''', shortly after KennyMac's example) is slightly misleading. You don't choose which experiments to combine on the basis of their outcomes - you either combine all relevant experiments or none. In this case, Professor Lenski chose to combine all the experiments and present a single analysis of them. That's fine.

:The issue of whether to weight the Z-test according to sample size is not a straightforward issue. Before Whitlock's recent paper, the consensus was that the P-value already depends on sample size so it should not be weighted according to sample size. (Basically, a high degree of significance, i.e. a low P-value, can be achieved by having either a large difference between the treatments or a large experiment or, of course, both.) Whitlock's work, based on computer simulations, is an interesting contribution but cannot be regarded as the last word on the subject because any computer simulation involves assumptions about the structure of the particular experiment simulated. I cannot imagine any editor of a scientific journal rejecting a paper because it used an unweighted Z-test rather than the weighted version (or vice-versa).

:The conclusion, therefore, is that while there is a quantitative difference in the level of significance obtained by weighted and unweighted Z-tests, there is undeniably a significant biological effect. ASchlafly and other contributors should not be concerned that there is anything incorrect about the biological conclusions of Professor Lenski and his students or that there was anything at all underhand about their analysis or presentation of their data. [[User:DavyJones|DavyJones]] 19:02, 2 November 2008 (EST)

:: DavyJones, Whitlock's paper is correct and Lenski should have applied it. You provide nothing meaningful to the contrary. Read my posting below and contribute to this encyclopedia, or go rant somewhere else. Your account will be blocked if you simply continue to rant here.

:: Moreover, as I already explained above, I found Lenski's description of his application of the Whitlock paper to be particularly misleading. Lenski's use of "whether or not" obscures the basic error that he did not apply Whitlock's paper in the straightforward, correct manner. I think the wording in the Lenski paper deliberately obscures this falsehood from the reader.--[[User:Aschlafly|Aschlafly]] 19:30, 2 November 2008 (EST)

:::Aschlafly,
:::1. A reasoned argument is not a rant. No-one should be afraid of a reasoned argument and it would be cowardly to use superior power (i.e. control over who can and cannot contribute to CP) to avoid having one.
:::2. Please see above for my comment regarding Whitlock's paper on whether or not to weight the Z-test. That paper is not decisive (it cannot be decisive as it only considereda limited number of scenarios in computer simulations) so it cannot be considered "correct" (your word). I would say that whether or not to weight the Z-test is purely a matter of choice at the present state of scientific understanding.
:::3. I and many others have pointed out on this page (including discussions which you've archived) that it doesn't actually matter in biological terms whether Lenski used the weighted or unweighted Z-test. The result is still significant, albeit at different levels.
:::4. I understand from that fact you're now arguing about the precise level of significance of Lenski's result that you've conceded my main point, that your Point 5 is not tenable. Can we at least agree on that question? [[User:DavyJones|DavyJones]] 18:19, 3 November 2008 (EST)

==Refereeing of Scientific Papers==

Another point that Aschlafly and others deleted was my explanation of why CP readers shouldn't be concerned about the fact that the Lenski paper was reviewed within 14 days. This is perfectly normal practice for a leading journal. If you're invited to review a paper for a leading journal and they give you 7/10/14/etc days, you only agree to review it if you're sure you're going to have time before the journal's deadline. So there's absolutely no reason to suppose the review wasn't done properly.

Again, if you disagree, discuss, don't delete and don't block. [[User:DavyJones|DavyJones]] 20:39, 31 October 2008 (EDT)

== References ==

<references/>

== Have we given up? ==

Not much activity here in the past few weeks. Have we given up on pursuing this matter further?
Conservapedia should work on continuing to keep the Lenski study and its flaws in the news.
Is there anything else we can do? Perhaps write to local officials about the misuse of public funds for studies like Lenski's, and also to complain about PNAS? --[[User:DRamon|DRamon]] 16:39, 31 October 2008 (EDT)

: We exposed five fundamental flaws in the study, and told the truth. The truth doesn't care whether some refuse to accept it. There will ''always'' be people who deny the truth, particularly when they stand to profit from falsehoods. For now, I've moved onto more pressing issues on this site.--[[User:Aschlafly|Aschlafly]] 16:56, 31 October 2008 (EDT)

:: What do you mean by "profit from falsehoods"? Are you seriously suggesting that everyone who has a different point of view from your own must have mercenary motives for disagreeing with you? That's a very bizarre point of view. [[User:DavyJones|DavyJones]] 20:39, 31 October 2008 (EDT)
:::The suggestion is that those who lie very frequently do so forr reasons of greed. Your denial of this self-evident fact, and your [[deceit]]ful twisting of Mr Schlafly's words, speak volumes of you, DavyJones. [[User:Bugler|Bugler]] 06:56, 1 November 2008 (EDT)

::::Well, I don't see how you can accuse me of twisting Aschlafly's words. The implication of his statement above is that he believe that what he wrote was true (although his Point 5, at least, was incorrect) and that people who disagree with him ("deny the truth", in his words) are seeking to profit by doing so, which is not correct.

::::More importantly, I don't see how Aschlafly can give up on an argument he started. It's plain from what KennyMac and other wrote that his Point 5 is not correct. Now, is he going to do CP readers the favour of reaching a rational conclusion to this discussion or is he going to resort to his ploy of blocking contributors with whom he doesn't agree? [[User:DavyJones|DavyJones]] 20:03, 1 November 2008 (EDT)

::::: "DavyJones" you're making false statements here and that will not be allowed. Point 5 is confirmed and you've provided nothing meaningful to rebut it. Also, [[evolution syndrome]] is not allowed here either. If you do not contribute in a meaningful way to non-evolution entries in this encyclopedia, then your account will be blocked.--[[User:Aschlafly|Aschlafly]] 19:26, 2 November 2008 (EST)

Talk:PNAS Response to Letter

2008-11-03T00:15:45Z

DavyJones: /* Referring of Scientific Papers */ spelling

Notice: misrepresentations are not going to be allowed on this page. Substantive comments only, please.

Note: earlier posts are archived [[Talk:PNAS_Response_to_Letter/Archive1|here]]. --[[User:BillA|BillA]] 17:05, 20 September 2008 (EDT)

== Point 5 Confirmed ==

I would like to contribute to this discussion because I have taught statistics to graduate biology students for 16 years.

The combination of data from several experiments is a specialist and sometimes difficult area of statistical theory but a simple example shows why Aschafly’s concern about combining the results of three different experiments is not justified and why this aspect of his criticism of Lenski’s recent paper in PNAS is not valid.

Suppose we want to conduct a test of whether or not men are taller than women on average. For the sake of the example, I generated random heights of people from a population in which men had an average height of 175cm (5’10’) and women of 165cm (5’6”). The standard deviations of height in both sexes were 7cm. I think these numbers are approximately correct for people in the UK but the details aren’t important.

Suppose we take 5 samples of 2 men and 2 women. Here are the numbers I generated:

{| class="wikitable"
|-
! Man1 !! Man2 !! Woman1 !! Woman2 !! Men mean !! Women mean !! Mean difference !! t !! P
|-
| 176 || 179 || 157 || 148 || 177.5 || 152.5 || 25 || 5.27 || 0.017
|-
| 180 || 176 || 160 || 164 || 178 || 162 || 16 || 5.66 || 0.015
|-
| 176 || 175 || 167 || 165 || 175.5 || 166 || 9.5 || 8.50 || 0.0068
|-
| 169 || 171 || 168 || 173 || 170 || 170.5 || -0.5 || -0.19 || 0.57
|-
| 179 || 175 || 166 || 178 || 177 || 172 || 5 || 0.79 || 0.26
|-
|}

P in the last column is the t-test probability for a one-side test of women being shorter than men. (Formally, it’s the probability of getting a value of t greater than that calculated from the data if women are in fact taller than men on average.)

Should the fact that, in the fourth sample, the average height of the women is taller than that of the men make us doubt that men are in fact taller on average? Should we be concerned about the last sample, in which the difference in height of the two sexes is rather small, though in the expected direction? No, in both cases. When we combine the data on all 10 men and all 10 women, we get this:

{| class="wikitable"
|-
! Men mean !! Women mean !! Mean difference !! t !! ''P''
|-
| 175.6 || 164.6 || 11 || 3.85 || 0.00058
|-
|}

Clearly, combining the data from several similar experiments strengthens the conclusions considerably, as shown by the fact that ''P'' is much smaller for the combined data than for any individual sample.

Although the combination of data from several experiments is a specialised area of statistics, I see nothing particularly incorrect about the approach used by Lenski and his colleagues. The general point is that it is valid to combine the results of different experiments if it is scientifically meaningful to do so. (For example: A. Combining the results of five samples of the heights of men and women is clearly valid. B. Combining three samples of heights of men and women with two samples of lengths of male and female squid clearly isn’t.) Generally speaking, the outcome of a combined analysis of several small experiments which all point in the same direction (or at least in a similar direction) will be more significant than that of any one of those experiments, as is shown in the larger table above.

I hope this clarifies the extensive discussion on this point and puts Aschafly’s mind at rest on this subject. [[User:KennyMac|KennyMac]] 08:20, 18 September 2008 (EDT)

:That's very nicely put, thanks. You should work on some of the stats pages here. Of course, technically any sample is ultimately just a combination of ''n'' samples of size 1. [[User:MikeR|MikeR]] 13:28, 18 September 2008 (EDT)

:I'll take a look at this Friday. It's not immediately obvious what the point is to your analysis above.--[[User:Aschlafly|Aschlafly]] 23:46, 18 September 2008 (EDT)
::"''The general point is that it is valid to combine the results of different experiments if it is scientifically meaningful to do so"''--[[User:KingOfNothing|KingOfNothing]] 00:57, 19 September 2008 (EDT)

:::This makes no sense as an argument. It may be true in this simple case that you can do one large or several small samples and get similar results - which is quite obvious and wouldn't need such a detailed rant. However, you provide no mathematical proof, just one example. [[User:Etc|Etc]] 01:08, 19 September 2008 (EDT)
:''"It's not immediately obvious what the point is to your analysis above"''. No surprise, Aschlafly, really. Maybe you should take your own advice: ''"I suggest you try harder with an open mind"''. --[[User:CrossC|CrossC]] 02:46, 19 September 2008 (EDT)

It is with great sadness that I note that the author of this - the only significant statistical explanation and discussion in this entire fiasco- has [http://www.conservapedia.com/index.php?title=Special%3ALog&type=block&user=DeanS&page=User%3AKennyMac just been blocked] for five years. Even his email is blocked, so he can't even appeal the action. I don't see such manouvers as having contributed to the much vaunted "open mind" of which various people here speak. [[User:BenHur|BenHur]] 10:27, 19 September 2008 (EDT)

'''REPLY''': I have now reviewed the above analysis, and it supports Point 5 rather than the PNAS paper. Point 5 stated, "The Third Experiment was erroneously combined with the other two experiments based on outcome rather than sample size, thereby yielding a false claim of overall statistical significance." The analysis above does nothing more than reinforce Point 5 by combining experiments based on sample size.

In Pavlovian manner, some Lenski types nod their head here in agreement at the above analysis, apparently unaware that it reinforces Point 5.

When combining results from samples that are vastly different in sample size, it is necessary to factor in the different sample sizes. Apparently the PNAS paper failed to do that, which helps explain why it refuses to provide a meaningful response to Point 5.--[[User:Aschlafly|Aschlafly]] 19:24, 19 September 2008 (EDT)

(rants below were deleted for being non-substantive in violation of this page's rules.)--[[User:Aschlafly|Aschlafly]] 19:24, 19 September 2008 (EDT)

:::I understand point 5 now, or at least I think I do. What we have as a "sample" is either:

::::1. Individual cultures (Schlafly)
::::2. Cultures that developed cit+. (Lenski)

:::Schlafly contends that the sample should be all the cultures and that Lenski has, improperly, filtered the sample by excluding the vast majority of it (i.e. all those cultures that did not become cit+). Am I right in thinking this is the argument? --[[User:Toffeeman|Toffeeman]] 19:57, 19 September 2008 (EDT)

:::: No, we're talking about how Lenski combined a large study (which did not really support Lenski's hypothesis) with small studies (which Lenski claims does support his hypothesis). The studies were not combined in a logical manner with proper weighting given to the much bigger size of the large study.--[[User:Aschlafly|Aschlafly]] 23:15, 19 September 2008 (EDT)
:::::Aschlafly, have you read the paper on z-transforms which explains the statistical technique used? You can download a .pdf copy of the paper for free [http://www3.interscience.wiley.com/journal/118663174/abstract here]. --[[User:BillA|BillA]] 06:30, 20 September 2008 (EDT)

:::::: You say "statistical technique used," but you should have said "statistical technique ''cited''." In fact, a close reading of the Z-transform paper provides more support for Point 5: combined studies must be weighted based on sample size:

::::::: "When there is variation in the sample size across studies, there can be a noticeable difference in the power of the two methods, with the weighted Z-approach being superior in all cases. As such, we should always prefer the weighted Z to the unweighted Z-approach when the independent studies test the same hypothesis."[http://www3.interscience.wiley.com/journal/118663174/abstract see p. 1371].

:::::: In other words, the cited paper actually ''supports'' Point 5.--[[User:Aschlafly|Aschlafly]] 09:34, 20 September 2008 (EDT)

(unindent)Lenski used the weighted method. See note 49 to the paper and the text around the combination. Of course there is the question of on what basis Lenski weighted the results. Lenski weighted the results on the basis of the Cit+ numbers and we may think it would have been better to weight on the basis of the number of replicates. I have below the calculations (not mine) of combined P-values based on 1) no weighting, 2) weighting on the basis of Cit+ and 3) weighting on the basis of replicates. The weighted Z-transformed = SUM(Weight x Z-score for each run)/SQRT(SUM(Weight^2 for each run))

{| class="wikitable"
|-
! Expt# !! p-value !! z-score !! #Cit+ muts !! #replicates
|-
| 1 || 0.0085 || 2.387 || 4 || 72
|-
| 2 || 0.0007 || 3.195 || 5 || 340
|-
| 3 || 0.0823 || 1.390 || 8 || 2800
|-
|}

Applying the formula described above..

{| class="wikitable"
|-
! Weighting !! Z transformed !! p
|-
| Equal || 4.025 || <0.001
|-
|By total Cit+|| 3.576 || <0.001
|-
|By total replicates|| 1.825 || 0.034
|-
|}

So weighting on the basis of the number of replicates considerably increases the P-value. It remains, however, well within the range of statistical significance (0<P<0.05). If we hold that Lenski should have weighted on the basis of replicates then he should have rejected the null hypothesis and reached exactly the same conclusions that he did. The entire paper would have been exactly the same except the sentence “the result is extremely significant (P<0.0001) whether or not….” Would read “the result is significant (P<0.04) whether or not”. Point 5 establishes one number and an “extremely”. Point 5, therefore, has no weight (excuse the pun).
--[[User:Toffeeman|Toffeeman]] 15:18, 20 September 2008 (EDT)

: Sorry, Toffeeman, a falsehood is still a falsehood. Based on your own posting, if Lenski had applied the Whitlock Z-transform paper in a logical manner, the results would not have been nearly as striking as Lenski claimed (his paper said the results were "extremely significant"). Moreover, I found Lenski's description of his application of the Whitlock paper to be particularly misleading. Lenski's use of "whether or not"<ref>"We also used the Z-transformation method (49) to combine the probabilities from our three experiments, and '''the result is extremely significant (P < 0.0001) whether or not''' the experiments are weighted by the number of independent Cit+ mutants observed in each one." (Lenski paper at 7902).</ref> obscures the basic error that he did not apply Whitlock's paper in the straightforward, correct manner. I think the wording in the Lenski paper deliberately obscures this falsehood from the reader.

: People have free will to embrace and defend falsehoods. I don't expect them to change quickly or admit they were wrong. But you'll find me defending and promoting the truth.

: Point 5 remains valid and the falsehood remains uncorrected by PNAS or Lenski. Four other points in higher priority remain uncorrected by them also.--[[User:Aschlafly|Aschlafly]] 16:47, 20 September 2008 (EDT)

::'''''"a falsehood is still a falsehood"'''''. Precisely, the null hypothesis should be considered false and the conclusions of the paper stand.

::Oh? Do you mean ''Lenski's falsehood''? And what falsehood is that? Lenski said that he had calculated the P-value without weighting and that had come out at <0.0001. That is true, not false. Lenski said he had calculated the P-value weighting on the basis of the Cit+ replicates and that had come out at <0.0001. That is true, not false. There is no falsehood. Lenski did not mention the results of weighting on the basis of replicate numbers. He thus made no claim about weighting on the basis of replicate numbers. If he made no claim he cannot have made a false claim.

::How do the words Lenski uses "mislead". If you read them as written what conclusion do you come to? You are lead to the conclusion that the mutation was not "rare-but-equal", instead it was contingent. That is the right conclusion. If Lenski had presented the data in a different manner (perhaps by including the results of weighting on the basis of replicate numbers) what conclusion do you come to? You are again lead to the conclusion that the mutation was not "rare-but-equal", instead it was contingent. That is the right conclusion. To mislead you must be lead to a conclusion that is incorrect. By Lenski's paper you are not lead to a conclusion that is incorrect. Thus is cannot be said to be "misleading".

::I shall not comment on your second paragraph, the temptation to ''"Tu Quoque"'' would be too great.

--[[User:Toffeeman|Toffeeman]] 17:13, 20 September 2008 (EDT)

::: The falsehood consists of pretending to apply the Whitlock Z-transform in a straightforward, logical and correct manner. I think the Lenski paper is intentionally misleading by using the "whether or not" wording, when both alternatives are nonsensical. Point 5 has been proven above to be correct in identify an error in the Lenski paper.

::: "Toffeeman", your blocking history suggests you have been less than straightforward yourself. Go elsewhere if you seek to be deceitful. You're not fooling anyone here.--[[User:Aschlafly|Aschlafly]] 17:54, 20 September 2008 (EDT)

::::Lenski did apply the Z-transformation correctly, both weighted and unweighted. The data points extracted from each replay are the ''generation numbers of those replicates that gave rise to Cit+ mutants''. Thus Replay 1 produced four data points: 30,500 31,500 32,500 32,500. Replay 2 produced five data points: 32,000 32,000 32,000 32,000 32,500. Replay 3 produced eight data points: 20,000 20,000 27,000 27,000 31,000 31,500 32,000 32,000. Thus the N for replay 1 is 4; replay 2 is 5 and replay 3 is 8. The fact that replay 3 used 38 times as many replicates as replay 1 does not mean that it should be weighted 38 times as much; it only produced twice as much data, not 38 times as much.

::::Suppose I want to find out what the average age of a murderer is in three cities. In L.A. I interview 72 random people and find that 4 of them were convicted of murder; I record the ages of the four. In Seattle I interview 340 people and find that 5 of them are convicted murderers; likewise in Singapore I interview 2800 and find 8 murderers. In the end, I have 4,5, and 8 data points from the three cities; the number of people I had to interview to obtain those data points doesn't factor into the analysis of what the average age of the murderers is.--[[User:Brossa|Brossa]] 00:06, 21 September 2008 (EDT)

::::: In your first paragraph you simply repeat the error underlying Lenski's paper. You, like the paper, incorrectly apply Whitlock's Z-transform.

::::: The quality and reliability of data is proportional to sample size, and when different studies are combined they need to be weighted accordingly. The results from a very large sample size would not be weighted equally with the results from a small sample size, as you and Lenski have done. That's basic logic, though I'm not optimistic that you or Lenski will admit it. Open-minded people who respect logic have no difficulty elevating logic over personal whim.-[[User:Aschlafly|Aschlafly]] 11:30, 21 September 2008 (EDT)

::::::Andy if you read Whitlock's paper you would see it say, and I quote, "Ideally each study is weighted proportional to the inverse of its error variance, that is, by the '''reciprocal of its squared standard error'''." It says nothing about weighting according to sample size, which is what you seem to be insisting should be done.
::::::Also Whitlock acknowledges in the paper that there is no preference for weighted versus equal weighting, so the fact that both equal weighting and weighting by the standard error give a statistically significant result shows that the 3 experiments combined support rejection of the null hypothesis. [[User:DanB|DanB]] 20:39, 21 September 2008 (EDT)

:::::::ASchlafly, you state that I incorrectly apply "Whitlock's Z-transform" (actually the test belongs to Mosteller & Bush<ref>Mosteller, F. & Bush, R.R. 1954. Selected quantitative techniques. In: ''Handbook of Social Psychology,'' Vol. 1 (G. Lindzey, ed.)</ref> and/or Liptak<ref>Liptak, T. 1958. On the combination of tests. ''Magyar Tud. Akad. Mat. Kutato Int. Kozl.'' '''3''': 171-197</ref>). Whitlock describes weighting by the reciprocal of the squared standard error. The standard error of the mean is proportional to 1/sqrt(N), so the reciprocal of the squared standard error is proportional to N. Thus larger studies ''are'' given more weight. I maintain that the sample sizes N of the three replays are 4, 5, and 8 respectively. Weighting based on those three N does not weight all three replays equally as you claim: it gives replay 2 25% more weight and replay 3 100% more weight than replay 1. Rather than simply repeating that I am wrong, will you please state what ''you'' think the sample sizes of the three replay experiments are, and, in your opinion, what the ''correct'' application of the Z-transformation would be?--[[User:Brossa|Brossa]] 18:00, 22 September 2008 (EDT)

:::::::: The Lenski paper states how it weighted the experiments, and that weighting is incorrect. Admit it. Moreover, the incorrect weighting in the Lenski paper was not likely an inadvertent error, as it inflated the significance of the results. I found the wording used by the Lenski paper to describe its (incorrect) weighting to be artfully misleading.

:::::::: Provide me with federal funding as Lenski received, and I'll write a paper for you. But I don't have to write an alternative paper to point out glaring errors in Lenski's paper.--[[User:Aschlafly|Aschlafly]] 08:35, 23 September 2008 (EDT)

::::::::: I've been following this discussion for a while and I have to agree with ASchlafly. It hardly seems fair that he should have to, in his spare time, replicate an experiment done by a professional just to "earn" the right to criticize it. I am unfamiliar with statistics, but if some complicated transform goes against common sense, common sense should prevail. After all, there are lies, damned lies, and statistics... [[User:AndyM|AndyM]] 10:57, 23 September 2008 (EDT)

(unindent)I'm not asking anyone to write a paper or replicate an experiment. I'm asking ASchlafly to support his statement "The results from a very large sample size would not be weighted equally with the results from a small sample size, '''as you and Lenski have done'''"(bolding mine). I have stated publicly, subject to challenge by others, that the sample sizes (n) of the three replays are four, five, and eight respectively. Furthermore, using n of 4, 5, and 8 in the weighted Z-method DOES NOT weight all the replay experiments equally - it weights replay 3 twice as much as replay 1 and 8/5 as much as replay 2. Tell you what: I'll drop all my questions about Monte Carlo and the Z-transform, and simply ask ASchlafly one question: '''what is the sample size, n, of the second replay experiment?''' He need not even do any calculations - a statement in words that will allow someone else to do the calculation will suffice. This is not a complicated question to answer; the paper states how many replicate cultures there were (340), how many cells there were in each replicate (3.9x10^8), how many replicates gave rise to Cit+ cells (5), and which generations those Cit+ replicates came from (4 from 32,000 and one from 32,500). I will even give ''my'' answer: '''five'''. Furthermore, I will say ''why'' I believe that, using the murderer/age analogy: performing the 340 replicates is the same as interviewing 340 people in order to find out if any of them are convicted murderers. Finding that five replicates gave rise to Cit+ mutants is the same as the survey finding that 5 of those 340 people were convicted murderers. Finding that the Cit+ mutants arose from 4 replicates from generation 32,000 and 1 from generation 32,500 is the same as finding the ages of the murderers. The five data points in the Lenski study allow one to calculate the 'mean generation of clones yielding Cit+': 32,100. This is the same as finding the mean age of the five murderers. If I want to compare this hypothetical murderer age study to some other study of the mean age of murderers, I would weight the studies based on how many murderers were in each study, not on how many non-murderers were included in the initial survey.

Surely ASchlafly can say ''what'' he thinks the n of the second replay is, even if he won't say ''why'' he thinks it. Is it five? 340? The number of replicates times the number of cells per replicate? Something else? No analysis need be performed on the resulting number.--[[User:Brossa|Brossa]] 15:54, 23 September 2008 (EDT)

:OK - would you care to put in writing that after ASchlafly gives you his response, you won't start obfuscating the issue with Monte Carlo and Z-transform issues? You understand: it is typical of liberals to, after being proven wrong, to start pretending that they were talking about an entirely different issue altogether. '''After ASchlafly states the sample size of the second replay experiment you will consider yourself answered.''' Correct?

:Brossa, your rant is misplaced. One cannot salvage an error in logic by questioning which of superior alternatives should be used instead. The sample size of an experiment is the number that comprises the underlying sample used in the experiment, not the number of a certain outcome from the experiment. Maybe you can debate yourself over what the correct underlying sample size is, but it is plainly not the number of a certain outcome from the experiment.--[[User:Aschlafly|Aschlafly]] 19:28, 23 September 2008 (EDT)

Maybe the Journal of Nature can be your next letter submission source. ''International Weekly Journal of Science'' -- [[Image:50 star flag.png|14px]] [[User:Jpatt|jp]] 21:17, 22 September 2008 (EDT)

==Point 5 Rejected==

Referring to ASchlafly's latest revert: OK, so let's forget about my specialist knowledge of the subject. It really doesn't matter. In science, what matters is what is said, not who says it. Remember that the most outstanding scientific discoveries of the 20th century were made by a patent clerk; the facts that he had no academic position at the time and a rather moderate educational record were irrelevant.

So, I repeat: if you don't agree with me, present a reasoned argument against my points and don't just delete my comments (it's not wiki etiquette to delete other people's comments on a Talk page unless they're abusive or obscence). At least you haven't been so feeble as to block me to prevent me from contributing to this page, as you've done to other contributors. So I now repeat once again my cut-and-paste from Longstop's contribution a couple of weeks ago - as I said, if you don't agree with it, present a rational argument against it.

:The main point he [Kennymac] makes is quite correct, that combining experiments will tend to give a more significant result (i.e. a lower P-value) than any single experiment on its own.

:The point that ASchlafly makes (headed '''REPLY''', shortly after KennyMac's example) is slightly misleading. You don't choose which experiments to combine on the basis of their outcomes - you either combine all relevant experiments or none. In this case, Professor Lenski chose to combine all the experiments and present a single analysis of them. That's fine.

:The issue of whether to weight the Z-test according to sample size is not a straightforward issue. Before Whitlock's recent paper, the consensus was that the P-value already depends on sample size so it should not be weighted according to sample size. (Basically, a high degree of significance, i.e. a low P-value, can be achieved by having either a large difference between the treatments or a large experiment or, of course, both.) Whitlock's work, based on computer simulations, is an interesting contribution but cannot be regarded as the last word on the subject because any computer simulation involves assumptions about the structure of the particular experiment simulated. I cannot imagine any editor of a scientific journal rejecting a paper because it used an unweighted Z-test rather than the weighted version (or vice-versa).

:The conclusion, therefore, is that while there is a quantitative difference in the level of significance obtained by weighted and unweighted Z-tests, there is undeniably a significant biological effect. ASchlafly and other contributors should not be concerned that there is anything incorrect about the biological conclusions of Professor Lenski and his students or that there was anything at all underhand about their analysis or presentation of their data. [[User:DavyJones|DavyJones]] 19:02, 2 November 2008 (EST)

==Refereeing of Scientific Papers==

Another point that Aschlafly and others deleted was my explanation of why CP readers shouldn't be concerned about the fact that the Lenski paper was reviewed within 14 days. This is perfectly normal practice for a leading journal. If you're invited to review a paper for a leading journal and they give you 7/10/14/etc days, you only agree to review it if you're sure you're going to have time before the journal's deadline. So there's absolutely no reason to suppose the review wasn't done properly.

Again, if you disagree, discuss, don't delete and don't block. [[User:DavyJones|DavyJones]] 20:39, 31 October 2008 (EDT)

== References ==

<references/>

== Have we given up? ==

Not much activity here in the past few weeks. Have we given up on pursuing this matter further?
Conservapedia should work on continuing to keep the Lenski study and its flaws in the news.
Is there anything else we can do? Perhaps write to local officials about the misuse of public funds for studies like Lenski's, and also to complain about PNAS? --[[User:DRamon|DRamon]] 16:39, 31 October 2008 (EDT)

: We exposed five fundamental flaws in the study, and told the truth. The truth doesn't care whether some refuse to accept it. There will ''always'' be people who deny the truth, particularly when they stand to profit from falsehoods. For now, I've moved onto more pressing issues on this site.--[[User:Aschlafly|Aschlafly]] 16:56, 31 October 2008 (EDT)

:: What do you mean by "profit from falsehoods"? Are you seriously suggesting that everyone who has a different point of view from your own must have mercenary motives for disagreeing with you? That's a very bizarre point of view. [[User:DavyJones|DavyJones]] 20:39, 31 October 2008 (EDT)
:::The suggestion is that those who lie very frequently do so forr reasons of greed. Your denial of this self-evident fact, and your [[deceit]]ful twisting of Mr Schlafly's words, speak volumes of you, DavyJones. [[User:Bugler|Bugler]] 06:56, 1 November 2008 (EDT)

::::Well, I don't see how you can accuse me of twisting Aschlafly's words. The implication of his statement above is that he believe that what he wrote was true (although his Point 5, at least, was incorrect) and that people who disagree with him ("deny the truth", in his words) are seeking to profit by doing so, which is not correct.

::::More importantly, I don't see how Aschlafly can give up on an argument he started. It's plain from what KennyMac and other wrote that his Point 5 is not correct. Now, is he going to do CP readers the favour of reaching a rational conclusion to this discussion or is he going to resort to his ploy of blocking contributors with whom he doesn't agree? [[User:DavyJones|DavyJones]] 20:03, 1 November 2008 (EDT)

Salman Rushdie

2008-11-03T00:14:49Z

DavyJones: Midnight's Children

Sir Ahmed '''Salman Rushdie''' is one of the leading living novelists in the English language. His most famous work, ''Midnight's Children'', depicts the independence and partition of India and Pakistan in allegorical form. It won the [[Booker Prize]] for the best novel of the year by an author writing in English in a [[Commonwealth]] country or Ireland. It subsequently won the 'Booker of Bookers' for the best of the first 25 winners of the Booker Prize.

His later novel ''The Satanic Verses'' aroused controversy, angering many [[Muslim]]s who believed that Rushdie's portrayal of the [[Prophet Muhammad]] (an illustration of a legend surrounding the prophet) was heretical and irreverent. Rushdie's book tells the story of original instructions from Muhammad that the Muslim people should worship three ancient pagan goddesses that had been worshipped in Mecca before the time of [[Islam]]. According to the story, Muhammad later recanted the verses, saying that the devil had persuaded him to add them as blasphemies. In 1989, [[Ayatollah Ruhollah Khomeini]] declared a [[fatwa]] on Rushdie, mandating his execution under Islamic law. Because of this, Rushdie was forced to live under police protection for many years.

Rushdie was knighted in his adopted country of the United Kingdom in June of 2007.

[[category:Authors|Rushdie, Salman]]

Rugby School

2008-11-03T00:09:24Z

DavyJones: Former pupils + other edits

'''Rugby School''' is a major public school (the equivalent of a private school in the US) in the town of [[Rugby, Warwickshire]], in the Midlands of [[England]]. Its claims to fame include Thomas Arnold, its headmaster from 1828 to 1841, who was the architect of the [[Victorian]] public school, with its emphasis on [[muscular Christianity]], sporting effort and the study of the classics; the famous novel by Thomas Hughes, ''[[Tom Brown's Schooldays]]'', inspired by Hughes' admiration for Arnold's reforms; and the sport of [[Rugby Union]], which was named after the school, having supposedly been invented by a scholar named William Webb-Ellis, who, according to legend, while playing [[football]], picked the ball up and ran with it. Numerous famous authors, lawyers and scientists are Old Rugbeians, as former pupils of Rugby are known, including [[Salman Rushdie]] and [[Anthony Horowitz]]. Politicians educated at Rugby include [[Neville Chamberlain]], whose disastrous policy of [[appeasement]] of [[Nazi]] Germany overshadowed a lifetime of achievement in the field of social reform.

==Further Information==
http://www.victorianweb.org/history/education/rugby/bradby.html

[[Category:Schools]]

Talk:PNAS Response to Letter

2008-11-03T00:02:10Z

DavyJones: Undo revision 547229 by Aschlafly (Talk) What matters is what is said, not who says it

Notice: misrepresentations are not going to be allowed on this page. Substantive comments only, please.

Note: earlier posts are archived [[Talk:PNAS_Response_to_Letter/Archive1|here]]. --[[User:BillA|BillA]] 17:05, 20 September 2008 (EDT)

== Point 5 Confirmed ==

I would like to contribute to this discussion because I have taught statistics to graduate biology students for 16 years.

The combination of data from several experiments is a specialist and sometimes difficult area of statistical theory but a simple example shows why Aschafly’s concern about combining the results of three different experiments is not justified and why this aspect of his criticism of Lenski’s recent paper in PNAS is not valid.

Suppose we want to conduct a test of whether or not men are taller than women on average. For the sake of the example, I generated random heights of people from a population in which men had an average height of 175cm (5’10’) and women of 165cm (5’6”). The standard deviations of height in both sexes were 7cm. I think these numbers are approximately correct for people in the UK but the details aren’t important.

Suppose we take 5 samples of 2 men and 2 women. Here are the numbers I generated:

{| class="wikitable"
|-
! Man1 !! Man2 !! Woman1 !! Woman2 !! Men mean !! Women mean !! Mean difference !! t !! P
|-
| 176 || 179 || 157 || 148 || 177.5 || 152.5 || 25 || 5.27 || 0.017
|-
| 180 || 176 || 160 || 164 || 178 || 162 || 16 || 5.66 || 0.015
|-
| 176 || 175 || 167 || 165 || 175.5 || 166 || 9.5 || 8.50 || 0.0068
|-
| 169 || 171 || 168 || 173 || 170 || 170.5 || -0.5 || -0.19 || 0.57
|-
| 179 || 175 || 166 || 178 || 177 || 172 || 5 || 0.79 || 0.26
|-
|}

P in the last column is the t-test probability for a one-side test of women being shorter than men. (Formally, it’s the probability of getting a value of t greater than that calculated from the data if women are in fact taller than men on average.)

Should the fact that, in the fourth sample, the average height of the women is taller than that of the men make us doubt that men are in fact taller on average? Should we be concerned about the last sample, in which the difference in height of the two sexes is rather small, though in the expected direction? No, in both cases. When we combine the data on all 10 men and all 10 women, we get this:

{| class="wikitable"
|-
! Men mean !! Women mean !! Mean difference !! t !! ''P''
|-
| 175.6 || 164.6 || 11 || 3.85 || 0.00058
|-
|}

Clearly, combining the data from several similar experiments strengthens the conclusions considerably, as shown by the fact that ''P'' is much smaller for the combined data than for any individual sample.

Although the combination of data from several experiments is a specialised area of statistics, I see nothing particularly incorrect about the approach used by Lenski and his colleagues. The general point is that it is valid to combine the results of different experiments if it is scientifically meaningful to do so. (For example: A. Combining the results of five samples of the heights of men and women is clearly valid. B. Combining three samples of heights of men and women with two samples of lengths of male and female squid clearly isn’t.) Generally speaking, the outcome of a combined analysis of several small experiments which all point in the same direction (or at least in a similar direction) will be more significant than that of any one of those experiments, as is shown in the larger table above.

I hope this clarifies the extensive discussion on this point and puts Aschafly’s mind at rest on this subject. [[User:KennyMac|KennyMac]] 08:20, 18 September 2008 (EDT)

:That's very nicely put, thanks. You should work on some of the stats pages here. Of course, technically any sample is ultimately just a combination of ''n'' samples of size 1. [[User:MikeR|MikeR]] 13:28, 18 September 2008 (EDT)

:I'll take a look at this Friday. It's not immediately obvious what the point is to your analysis above.--[[User:Aschlafly|Aschlafly]] 23:46, 18 September 2008 (EDT)
::"''The general point is that it is valid to combine the results of different experiments if it is scientifically meaningful to do so"''--[[User:KingOfNothing|KingOfNothing]] 00:57, 19 September 2008 (EDT)

:::This makes no sense as an argument. It may be true in this simple case that you can do one large or several small samples and get similar results - which is quite obvious and wouldn't need such a detailed rant. However, you provide no mathematical proof, just one example. [[User:Etc|Etc]] 01:08, 19 September 2008 (EDT)
:''"It's not immediately obvious what the point is to your analysis above"''. No surprise, Aschlafly, really. Maybe you should take your own advice: ''"I suggest you try harder with an open mind"''. --[[User:CrossC|CrossC]] 02:46, 19 September 2008 (EDT)

It is with great sadness that I note that the author of this - the only significant statistical explanation and discussion in this entire fiasco- has [http://www.conservapedia.com/index.php?title=Special%3ALog&type=block&user=DeanS&page=User%3AKennyMac just been blocked] for five years. Even his email is blocked, so he can't even appeal the action. I don't see such manouvers as having contributed to the much vaunted "open mind" of which various people here speak. [[User:BenHur|BenHur]] 10:27, 19 September 2008 (EDT)

'''REPLY''': I have now reviewed the above analysis, and it supports Point 5 rather than the PNAS paper. Point 5 stated, "The Third Experiment was erroneously combined with the other two experiments based on outcome rather than sample size, thereby yielding a false claim of overall statistical significance." The analysis above does nothing more than reinforce Point 5 by combining experiments based on sample size.

In Pavlovian manner, some Lenski types nod their head here in agreement at the above analysis, apparently unaware that it reinforces Point 5.

When combining results from samples that are vastly different in sample size, it is necessary to factor in the different sample sizes. Apparently the PNAS paper failed to do that, which helps explain why it refuses to provide a meaningful response to Point 5.--[[User:Aschlafly|Aschlafly]] 19:24, 19 September 2008 (EDT)

(rants below were deleted for being non-substantive in violation of this page's rules.)--[[User:Aschlafly|Aschlafly]] 19:24, 19 September 2008 (EDT)

:::I understand point 5 now, or at least I think I do. What we have as a "sample" is either:

::::1. Individual cultures (Schlafly)
::::2. Cultures that developed cit+. (Lenski)

:::Schlafly contends that the sample should be all the cultures and that Lenski has, improperly, filtered the sample by excluding the vast majority of it (i.e. all those cultures that did not become cit+). Am I right in thinking this is the argument? --[[User:Toffeeman|Toffeeman]] 19:57, 19 September 2008 (EDT)

:::: No, we're talking about how Lenski combined a large study (which did not really support Lenski's hypothesis) with small studies (which Lenski claims does support his hypothesis). The studies were not combined in a logical manner with proper weighting given to the much bigger size of the large study.--[[User:Aschlafly|Aschlafly]] 23:15, 19 September 2008 (EDT)
:::::Aschlafly, have you read the paper on z-transforms which explains the statistical technique used? You can download a .pdf copy of the paper for free [http://www3.interscience.wiley.com/journal/118663174/abstract here]. --[[User:BillA|BillA]] 06:30, 20 September 2008 (EDT)

:::::: You say "statistical technique used," but you should have said "statistical technique ''cited''." In fact, a close reading of the Z-transform paper provides more support for Point 5: combined studies must be weighted based on sample size:

::::::: "When there is variation in the sample size across studies, there can be a noticeable difference in the power of the two methods, with the weighted Z-approach being superior in all cases. As such, we should always prefer the weighted Z to the unweighted Z-approach when the independent studies test the same hypothesis."[http://www3.interscience.wiley.com/journal/118663174/abstract see p. 1371].

:::::: In other words, the cited paper actually ''supports'' Point 5.--[[User:Aschlafly|Aschlafly]] 09:34, 20 September 2008 (EDT)

(unindent)Lenski used the weighted method. See note 49 to the paper and the text around the combination. Of course there is the question of on what basis Lenski weighted the results. Lenski weighted the results on the basis of the Cit+ numbers and we may think it would have been better to weight on the basis of the number of replicates. I have below the calculations (not mine) of combined P-values based on 1) no weighting, 2) weighting on the basis of Cit+ and 3) weighting on the basis of replicates. The weighted Z-transformed = SUM(Weight x Z-score for each run)/SQRT(SUM(Weight^2 for each run))

{| class="wikitable"
|-
! Expt# !! p-value !! z-score !! #Cit+ muts !! #replicates
|-
| 1 || 0.0085 || 2.387 || 4 || 72
|-
| 2 || 0.0007 || 3.195 || 5 || 340
|-
| 3 || 0.0823 || 1.390 || 8 || 2800
|-
|}

Applying the formula described above..

{| class="wikitable"
|-
! Weighting !! Z transformed !! p
|-
| Equal || 4.025 || <0.001
|-
|By total Cit+|| 3.576 || <0.001
|-
|By total replicates|| 1.825 || 0.034
|-
|}

So weighting on the basis of the number of replicates considerably increases the P-value. It remains, however, well within the range of statistical significance (0<P<0.05). If we hold that Lenski should have weighted on the basis of replicates then he should have rejected the null hypothesis and reached exactly the same conclusions that he did. The entire paper would have been exactly the same except the sentence “the result is extremely significant (P<0.0001) whether or not….” Would read “the result is significant (P<0.04) whether or not”. Point 5 establishes one number and an “extremely”. Point 5, therefore, has no weight (excuse the pun).
--[[User:Toffeeman|Toffeeman]] 15:18, 20 September 2008 (EDT)

: Sorry, Toffeeman, a falsehood is still a falsehood. Based on your own posting, if Lenski had applied the Whitlock Z-transform paper in a logical manner, the results would not have been nearly as striking as Lenski claimed (his paper said the results were "extremely significant"). Moreover, I found Lenski's description of his application of the Whitlock paper to be particularly misleading. Lenski's use of "whether or not"<ref>"We also used the Z-transformation method (49) to combine the probabilities from our three experiments, and '''the result is extremely significant (P < 0.0001) whether or not''' the experiments are weighted by the number of independent Cit+ mutants observed in each one." (Lenski paper at 7902).</ref> obscures the basic error that he did not apply Whitlock's paper in the straightforward, correct manner. I think the wording in the Lenski paper deliberately obscures this falsehood from the reader.

: People have free will to embrace and defend falsehoods. I don't expect them to change quickly or admit they were wrong. But you'll find me defending and promoting the truth.

: Point 5 remains valid and the falsehood remains uncorrected by PNAS or Lenski. Four other points in higher priority remain uncorrected by them also.--[[User:Aschlafly|Aschlafly]] 16:47, 20 September 2008 (EDT)

::'''''"a falsehood is still a falsehood"'''''. Precisely, the null hypothesis should be considered false and the conclusions of the paper stand.

::Oh? Do you mean ''Lenski's falsehood''? And what falsehood is that? Lenski said that he had calculated the P-value without weighting and that had come out at <0.0001. That is true, not false. Lenski said he had calculated the P-value weighting on the basis of the Cit+ replicates and that had come out at <0.0001. That is true, not false. There is no falsehood. Lenski did not mention the results of weighting on the basis of replicate numbers. He thus made no claim about weighting on the basis of replicate numbers. If he made no claim he cannot have made a false claim.

::How do the words Lenski uses "mislead". If you read them as written what conclusion do you come to? You are lead to the conclusion that the mutation was not "rare-but-equal", instead it was contingent. That is the right conclusion. If Lenski had presented the data in a different manner (perhaps by including the results of weighting on the basis of replicate numbers) what conclusion do you come to? You are again lead to the conclusion that the mutation was not "rare-but-equal", instead it was contingent. That is the right conclusion. To mislead you must be lead to a conclusion that is incorrect. By Lenski's paper you are not lead to a conclusion that is incorrect. Thus is cannot be said to be "misleading".

::I shall not comment on your second paragraph, the temptation to ''"Tu Quoque"'' would be too great.

--[[User:Toffeeman|Toffeeman]] 17:13, 20 September 2008 (EDT)

::: The falsehood consists of pretending to apply the Whitlock Z-transform in a straightforward, logical and correct manner. I think the Lenski paper is intentionally misleading by using the "whether or not" wording, when both alternatives are nonsensical. Point 5 has been proven above to be correct in identify an error in the Lenski paper.

::: "Toffeeman", your blocking history suggests you have been less than straightforward yourself. Go elsewhere if you seek to be deceitful. You're not fooling anyone here.--[[User:Aschlafly|Aschlafly]] 17:54, 20 September 2008 (EDT)

::::Lenski did apply the Z-transformation correctly, both weighted and unweighted. The data points extracted from each replay are the ''generation numbers of those replicates that gave rise to Cit+ mutants''. Thus Replay 1 produced four data points: 30,500 31,500 32,500 32,500. Replay 2 produced five data points: 32,000 32,000 32,000 32,000 32,500. Replay 3 produced eight data points: 20,000 20,000 27,000 27,000 31,000 31,500 32,000 32,000. Thus the N for replay 1 is 4; replay 2 is 5 and replay 3 is 8. The fact that replay 3 used 38 times as many replicates as replay 1 does not mean that it should be weighted 38 times as much; it only produced twice as much data, not 38 times as much.

::::Suppose I want to find out what the average age of a murderer is in three cities. In L.A. I interview 72 random people and find that 4 of them were convicted of murder; I record the ages of the four. In Seattle I interview 340 people and find that 5 of them are convicted murderers; likewise in Singapore I interview 2800 and find 8 murderers. In the end, I have 4,5, and 8 data points from the three cities; the number of people I had to interview to obtain those data points doesn't factor into the analysis of what the average age of the murderers is.--[[User:Brossa|Brossa]] 00:06, 21 September 2008 (EDT)

::::: In your first paragraph you simply repeat the error underlying Lenski's paper. You, like the paper, incorrectly apply Whitlock's Z-transform.

::::: The quality and reliability of data is proportional to sample size, and when different studies are combined they need to be weighted accordingly. The results from a very large sample size would not be weighted equally with the results from a small sample size, as you and Lenski have done. That's basic logic, though I'm not optimistic that you or Lenski will admit it. Open-minded people who respect logic have no difficulty elevating logic over personal whim.-[[User:Aschlafly|Aschlafly]] 11:30, 21 September 2008 (EDT)

::::::Andy if you read Whitlock's paper you would see it say, and I quote, "Ideally each study is weighted proportional to the inverse of its error variance, that is, by the '''reciprocal of its squared standard error'''." It says nothing about weighting according to sample size, which is what you seem to be insisting should be done.
::::::Also Whitlock acknowledges in the paper that there is no preference for weighted versus equal weighting, so the fact that both equal weighting and weighting by the standard error give a statistically significant result shows that the 3 experiments combined support rejection of the null hypothesis. [[User:DanB|DanB]] 20:39, 21 September 2008 (EDT)

:::::::ASchlafly, you state that I incorrectly apply "Whitlock's Z-transform" (actually the test belongs to Mosteller & Bush<ref>Mosteller, F. & Bush, R.R. 1954. Selected quantitative techniques. In: ''Handbook of Social Psychology,'' Vol. 1 (G. Lindzey, ed.)</ref> and/or Liptak<ref>Liptak, T. 1958. On the combination of tests. ''Magyar Tud. Akad. Mat. Kutato Int. Kozl.'' '''3''': 171-197</ref>). Whitlock describes weighting by the reciprocal of the squared standard error. The standard error of the mean is proportional to 1/sqrt(N), so the reciprocal of the squared standard error is proportional to N. Thus larger studies ''are'' given more weight. I maintain that the sample sizes N of the three replays are 4, 5, and 8 respectively. Weighting based on those three N does not weight all three replays equally as you claim: it gives replay 2 25% more weight and replay 3 100% more weight than replay 1. Rather than simply repeating that I am wrong, will you please state what ''you'' think the sample sizes of the three replay experiments are, and, in your opinion, what the ''correct'' application of the Z-transformation would be?--[[User:Brossa|Brossa]] 18:00, 22 September 2008 (EDT)

:::::::: The Lenski paper states how it weighted the experiments, and that weighting is incorrect. Admit it. Moreover, the incorrect weighting in the Lenski paper was not likely an inadvertent error, as it inflated the significance of the results. I found the wording used by the Lenski paper to describe its (incorrect) weighting to be artfully misleading.

:::::::: Provide me with federal funding as Lenski received, and I'll write a paper for you. But I don't have to write an alternative paper to point out glaring errors in Lenski's paper.--[[User:Aschlafly|Aschlafly]] 08:35, 23 September 2008 (EDT)

::::::::: I've been following this discussion for a while and I have to agree with ASchlafly. It hardly seems fair that he should have to, in his spare time, replicate an experiment done by a professional just to "earn" the right to criticize it. I am unfamiliar with statistics, but if some complicated transform goes against common sense, common sense should prevail. After all, there are lies, damned lies, and statistics... [[User:AndyM|AndyM]] 10:57, 23 September 2008 (EDT)

(unindent)I'm not asking anyone to write a paper or replicate an experiment. I'm asking ASchlafly to support his statement "The results from a very large sample size would not be weighted equally with the results from a small sample size, '''as you and Lenski have done'''"(bolding mine). I have stated publicly, subject to challenge by others, that the sample sizes (n) of the three replays are four, five, and eight respectively. Furthermore, using n of 4, 5, and 8 in the weighted Z-method DOES NOT weight all the replay experiments equally - it weights replay 3 twice as much as replay 1 and 8/5 as much as replay 2. Tell you what: I'll drop all my questions about Monte Carlo and the Z-transform, and simply ask ASchlafly one question: '''what is the sample size, n, of the second replay experiment?''' He need not even do any calculations - a statement in words that will allow someone else to do the calculation will suffice. This is not a complicated question to answer; the paper states how many replicate cultures there were (340), how many cells there were in each replicate (3.9x10^8), how many replicates gave rise to Cit+ cells (5), and which generations those Cit+ replicates came from (4 from 32,000 and one from 32,500). I will even give ''my'' answer: '''five'''. Furthermore, I will say ''why'' I believe that, using the murderer/age analogy: performing the 340 replicates is the same as interviewing 340 people in order to find out if any of them are convicted murderers. Finding that five replicates gave rise to Cit+ mutants is the same as the survey finding that 5 of those 340 people were convicted murderers. Finding that the Cit+ mutants arose from 4 replicates from generation 32,000 and 1 from generation 32,500 is the same as finding the ages of the murderers. The five data points in the Lenski study allow one to calculate the 'mean generation of clones yielding Cit+': 32,100. This is the same as finding the mean age of the five murderers. If I want to compare this hypothetical murderer age study to some other study of the mean age of murderers, I would weight the studies based on how many murderers were in each study, not on how many non-murderers were included in the initial survey.

Surely ASchlafly can say ''what'' he thinks the n of the second replay is, even if he won't say ''why'' he thinks it. Is it five? 340? The number of replicates times the number of cells per replicate? Something else? No analysis need be performed on the resulting number.--[[User:Brossa|Brossa]] 15:54, 23 September 2008 (EDT)

:OK - would you care to put in writing that after ASchlafly gives you his response, you won't start obfuscating the issue with Monte Carlo and Z-transform issues? You understand: it is typical of liberals to, after being proven wrong, to start pretending that they were talking about an entirely different issue altogether. '''After ASchlafly states the sample size of the second replay experiment you will consider yourself answered.''' Correct?

:Brossa, your rant is misplaced. One cannot salvage an error in logic by questioning which of superior alternatives should be used instead. The sample size of an experiment is the number that comprises the underlying sample used in the experiment, not the number of a certain outcome from the experiment. Maybe you can debate yourself over what the correct underlying sample size is, but it is plainly not the number of a certain outcome from the experiment.--[[User:Aschlafly|Aschlafly]] 19:28, 23 September 2008 (EDT)

Maybe the Journal of Nature can be your next letter submission source. ''International Weekly Journal of Science'' -- [[Image:50 star flag.png|14px]] [[User:Jpatt|jp]] 21:17, 22 September 2008 (EDT)

==Point 5 Rejected==

Referring to ASchlafly's latest revert: OK, so let's forget about my specialist knowledge of the subject. It really doesn't matter. In science, what matters is what is said, not who says it. Remember that the most outstanding scientific discoveries of the 20th century were made by a patent clerk; the facts that he had no academic position at the time and a rather moderate educational record were irrelevant.

So, I repeat: if you don't agree with me, present a reasoned argument against my points and don't just delete my comments (it's not wiki etiquette to delete other people's comments on a Talk page unless they're abusive or obscence). At least you haven't been so feeble as to block me to prevent me from contributing to this page, as you've done to other contributors. So I now repeat once again my cut-and-paste from Longstop's contribution a couple of weeks ago - as I said, if you don't agree with it, present a rational argument against it.

:The main point he [Kennymac] makes is quite correct, that combining experiments will tend to give a more significant result (i.e. a lower P-value) than any single experiment on its own.

:The point that ASchlafly makes (headed '''REPLY''', shortly after KennyMac's example) is slightly misleading. You don't choose which experiments to combine on the basis of their outcomes - you either combine all relevant experiments or none. In this case, Professor Lenski chose to combine all the experiments and present a single analysis of them. That's fine.

:The issue of whether to weight the Z-test according to sample size is not a straightforward issue. Before Whitlock's recent paper, the consensus was that the P-value already depends on sample size so it should not be weighted according to sample size. (Basically, a high degree of significance, i.e. a low P-value, can be achieved by having either a large difference between the treatments or a large experiment or, of course, both.) Whitlock's work, based on computer simulations, is an interesting contribution but cannot be regarded as the last word on the subject because any computer simulation involves assumptions about the structure of the particular experiment simulated. I cannot imagine any editor of a scientific journal rejecting a paper because it used an unweighted Z-test rather than the weighted version (or vice-versa).

:The conclusion, therefore, is that while there is a quantitative difference in the level of significance obtained by weighted and unweighted Z-tests, there is undeniably a significant biological effect. ASchlafly and other contributors should not be concerned that there is anything incorrect about the biological conclusions of Professor Lenski and his students or that there was anything at all underhand about their analysis or presentation of their data. [[User:DavyJones|DavyJones]] 19:02, 2 November 2008 (EST)

==Referring of Scientific Papers==

Another point that Aschlafly and others deleted was my explanation of why CP readers shouldn't be concerned about the fact that the Lenski paper was reviewed within 14 days. This is perfectly normal practice for a leading journal. If you're invited to review a paper for a leading journal and they give you 7/10/14/etc days, you only agree to review it if you're sure you're going to have time before the journal's deadline. So there's absolutely no reason to suppose the review wasn't done properly.

Again, if you disagree, discuss, don't delete and don't block. [[User:DavyJones|DavyJones]] 20:39, 31 October 2008 (EDT)

== References ==

<references/>

== Have we given up? ==

Not much activity here in the past few weeks. Have we given up on pursuing this matter further?
Conservapedia should work on continuing to keep the Lenski study and its flaws in the news.
Is there anything else we can do? Perhaps write to local officials about the misuse of public funds for studies like Lenski's, and also to complain about PNAS? --[[User:DRamon|DRamon]] 16:39, 31 October 2008 (EDT)

: We exposed five fundamental flaws in the study, and told the truth. The truth doesn't care whether some refuse to accept it. There will ''always'' be people who deny the truth, particularly when they stand to profit from falsehoods. For now, I've moved onto more pressing issues on this site.--[[User:Aschlafly|Aschlafly]] 16:56, 31 October 2008 (EDT)

:: What do you mean by "profit from falsehoods"? Are you seriously suggesting that everyone who has a different point of view from your own must have mercenary motives for disagreeing with you? That's a very bizarre point of view. [[User:DavyJones|DavyJones]] 20:39, 31 October 2008 (EDT)
:::The suggestion is that those who lie very frequently do so forr reasons of greed. Your denial of this self-evident fact, and your [[deceit]]ful twisting of Mr Schlafly's words, speak volumes of you, DavyJones. [[User:Bugler|Bugler]] 06:56, 1 November 2008 (EDT)

::::Well, I don't see how you can accuse me of twisting Aschlafly's words. The implication of his statement above is that he believe that what he wrote was true (although his Point 5, at least, was incorrect) and that people who disagree with him ("deny the truth", in his words) are seeking to profit by doing so, which is not correct.

::::More importantly, I don't see how Aschlafly can give up on an argument he started. It's plain from what KennyMac and other wrote that his Point 5 is not correct. Now, is he going to do CP readers the favour of reaching a rational conclusion to this discussion or is he going to resort to his ploy of blocking contributors with whom he doesn't agree? [[User:DavyJones|DavyJones]] 20:03, 1 November 2008 (EDT)

Talk:Essay:Women wearing pants

2008-11-02T23:52:32Z

DavyJones: /* Other cultures */ new section

Essay? [[User:DanH|DanH]] 14:30, 9 December 2007 (EST)

:Merge to [[cross dressing]]? --[[User:Ed Poor|Ed Poor]] <sup>[[User talk:Ed Poor|Talk]]</sup> 14:47, 9 December 2007 (EST)

::These crazy girls today! With their [[pants]]. [[User:Feebasfactor|Feebasfactor]] 15:11, 9 December 2007 (EST)

::Sorry... to be serious, I would also suggest simply adding it as a section to the [[cross dressing]], to demonstrate that some people believe "women wearing pants" constitutes cross dressing as well. Unfortunately, that article doesn't currently exist... [[User:Feebasfactor|Feebasfactor]] 15:13, 9 December 2007 (EST)
:::It should probably be [[cross-dressing]] at any rate. [[User:HelpJazz|Help]][[User talk:HelpJazz|Jazz]] 15:16, 9 December 2007 (EST)

::::Oops! Sorry about that, then! [[User:Feebasfactor|Feebasfactor]] 15:17, 9 December 2007 (EST)

==Essay?==

Ed, can you structure the text to show what part of the essay is the quote from John Quinn, and what is your original content? In its current form it looks like it's just the quote.

That said, isn't this a non-issue? When I look at paintings and drawings of men in Biblical times they're not wearing pants, but they weren't cross-dressing (nor are Scotsmen in traditional garb). Form follows function, which is why nurses wear scrubs instead of the starched white dress and pointed hat that was the norm as late as the 1970's --[[User:DinsdaleP|DinsdaleP]] 14:45, 10 June 2008 (EDT)

The history is a bit debatable - what are bloomers if not pants? And Audrey Hepburn was much later than 1857. [[User:Canuck|Canuck]] 00:04, 2 November 2008 (EDT)

== Other cultures ==

In Punjab (both sides of the border), traditional clothing for women is a loose shirt and baggy trousers, known as shalwar-kamiz (shalwar is the trousers, kamiz the blouse). So to which culture(s) does your condemnation of trousers as clothing for women apply? To the USA? North America? Or more widely? [[User:DavyJones|DavyJones]] 18:52, 2 November 2008 (EST)

Talk:PNAS Response to Letter

2008-11-02T00:03:54Z

DavyJones: /* Have we given up? */

Notice: misrepresentations are not going to be allowed on this page. Substantive comments only, please.

Note: earlier posts are archived [[Talk:PNAS_Response_to_Letter/Archive1|here]]. --[[User:BillA|BillA]] 17:05, 20 September 2008 (EDT)

== Point 5 Confirmed ==

I would like to contribute to this discussion because I have taught statistics to graduate biology students for 16 years.

The combination of data from several experiments is a specialist and sometimes difficult area of statistical theory but a simple example shows why Aschafly’s concern about combining the results of three different experiments is not justified and why this aspect of his criticism of Lenski’s recent paper in PNAS is not valid.

Suppose we want to conduct a test of whether or not men are taller than women on average. For the sake of the example, I generated random heights of people from a population in which men had an average height of 175cm (5’10’) and women of 165cm (5’6”). The standard deviations of height in both sexes were 7cm. I think these numbers are approximately correct for people in the UK but the details aren’t important.

Suppose we take 5 samples of 2 men and 2 women. Here are the numbers I generated:

{| class="wikitable"
|-
! Man1 !! Man2 !! Woman1 !! Woman2 !! Men mean !! Women mean !! Mean difference !! t !! P
|-
| 176 || 179 || 157 || 148 || 177.5 || 152.5 || 25 || 5.27 || 0.017
|-
| 180 || 176 || 160 || 164 || 178 || 162 || 16 || 5.66 || 0.015
|-
| 176 || 175 || 167 || 165 || 175.5 || 166 || 9.5 || 8.50 || 0.0068
|-
| 169 || 171 || 168 || 173 || 170 || 170.5 || -0.5 || -0.19 || 0.57
|-
| 179 || 175 || 166 || 178 || 177 || 172 || 5 || 0.79 || 0.26
|-
|}

P in the last column is the t-test probability for a one-side test of women being shorter than men. (Formally, it’s the probability of getting a value of t greater than that calculated from the data if women are in fact taller than men on average.)

Should the fact that, in the fourth sample, the average height of the women is taller than that of the men make us doubt that men are in fact taller on average? Should we be concerned about the last sample, in which the difference in height of the two sexes is rather small, though in the expected direction? No, in both cases. When we combine the data on all 10 men and all 10 women, we get this:

{| class="wikitable"
|-
! Men mean !! Women mean !! Mean difference !! t !! ''P''
|-
| 175.6 || 164.6 || 11 || 3.85 || 0.00058
|-
|}

Clearly, combining the data from several similar experiments strengthens the conclusions considerably, as shown by the fact that ''P'' is much smaller for the combined data than for any individual sample.

Although the combination of data from several experiments is a specialised area of statistics, I see nothing particularly incorrect about the approach used by Lenski and his colleagues. The general point is that it is valid to combine the results of different experiments if it is scientifically meaningful to do so. (For example: A. Combining the results of five samples of the heights of men and women is clearly valid. B. Combining three samples of heights of men and women with two samples of lengths of male and female squid clearly isn’t.) Generally speaking, the outcome of a combined analysis of several small experiments which all point in the same direction (or at least in a similar direction) will be more significant than that of any one of those experiments, as is shown in the larger table above.

I hope this clarifies the extensive discussion on this point and puts Aschafly’s mind at rest on this subject. [[User:KennyMac|KennyMac]] 08:20, 18 September 2008 (EDT)

:That's very nicely put, thanks. You should work on some of the stats pages here. Of course, technically any sample is ultimately just a combination of ''n'' samples of size 1. [[User:MikeR|MikeR]] 13:28, 18 September 2008 (EDT)

:I'll take a look at this Friday. It's not immediately obvious what the point is to your analysis above.--[[User:Aschlafly|Aschlafly]] 23:46, 18 September 2008 (EDT)
::"''The general point is that it is valid to combine the results of different experiments if it is scientifically meaningful to do so"''--[[User:KingOfNothing|KingOfNothing]] 00:57, 19 September 2008 (EDT)

:::This makes no sense as an argument. It may be true in this simple case that you can do one large or several small samples and get similar results - which is quite obvious and wouldn't need such a detailed rant. However, you provide no mathematical proof, just one example. [[User:Etc|Etc]] 01:08, 19 September 2008 (EDT)
:''"It's not immediately obvious what the point is to your analysis above"''. No surprise, Aschlafly, really. Maybe you should take your own advice: ''"I suggest you try harder with an open mind"''. --[[User:CrossC|CrossC]] 02:46, 19 September 2008 (EDT)

It is with great sadness that I note that the author of this - the only significant statistical explanation and discussion in this entire fiasco- has [http://www.conservapedia.com/index.php?title=Special%3ALog&type=block&user=DeanS&page=User%3AKennyMac just been blocked] for five years. Even his email is blocked, so he can't even appeal the action. I don't see such manouvers as having contributed to the much vaunted "open mind" of which various people here speak. [[User:BenHur|BenHur]] 10:27, 19 September 2008 (EDT)

'''REPLY''': I have now reviewed the above analysis, and it supports Point 5 rather than the PNAS paper. Point 5 stated, "The Third Experiment was erroneously combined with the other two experiments based on outcome rather than sample size, thereby yielding a false claim of overall statistical significance." The analysis above does nothing more than reinforce Point 5 by combining experiments based on sample size.

In Pavlovian manner, some Lenski types nod their head here in agreement at the above analysis, apparently unaware that it reinforces Point 5.

When combining results from samples that are vastly different in sample size, it is necessary to factor in the different sample sizes. Apparently the PNAS paper failed to do that, which helps explain why it refuses to provide a meaningful response to Point 5.--[[User:Aschlafly|Aschlafly]] 19:24, 19 September 2008 (EDT)

(rants below were deleted for being non-substantive in violation of this page's rules.)--[[User:Aschlafly|Aschlafly]] 19:24, 19 September 2008 (EDT)

:::I understand point 5 now, or at least I think I do. What we have as a "sample" is either:

::::1. Individual cultures (Schlafly)
::::2. Cultures that developed cit+. (Lenski)

:::Schlafly contends that the sample should be all the cultures and that Lenski has, improperly, filtered the sample by excluding the vast majority of it (i.e. all those cultures that did not become cit+). Am I right in thinking this is the argument? --[[User:Toffeeman|Toffeeman]] 19:57, 19 September 2008 (EDT)

:::: No, we're talking about how Lenski combined a large study (which did not really support Lenski's hypothesis) with small studies (which Lenski claims does support his hypothesis). The studies were not combined in a logical manner with proper weighting given to the much bigger size of the large study.--[[User:Aschlafly|Aschlafly]] 23:15, 19 September 2008 (EDT)
:::::Aschlafly, have you read the paper on z-transforms which explains the statistical technique used? You can download a .pdf copy of the paper for free [http://www3.interscience.wiley.com/journal/118663174/abstract here]. --[[User:BillA|BillA]] 06:30, 20 September 2008 (EDT)

:::::: You say "statistical technique used," but you should have said "statistical technique ''cited''." In fact, a close reading of the Z-transform paper provides more support for Point 5: combined studies must be weighted based on sample size:

::::::: "When there is variation in the sample size across studies, there can be a noticeable difference in the power of the two methods, with the weighted Z-approach being superior in all cases. As such, we should always prefer the weighted Z to the unweighted Z-approach when the independent studies test the same hypothesis."[http://www3.interscience.wiley.com/journal/118663174/abstract see p. 1371].

:::::: In other words, the cited paper actually ''supports'' Point 5.--[[User:Aschlafly|Aschlafly]] 09:34, 20 September 2008 (EDT)

(unindent)Lenski used the weighted method. See note 49 to the paper and the text around the combination. Of course there is the question of on what basis Lenski weighted the results. Lenski weighted the results on the basis of the Cit+ numbers and we may think it would have been better to weight on the basis of the number of replicates. I have below the calculations (not mine) of combined P-values based on 1) no weighting, 2) weighting on the basis of Cit+ and 3) weighting on the basis of replicates. The weighted Z-transformed = SUM(Weight x Z-score for each run)/SQRT(SUM(Weight^2 for each run))

{| class="wikitable"
|-
! Expt# !! p-value !! z-score !! #Cit+ muts !! #replicates
|-
| 1 || 0.0085 || 2.387 || 4 || 72
|-
| 2 || 0.0007 || 3.195 || 5 || 340
|-
| 3 || 0.0823 || 1.390 || 8 || 2800
|-
|}

Applying the formula described above..

{| class="wikitable"
|-
! Weighting !! Z transformed !! p
|-
| Equal || 4.025 || <0.001
|-
|By total Cit+|| 3.576 || <0.001
|-
|By total replicates|| 1.825 || 0.034
|-
|}

So weighting on the basis of the number of replicates considerably increases the P-value. It remains, however, well within the range of statistical significance (0<P<0.05). If we hold that Lenski should have weighted on the basis of replicates then he should have rejected the null hypothesis and reached exactly the same conclusions that he did. The entire paper would have been exactly the same except the sentence “the result is extremely significant (P<0.0001) whether or not….” Would read “the result is significant (P<0.04) whether or not”. Point 5 establishes one number and an “extremely”. Point 5, therefore, has no weight (excuse the pun).
--[[User:Toffeeman|Toffeeman]] 15:18, 20 September 2008 (EDT)

: Sorry, Toffeeman, a falsehood is still a falsehood. Based on your own posting, if Lenski had applied the Whitlock Z-transform paper in a logical manner, the results would not have been nearly as striking as Lenski claimed (his paper said the results were "extremely significant"). Moreover, I found Lenski's description of his application of the Whitlock paper to be particularly misleading. Lenski's use of "whether or not"<ref>"We also used the Z-transformation method (49) to combine the probabilities from our three experiments, and '''the result is extremely significant (P < 0.0001) whether or not''' the experiments are weighted by the number of independent Cit+ mutants observed in each one." (Lenski paper at 7902).</ref> obscures the basic error that he did not apply Whitlock's paper in the straightforward, correct manner. I think the wording in the Lenski paper deliberately obscures this falsehood from the reader.

: People have free will to embrace and defend falsehoods. I don't expect them to change quickly or admit they were wrong. But you'll find me defending and promoting the truth.

: Point 5 remains valid and the falsehood remains uncorrected by PNAS or Lenski. Four other points in higher priority remain uncorrected by them also.--[[User:Aschlafly|Aschlafly]] 16:47, 20 September 2008 (EDT)

::'''''"a falsehood is still a falsehood"'''''. Precisely, the null hypothesis should be considered false and the conclusions of the paper stand.

::Oh? Do you mean ''Lenski's falsehood''? And what falsehood is that? Lenski said that he had calculated the P-value without weighting and that had come out at <0.0001. That is true, not false. Lenski said he had calculated the P-value weighting on the basis of the Cit+ replicates and that had come out at <0.0001. That is true, not false. There is no falsehood. Lenski did not mention the results of weighting on the basis of replicate numbers. He thus made no claim about weighting on the basis of replicate numbers. If he made no claim he cannot have made a false claim.

::How do the words Lenski uses "mislead". If you read them as written what conclusion do you come to? You are lead to the conclusion that the mutation was not "rare-but-equal", instead it was contingent. That is the right conclusion. If Lenski had presented the data in a different manner (perhaps by including the results of weighting on the basis of replicate numbers) what conclusion do you come to? You are again lead to the conclusion that the mutation was not "rare-but-equal", instead it was contingent. That is the right conclusion. To mislead you must be lead to a conclusion that is incorrect. By Lenski's paper you are not lead to a conclusion that is incorrect. Thus is cannot be said to be "misleading".

::I shall not comment on your second paragraph, the temptation to ''"Tu Quoque"'' would be too great.

--[[User:Toffeeman|Toffeeman]] 17:13, 20 September 2008 (EDT)

::: The falsehood consists of pretending to apply the Whitlock Z-transform in a straightforward, logical and correct manner. I think the Lenski paper is intentionally misleading by using the "whether or not" wording, when both alternatives are nonsensical. Point 5 has been proven above to be correct in identify an error in the Lenski paper.

::: "Toffeeman", your blocking history suggests you have been less than straightforward yourself. Go elsewhere if you seek to be deceitful. You're not fooling anyone here.--[[User:Aschlafly|Aschlafly]] 17:54, 20 September 2008 (EDT)

::::Lenski did apply the Z-transformation correctly, both weighted and unweighted. The data points extracted from each replay are the ''generation numbers of those replicates that gave rise to Cit+ mutants''. Thus Replay 1 produced four data points: 30,500 31,500 32,500 32,500. Replay 2 produced five data points: 32,000 32,000 32,000 32,000 32,500. Replay 3 produced eight data points: 20,000 20,000 27,000 27,000 31,000 31,500 32,000 32,000. Thus the N for replay 1 is 4; replay 2 is 5 and replay 3 is 8. The fact that replay 3 used 38 times as many replicates as replay 1 does not mean that it should be weighted 38 times as much; it only produced twice as much data, not 38 times as much.

::::Suppose I want to find out what the average age of a murderer is in three cities. In L.A. I interview 72 random people and find that 4 of them were convicted of murder; I record the ages of the four. In Seattle I interview 340 people and find that 5 of them are convicted murderers; likewise in Singapore I interview 2800 and find 8 murderers. In the end, I have 4,5, and 8 data points from the three cities; the number of people I had to interview to obtain those data points doesn't factor into the analysis of what the average age of the murderers is.--[[User:Brossa|Brossa]] 00:06, 21 September 2008 (EDT)

::::: In your first paragraph you simply repeat the error underlying Lenski's paper. You, like the paper, incorrectly apply Whitlock's Z-transform.

::::: The quality and reliability of data is proportional to sample size, and when different studies are combined they need to be weighted accordingly. The results from a very large sample size would not be weighted equally with the results from a small sample size, as you and Lenski have done. That's basic logic, though I'm not optimistic that you or Lenski will admit it. Open-minded people who respect logic have no difficulty elevating logic over personal whim.-[[User:Aschlafly|Aschlafly]] 11:30, 21 September 2008 (EDT)

::::::Andy if you read Whitlock's paper you would see it say, and I quote, "Ideally each study is weighted proportional to the inverse of its error variance, that is, by the '''reciprocal of its squared standard error'''." It says nothing about weighting according to sample size, which is what you seem to be insisting should be done.
::::::Also Whitlock acknowledges in the paper that there is no preference for weighted versus equal weighting, so the fact that both equal weighting and weighting by the standard error give a statistically significant result shows that the 3 experiments combined support rejection of the null hypothesis. [[User:DanB|DanB]] 20:39, 21 September 2008 (EDT)

:::::::ASchlafly, you state that I incorrectly apply "Whitlock's Z-transform" (actually the test belongs to Mosteller & Bush<ref>Mosteller, F. & Bush, R.R. 1954. Selected quantitative techniques. In: ''Handbook of Social Psychology,'' Vol. 1 (G. Lindzey, ed.)</ref> and/or Liptak<ref>Liptak, T. 1958. On the combination of tests. ''Magyar Tud. Akad. Mat. Kutato Int. Kozl.'' '''3''': 171-197</ref>). Whitlock describes weighting by the reciprocal of the squared standard error. The standard error of the mean is proportional to 1/sqrt(N), so the reciprocal of the squared standard error is proportional to N. Thus larger studies ''are'' given more weight. I maintain that the sample sizes N of the three replays are 4, 5, and 8 respectively. Weighting based on those three N does not weight all three replays equally as you claim: it gives replay 2 25% more weight and replay 3 100% more weight than replay 1. Rather than simply repeating that I am wrong, will you please state what ''you'' think the sample sizes of the three replay experiments are, and, in your opinion, what the ''correct'' application of the Z-transformation would be?--[[User:Brossa|Brossa]] 18:00, 22 September 2008 (EDT)

:::::::: The Lenski paper states how it weighted the experiments, and that weighting is incorrect. Admit it. Moreover, the incorrect weighting in the Lenski paper was not likely an inadvertent error, as it inflated the significance of the results. I found the wording used by the Lenski paper to describe its (incorrect) weighting to be artfully misleading.

:::::::: Provide me with federal funding as Lenski received, and I'll write a paper for you. But I don't have to write an alternative paper to point out glaring errors in Lenski's paper.--[[User:Aschlafly|Aschlafly]] 08:35, 23 September 2008 (EDT)

::::::::: I've been following this discussion for a while and I have to agree with ASchlafly. It hardly seems fair that he should have to, in his spare time, replicate an experiment done by a professional just to "earn" the right to criticize it. I am unfamiliar with statistics, but if some complicated transform goes against common sense, common sense should prevail. After all, there are lies, damned lies, and statistics... [[User:AndyM|AndyM]] 10:57, 23 September 2008 (EDT)

(unindent)I'm not asking anyone to write a paper or replicate an experiment. I'm asking ASchlafly to support his statement "The results from a very large sample size would not be weighted equally with the results from a small sample size, '''as you and Lenski have done'''"(bolding mine). I have stated publicly, subject to challenge by others, that the sample sizes (n) of the three replays are four, five, and eight respectively. Furthermore, using n of 4, 5, and 8 in the weighted Z-method DOES NOT weight all the replay experiments equally - it weights replay 3 twice as much as replay 1 and 8/5 as much as replay 2. Tell you what: I'll drop all my questions about Monte Carlo and the Z-transform, and simply ask ASchlafly one question: '''what is the sample size, n, of the second replay experiment?''' He need not even do any calculations - a statement in words that will allow someone else to do the calculation will suffice. This is not a complicated question to answer; the paper states how many replicate cultures there were (340), how many cells there were in each replicate (3.9x10^8), how many replicates gave rise to Cit+ cells (5), and which generations those Cit+ replicates came from (4 from 32,000 and one from 32,500). I will even give ''my'' answer: '''five'''. Furthermore, I will say ''why'' I believe that, using the murderer/age analogy: performing the 340 replicates is the same as interviewing 340 people in order to find out if any of them are convicted murderers. Finding that five replicates gave rise to Cit+ mutants is the same as the survey finding that 5 of those 340 people were convicted murderers. Finding that the Cit+ mutants arose from 4 replicates from generation 32,000 and 1 from generation 32,500 is the same as finding the ages of the murderers. The five data points in the Lenski study allow one to calculate the 'mean generation of clones yielding Cit+': 32,100. This is the same as finding the mean age of the five murderers. If I want to compare this hypothetical murderer age study to some other study of the mean age of murderers, I would weight the studies based on how many murderers were in each study, not on how many non-murderers were included in the initial survey.

Surely ASchlafly can say ''what'' he thinks the n of the second replay is, even if he won't say ''why'' he thinks it. Is it five? 340? The number of replicates times the number of cells per replicate? Something else? No analysis need be performed on the resulting number.--[[User:Brossa|Brossa]] 15:54, 23 September 2008 (EDT)

:OK - would you care to put in writing that after ASchlafly gives you his response, you won't start obfuscating the issue with Monte Carlo and Z-transform issues? You understand: it is typical of liberals to, after being proven wrong, to start pretending that they were talking about an entirely different issue altogether. '''After ASchlafly states the sample size of the second replay experiment you will consider yourself answered.''' Correct?

:Brossa, your rant is misplaced. One cannot salvage an error in logic by questioning which of superior alternatives should be used instead. The sample size of an experiment is the number that comprises the underlying sample used in the experiment, not the number of a certain outcome from the experiment. Maybe you can debate yourself over what the correct underlying sample size is, but it is plainly not the number of a certain outcome from the experiment.--[[User:Aschlafly|Aschlafly]] 19:28, 23 September 2008 (EDT)

Maybe the Journal of Nature can be your next letter submission source. ''International Weekly Journal of Science'' -- [[Image:50 star flag.png|14px]] [[User:Jpatt|jp]] 21:17, 22 September 2008 (EDT)

==Point 5 Rejected==

ASchlafly and others: if you don't agree with me, present a reasoned argument against my points. Don't delete other people's comments on a Talk page and for goodness sake, don't be so spineless as to block me to prevent me from replying to you. I repeat what I wrote last week before you deleted my contribution to this discussion and blocked me.

I ''do'' have specialist knowledge of this area, despite Bugler's assertions to the contrary (made without any evidence whatsoever, may I say). But I repeat, it really doesn't matter whether I have particular qualifications or not. In science, what matters is what is said, not who says it. The most outstanding scientific discoveries of the 20th century were made by a patent clerk who had no academic position at the time.

I now repeat again my cut-and-paste from Longstop's contribution a couple of weeks ago. If you don't agree with it, discuss it, don't delete it.

:The main point he [Kennymac] makes is quite correct, that combining experiments will tend to give a more significant result (i.e. a lower P-value) than any single experiment on its own.

:The point that ASchlafly makes (headed '''REPLY''', shortly after KennyMac's example) is slightly misleading. You don't choose which experiments to combine on the basis of their outcomes - you either combine all relevant experiments or none. In this case, Professor Lenski chose to combine all the experiments and present a single analysis of them. That's fine.

:The issue of whether to weight the Z-test according to sample size is not a straightforward issue. Before Whitlock's recent paper, the consensus was that the P-value already depends on sample size so it should not be weighted according to sample size. (Basically, a high degree of significance, i.e. a low P-value, can be achieved by having either a large difference between the treatments or a large experiment or, of course, both.) Whitlock's work, based on computer simulations, is an interesting contribution but cannot be regarded as the last word on the subject because any computer simulation involves assumptions about the structure of the particular experiment simulated. I cannot imagine any editor of a scientific journal rejecting a paper because it used an unweighted Z-test rather than the weighted version (or vice-versa).

:The conclusion, therefore, is that while there is a quantitative difference in the level of significance obtained by weighted and unweighted Z-tests, there is undeniably a significant biological effect. ASchlafly and other contributors should not be concerned that there is anything incorrect about the biological conclusions of Professor Lenski and his students or that there was anything at all underhand about their analysis or presentation of their data. [[User:DavyJones|DavyJones]] 20:39, 31 October 2008 (EDT)

==Referring of Scientific Papers==

Another point that Aschlafly and others deleted was my explanation of why CP readers shouldn't be concerned about the fact that the Lenski paper was reviewed within 14 days. This is perfectly normal practice for a leading journal. If you're invited to review a paper for a leading journal and they give you 7/10/14/etc days, you only agree to review it if you're sure you're going to have time before the journal's deadline. So there's absolutely no reason to suppose the review wasn't done properly.

Again, if you disagree, discuss, don't delete and don't block. [[User:DavyJones|DavyJones]] 20:39, 31 October 2008 (EDT)

== References ==

<references/>

== Have we given up? ==

Not much activity here in the past few weeks. Have we given up on pursuing this matter further?
Conservapedia should work on continuing to keep the Lenski study and its flaws in the news.
Is there anything else we can do? Perhaps write to local officials about the misuse of public funds for studies like Lenski's, and also to complain about PNAS? --[[User:DRamon|DRamon]] 16:39, 31 October 2008 (EDT)

: We exposed five fundamental flaws in the study, and told the truth. The truth doesn't care whether some refuse to accept it. There will ''always'' be people who deny the truth, particularly when they stand to profit from falsehoods. For now, I've moved onto more pressing issues on this site.--[[User:Aschlafly|Aschlafly]] 16:56, 31 October 2008 (EDT)

:: What do you mean by "profit from falsehoods"? Are you seriously suggesting that everyone who has a different point of view from your own must have mercenary motives for disagreeing with you? That's a very bizarre point of view. [[User:DavyJones|DavyJones]] 20:39, 31 October 2008 (EDT)
:::The suggestion is that those who lie very frequently do so forr reasons of greed. Your denial of this self-evident fact, and your [[deceit]]ful twisting of Mr Schlafly's words, speak volumes of you, DavyJones. [[User:Bugler|Bugler]] 06:56, 1 November 2008 (EDT)

::::Well, I don't see how you can accuse me of twisting Aschlafly's words. The implication of his statement above is that he believe that what he wrote was true (although his Point 5, at least, was incorrect) and that people who disagree with him ("deny the truth", in his words) are seeking to profit by doing so, which is not correct.

::::More importantly, I don't see how Aschlafly can give up on an argument he started. It's plain from what KennyMac and other wrote that his Point 5 is not correct. Now, is he going to do CP readers the favour of reaching a rational conclusion to this discussion or is he going to resort to his ploy of blocking contributors with whom he doesn't agree? [[User:DavyJones|DavyJones]] 20:03, 1 November 2008 (EDT)

Talk:PNAS Response to Letter

2008-11-01T23:58:27Z

DavyJones: /* Point 5 Rejected */ formatting

Notice: misrepresentations are not going to be allowed on this page. Substantive comments only, please.

Note: earlier posts are archived [[Talk:PNAS_Response_to_Letter/Archive1|here]]. --[[User:BillA|BillA]] 17:05, 20 September 2008 (EDT)

== Point 5 Confirmed ==

I would like to contribute to this discussion because I have taught statistics to graduate biology students for 16 years.

The combination of data from several experiments is a specialist and sometimes difficult area of statistical theory but a simple example shows why Aschafly’s concern about combining the results of three different experiments is not justified and why this aspect of his criticism of Lenski’s recent paper in PNAS is not valid.

Suppose we want to conduct a test of whether or not men are taller than women on average. For the sake of the example, I generated random heights of people from a population in which men had an average height of 175cm (5’10’) and women of 165cm (5’6”). The standard deviations of height in both sexes were 7cm. I think these numbers are approximately correct for people in the UK but the details aren’t important.

Suppose we take 5 samples of 2 men and 2 women. Here are the numbers I generated:

{| class="wikitable"
|-
! Man1 !! Man2 !! Woman1 !! Woman2 !! Men mean !! Women mean !! Mean difference !! t !! P
|-
| 176 || 179 || 157 || 148 || 177.5 || 152.5 || 25 || 5.27 || 0.017
|-
| 180 || 176 || 160 || 164 || 178 || 162 || 16 || 5.66 || 0.015
|-
| 176 || 175 || 167 || 165 || 175.5 || 166 || 9.5 || 8.50 || 0.0068
|-
| 169 || 171 || 168 || 173 || 170 || 170.5 || -0.5 || -0.19 || 0.57
|-
| 179 || 175 || 166 || 178 || 177 || 172 || 5 || 0.79 || 0.26
|-
|}

P in the last column is the t-test probability for a one-side test of women being shorter than men. (Formally, it’s the probability of getting a value of t greater than that calculated from the data if women are in fact taller than men on average.)

Should the fact that, in the fourth sample, the average height of the women is taller than that of the men make us doubt that men are in fact taller on average? Should we be concerned about the last sample, in which the difference in height of the two sexes is rather small, though in the expected direction? No, in both cases. When we combine the data on all 10 men and all 10 women, we get this:

{| class="wikitable"
|-
! Men mean !! Women mean !! Mean difference !! t !! ''P''
|-
| 175.6 || 164.6 || 11 || 3.85 || 0.00058
|-
|}

Clearly, combining the data from several similar experiments strengthens the conclusions considerably, as shown by the fact that ''P'' is much smaller for the combined data than for any individual sample.

Although the combination of data from several experiments is a specialised area of statistics, I see nothing particularly incorrect about the approach used by Lenski and his colleagues. The general point is that it is valid to combine the results of different experiments if it is scientifically meaningful to do so. (For example: A. Combining the results of five samples of the heights of men and women is clearly valid. B. Combining three samples of heights of men and women with two samples of lengths of male and female squid clearly isn’t.) Generally speaking, the outcome of a combined analysis of several small experiments which all point in the same direction (or at least in a similar direction) will be more significant than that of any one of those experiments, as is shown in the larger table above.

I hope this clarifies the extensive discussion on this point and puts Aschafly’s mind at rest on this subject. [[User:KennyMac|KennyMac]] 08:20, 18 September 2008 (EDT)

:That's very nicely put, thanks. You should work on some of the stats pages here. Of course, technically any sample is ultimately just a combination of ''n'' samples of size 1. [[User:MikeR|MikeR]] 13:28, 18 September 2008 (EDT)

:I'll take a look at this Friday. It's not immediately obvious what the point is to your analysis above.--[[User:Aschlafly|Aschlafly]] 23:46, 18 September 2008 (EDT)
::"''The general point is that it is valid to combine the results of different experiments if it is scientifically meaningful to do so"''--[[User:KingOfNothing|KingOfNothing]] 00:57, 19 September 2008 (EDT)

:::This makes no sense as an argument. It may be true in this simple case that you can do one large or several small samples and get similar results - which is quite obvious and wouldn't need such a detailed rant. However, you provide no mathematical proof, just one example. [[User:Etc|Etc]] 01:08, 19 September 2008 (EDT)
:''"It's not immediately obvious what the point is to your analysis above"''. No surprise, Aschlafly, really. Maybe you should take your own advice: ''"I suggest you try harder with an open mind"''. --[[User:CrossC|CrossC]] 02:46, 19 September 2008 (EDT)

It is with great sadness that I note that the author of this - the only significant statistical explanation and discussion in this entire fiasco- has [http://www.conservapedia.com/index.php?title=Special%3ALog&type=block&user=DeanS&page=User%3AKennyMac just been blocked] for five years. Even his email is blocked, so he can't even appeal the action. I don't see such manouvers as having contributed to the much vaunted "open mind" of which various people here speak. [[User:BenHur|BenHur]] 10:27, 19 September 2008 (EDT)

'''REPLY''': I have now reviewed the above analysis, and it supports Point 5 rather than the PNAS paper. Point 5 stated, "The Third Experiment was erroneously combined with the other two experiments based on outcome rather than sample size, thereby yielding a false claim of overall statistical significance." The analysis above does nothing more than reinforce Point 5 by combining experiments based on sample size.

In Pavlovian manner, some Lenski types nod their head here in agreement at the above analysis, apparently unaware that it reinforces Point 5.

When combining results from samples that are vastly different in sample size, it is necessary to factor in the different sample sizes. Apparently the PNAS paper failed to do that, which helps explain why it refuses to provide a meaningful response to Point 5.--[[User:Aschlafly|Aschlafly]] 19:24, 19 September 2008 (EDT)

(rants below were deleted for being non-substantive in violation of this page's rules.)--[[User:Aschlafly|Aschlafly]] 19:24, 19 September 2008 (EDT)

:::I understand point 5 now, or at least I think I do. What we have as a "sample" is either:

::::1. Individual cultures (Schlafly)
::::2. Cultures that developed cit+. (Lenski)

:::Schlafly contends that the sample should be all the cultures and that Lenski has, improperly, filtered the sample by excluding the vast majority of it (i.e. all those cultures that did not become cit+). Am I right in thinking this is the argument? --[[User:Toffeeman|Toffeeman]] 19:57, 19 September 2008 (EDT)

:::: No, we're talking about how Lenski combined a large study (which did not really support Lenski's hypothesis) with small studies (which Lenski claims does support his hypothesis). The studies were not combined in a logical manner with proper weighting given to the much bigger size of the large study.--[[User:Aschlafly|Aschlafly]] 23:15, 19 September 2008 (EDT)
:::::Aschlafly, have you read the paper on z-transforms which explains the statistical technique used? You can download a .pdf copy of the paper for free [http://www3.interscience.wiley.com/journal/118663174/abstract here]. --[[User:BillA|BillA]] 06:30, 20 September 2008 (EDT)

:::::: You say "statistical technique used," but you should have said "statistical technique ''cited''." In fact, a close reading of the Z-transform paper provides more support for Point 5: combined studies must be weighted based on sample size:

::::::: "When there is variation in the sample size across studies, there can be a noticeable difference in the power of the two methods, with the weighted Z-approach being superior in all cases. As such, we should always prefer the weighted Z to the unweighted Z-approach when the independent studies test the same hypothesis."[http://www3.interscience.wiley.com/journal/118663174/abstract see p. 1371].

:::::: In other words, the cited paper actually ''supports'' Point 5.--[[User:Aschlafly|Aschlafly]] 09:34, 20 September 2008 (EDT)

(unindent)Lenski used the weighted method. See note 49 to the paper and the text around the combination. Of course there is the question of on what basis Lenski weighted the results. Lenski weighted the results on the basis of the Cit+ numbers and we may think it would have been better to weight on the basis of the number of replicates. I have below the calculations (not mine) of combined P-values based on 1) no weighting, 2) weighting on the basis of Cit+ and 3) weighting on the basis of replicates. The weighted Z-transformed = SUM(Weight x Z-score for each run)/SQRT(SUM(Weight^2 for each run))

{| class="wikitable"
|-
! Expt# !! p-value !! z-score !! #Cit+ muts !! #replicates
|-
| 1 || 0.0085 || 2.387 || 4 || 72
|-
| 2 || 0.0007 || 3.195 || 5 || 340
|-
| 3 || 0.0823 || 1.390 || 8 || 2800
|-
|}

Applying the formula described above..

{| class="wikitable"
|-
! Weighting !! Z transformed !! p
|-
| Equal || 4.025 || <0.001
|-
|By total Cit+|| 3.576 || <0.001
|-
|By total replicates|| 1.825 || 0.034
|-
|}

So weighting on the basis of the number of replicates considerably increases the P-value. It remains, however, well within the range of statistical significance (0<P<0.05). If we hold that Lenski should have weighted on the basis of replicates then he should have rejected the null hypothesis and reached exactly the same conclusions that he did. The entire paper would have been exactly the same except the sentence “the result is extremely significant (P<0.0001) whether or not….” Would read “the result is significant (P<0.04) whether or not”. Point 5 establishes one number and an “extremely”. Point 5, therefore, has no weight (excuse the pun).
--[[User:Toffeeman|Toffeeman]] 15:18, 20 September 2008 (EDT)

: Sorry, Toffeeman, a falsehood is still a falsehood. Based on your own posting, if Lenski had applied the Whitlock Z-transform paper in a logical manner, the results would not have been nearly as striking as Lenski claimed (his paper said the results were "extremely significant"). Moreover, I found Lenski's description of his application of the Whitlock paper to be particularly misleading. Lenski's use of "whether or not"<ref>"We also used the Z-transformation method (49) to combine the probabilities from our three experiments, and '''the result is extremely significant (P < 0.0001) whether or not''' the experiments are weighted by the number of independent Cit+ mutants observed in each one." (Lenski paper at 7902).</ref> obscures the basic error that he did not apply Whitlock's paper in the straightforward, correct manner. I think the wording in the Lenski paper deliberately obscures this falsehood from the reader.

: People have free will to embrace and defend falsehoods. I don't expect them to change quickly or admit they were wrong. But you'll find me defending and promoting the truth.

: Point 5 remains valid and the falsehood remains uncorrected by PNAS or Lenski. Four other points in higher priority remain uncorrected by them also.--[[User:Aschlafly|Aschlafly]] 16:47, 20 September 2008 (EDT)

::'''''"a falsehood is still a falsehood"'''''. Precisely, the null hypothesis should be considered false and the conclusions of the paper stand.

::Oh? Do you mean ''Lenski's falsehood''? And what falsehood is that? Lenski said that he had calculated the P-value without weighting and that had come out at <0.0001. That is true, not false. Lenski said he had calculated the P-value weighting on the basis of the Cit+ replicates and that had come out at <0.0001. That is true, not false. There is no falsehood. Lenski did not mention the results of weighting on the basis of replicate numbers. He thus made no claim about weighting on the basis of replicate numbers. If he made no claim he cannot have made a false claim.

::How do the words Lenski uses "mislead". If you read them as written what conclusion do you come to? You are lead to the conclusion that the mutation was not "rare-but-equal", instead it was contingent. That is the right conclusion. If Lenski had presented the data in a different manner (perhaps by including the results of weighting on the basis of replicate numbers) what conclusion do you come to? You are again lead to the conclusion that the mutation was not "rare-but-equal", instead it was contingent. That is the right conclusion. To mislead you must be lead to a conclusion that is incorrect. By Lenski's paper you are not lead to a conclusion that is incorrect. Thus is cannot be said to be "misleading".

::I shall not comment on your second paragraph, the temptation to ''"Tu Quoque"'' would be too great.

--[[User:Toffeeman|Toffeeman]] 17:13, 20 September 2008 (EDT)

::: The falsehood consists of pretending to apply the Whitlock Z-transform in a straightforward, logical and correct manner. I think the Lenski paper is intentionally misleading by using the "whether or not" wording, when both alternatives are nonsensical. Point 5 has been proven above to be correct in identify an error in the Lenski paper.

::: "Toffeeman", your blocking history suggests you have been less than straightforward yourself. Go elsewhere if you seek to be deceitful. You're not fooling anyone here.--[[User:Aschlafly|Aschlafly]] 17:54, 20 September 2008 (EDT)

::::Lenski did apply the Z-transformation correctly, both weighted and unweighted. The data points extracted from each replay are the ''generation numbers of those replicates that gave rise to Cit+ mutants''. Thus Replay 1 produced four data points: 30,500 31,500 32,500 32,500. Replay 2 produced five data points: 32,000 32,000 32,000 32,000 32,500. Replay 3 produced eight data points: 20,000 20,000 27,000 27,000 31,000 31,500 32,000 32,000. Thus the N for replay 1 is 4; replay 2 is 5 and replay 3 is 8. The fact that replay 3 used 38 times as many replicates as replay 1 does not mean that it should be weighted 38 times as much; it only produced twice as much data, not 38 times as much.

::::Suppose I want to find out what the average age of a murderer is in three cities. In L.A. I interview 72 random people and find that 4 of them were convicted of murder; I record the ages of the four. In Seattle I interview 340 people and find that 5 of them are convicted murderers; likewise in Singapore I interview 2800 and find 8 murderers. In the end, I have 4,5, and 8 data points from the three cities; the number of people I had to interview to obtain those data points doesn't factor into the analysis of what the average age of the murderers is.--[[User:Brossa|Brossa]] 00:06, 21 September 2008 (EDT)

::::: In your first paragraph you simply repeat the error underlying Lenski's paper. You, like the paper, incorrectly apply Whitlock's Z-transform.

::::: The quality and reliability of data is proportional to sample size, and when different studies are combined they need to be weighted accordingly. The results from a very large sample size would not be weighted equally with the results from a small sample size, as you and Lenski have done. That's basic logic, though I'm not optimistic that you or Lenski will admit it. Open-minded people who respect logic have no difficulty elevating logic over personal whim.-[[User:Aschlafly|Aschlafly]] 11:30, 21 September 2008 (EDT)

::::::Andy if you read Whitlock's paper you would see it say, and I quote, "Ideally each study is weighted proportional to the inverse of its error variance, that is, by the '''reciprocal of its squared standard error'''." It says nothing about weighting according to sample size, which is what you seem to be insisting should be done.
::::::Also Whitlock acknowledges in the paper that there is no preference for weighted versus equal weighting, so the fact that both equal weighting and weighting by the standard error give a statistically significant result shows that the 3 experiments combined support rejection of the null hypothesis. [[User:DanB|DanB]] 20:39, 21 September 2008 (EDT)

:::::::ASchlafly, you state that I incorrectly apply "Whitlock's Z-transform" (actually the test belongs to Mosteller & Bush<ref>Mosteller, F. & Bush, R.R. 1954. Selected quantitative techniques. In: ''Handbook of Social Psychology,'' Vol. 1 (G. Lindzey, ed.)</ref> and/or Liptak<ref>Liptak, T. 1958. On the combination of tests. ''Magyar Tud. Akad. Mat. Kutato Int. Kozl.'' '''3''': 171-197</ref>). Whitlock describes weighting by the reciprocal of the squared standard error. The standard error of the mean is proportional to 1/sqrt(N), so the reciprocal of the squared standard error is proportional to N. Thus larger studies ''are'' given more weight. I maintain that the sample sizes N of the three replays are 4, 5, and 8 respectively. Weighting based on those three N does not weight all three replays equally as you claim: it gives replay 2 25% more weight and replay 3 100% more weight than replay 1. Rather than simply repeating that I am wrong, will you please state what ''you'' think the sample sizes of the three replay experiments are, and, in your opinion, what the ''correct'' application of the Z-transformation would be?--[[User:Brossa|Brossa]] 18:00, 22 September 2008 (EDT)

:::::::: The Lenski paper states how it weighted the experiments, and that weighting is incorrect. Admit it. Moreover, the incorrect weighting in the Lenski paper was not likely an inadvertent error, as it inflated the significance of the results. I found the wording used by the Lenski paper to describe its (incorrect) weighting to be artfully misleading.

:::::::: Provide me with federal funding as Lenski received, and I'll write a paper for you. But I don't have to write an alternative paper to point out glaring errors in Lenski's paper.--[[User:Aschlafly|Aschlafly]] 08:35, 23 September 2008 (EDT)

::::::::: I've been following this discussion for a while and I have to agree with ASchlafly. It hardly seems fair that he should have to, in his spare time, replicate an experiment done by a professional just to "earn" the right to criticize it. I am unfamiliar with statistics, but if some complicated transform goes against common sense, common sense should prevail. After all, there are lies, damned lies, and statistics... [[User:AndyM|AndyM]] 10:57, 23 September 2008 (EDT)

(unindent)I'm not asking anyone to write a paper or replicate an experiment. I'm asking ASchlafly to support his statement "The results from a very large sample size would not be weighted equally with the results from a small sample size, '''as you and Lenski have done'''"(bolding mine). I have stated publicly, subject to challenge by others, that the sample sizes (n) of the three replays are four, five, and eight respectively. Furthermore, using n of 4, 5, and 8 in the weighted Z-method DOES NOT weight all the replay experiments equally - it weights replay 3 twice as much as replay 1 and 8/5 as much as replay 2. Tell you what: I'll drop all my questions about Monte Carlo and the Z-transform, and simply ask ASchlafly one question: '''what is the sample size, n, of the second replay experiment?''' He need not even do any calculations - a statement in words that will allow someone else to do the calculation will suffice. This is not a complicated question to answer; the paper states how many replicate cultures there were (340), how many cells there were in each replicate (3.9x10^8), how many replicates gave rise to Cit+ cells (5), and which generations those Cit+ replicates came from (4 from 32,000 and one from 32,500). I will even give ''my'' answer: '''five'''. Furthermore, I will say ''why'' I believe that, using the murderer/age analogy: performing the 340 replicates is the same as interviewing 340 people in order to find out if any of them are convicted murderers. Finding that five replicates gave rise to Cit+ mutants is the same as the survey finding that 5 of those 340 people were convicted murderers. Finding that the Cit+ mutants arose from 4 replicates from generation 32,000 and 1 from generation 32,500 is the same as finding the ages of the murderers. The five data points in the Lenski study allow one to calculate the 'mean generation of clones yielding Cit+': 32,100. This is the same as finding the mean age of the five murderers. If I want to compare this hypothetical murderer age study to some other study of the mean age of murderers, I would weight the studies based on how many murderers were in each study, not on how many non-murderers were included in the initial survey.

Surely ASchlafly can say ''what'' he thinks the n of the second replay is, even if he won't say ''why'' he thinks it. Is it five? 340? The number of replicates times the number of cells per replicate? Something else? No analysis need be performed on the resulting number.--[[User:Brossa|Brossa]] 15:54, 23 September 2008 (EDT)

:OK - would you care to put in writing that after ASchlafly gives you his response, you won't start obfuscating the issue with Monte Carlo and Z-transform issues? You understand: it is typical of liberals to, after being proven wrong, to start pretending that they were talking about an entirely different issue altogether. '''After ASchlafly states the sample size of the second replay experiment you will consider yourself answered.''' Correct?

:Brossa, your rant is misplaced. One cannot salvage an error in logic by questioning which of superior alternatives should be used instead. The sample size of an experiment is the number that comprises the underlying sample used in the experiment, not the number of a certain outcome from the experiment. Maybe you can debate yourself over what the correct underlying sample size is, but it is plainly not the number of a certain outcome from the experiment.--[[User:Aschlafly|Aschlafly]] 19:28, 23 September 2008 (EDT)

Maybe the Journal of Nature can be your next letter submission source. ''International Weekly Journal of Science'' -- [[Image:50 star flag.png|14px]] [[User:Jpatt|jp]] 21:17, 22 September 2008 (EDT)

==Point 5 Rejected==

ASchlafly and others: if you don't agree with me, present a reasoned argument against my points. Don't delete other people's comments on a Talk page and for goodness sake, don't be so spineless as to block me to prevent me from replying to you. I repeat what I wrote last week before you deleted my contribution to this discussion and blocked me.

I ''do'' have specialist knowledge of this area, despite Bugler's assertions to the contrary (made without any evidence whatsoever, may I say). But I repeat, it really doesn't matter whether I have particular qualifications or not. In science, what matters is what is said, not who says it. The most outstanding scientific discoveries of the 20th century were made by a patent clerk who had no academic position at the time.

I now repeat again my cut-and-paste from Longstop's contribution a couple of weeks ago. If you don't agree with it, discuss it, don't delete it.

:The main point he [Kennymac] makes is quite correct, that combining experiments will tend to give a more significant result (i.e. a lower P-value) than any single experiment on its own.

:The point that ASchlafly makes (headed '''REPLY''', shortly after KennyMac's example) is slightly misleading. You don't choose which experiments to combine on the basis of their outcomes - you either combine all relevant experiments or none. In this case, Professor Lenski chose to combine all the experiments and present a single analysis of them. That's fine.

:The issue of whether to weight the Z-test according to sample size is not a straightforward issue. Before Whitlock's recent paper, the consensus was that the P-value already depends on sample size so it should not be weighted according to sample size. (Basically, a high degree of significance, i.e. a low P-value, can be achieved by having either a large difference between the treatments or a large experiment or, of course, both.) Whitlock's work, based on computer simulations, is an interesting contribution but cannot be regarded as the last word on the subject because any computer simulation involves assumptions about the structure of the particular experiment simulated. I cannot imagine any editor of a scientific journal rejecting a paper because it used an unweighted Z-test rather than the weighted version (or vice-versa).

:The conclusion, therefore, is that while there is a quantitative difference in the level of significance obtained by weighted and unweighted Z-tests, there is undeniably a significant biological effect. ASchlafly and other contributors should not be concerned that there is anything incorrect about the biological conclusions of Professor Lenski and his students or that there was anything at all underhand about their analysis or presentation of their data. [[User:DavyJones|DavyJones]] 20:39, 31 October 2008 (EDT)

==Referring of Scientific Papers==

Another point that Aschlafly and others deleted was my explanation of why CP readers shouldn't be concerned about the fact that the Lenski paper was reviewed within 14 days. This is perfectly normal practice for a leading journal. If you're invited to review a paper for a leading journal and they give you 7/10/14/etc days, you only agree to review it if you're sure you're going to have time before the journal's deadline. So there's absolutely no reason to suppose the review wasn't done properly.

Again, if you disagree, discuss, don't delete and don't block. [[User:DavyJones|DavyJones]] 20:39, 31 October 2008 (EDT)

== References ==

<references/>

== Have we given up? ==

Not much activity here in the past few weeks. Have we given up on pursuing this matter further?
Conservapedia should work on continuing to keep the Lenski study and its flaws in the news.
Is there anything else we can do? Perhaps write to local officials about the misuse of public funds for studies like Lenski's, and also to complain about PNAS? --[[User:DRamon|DRamon]] 16:39, 31 October 2008 (EDT)

: We exposed five fundamental flaws in the study, and told the truth. The truth doesn't care whether some refuse to accept it. There will ''always'' be people who deny the truth, particularly when they stand to profit from falsehoods. For now, I've moved onto more pressing issues on this site.--[[User:Aschlafly|Aschlafly]] 16:56, 31 October 2008 (EDT)

:: What do you mean by "profit from falsehoods"? Are you seriously suggesting that everyone who has a different point of view from your own must have mercenary motives for disagreeing with you? That's a very bizarre point of view. [[User:DavyJones|DavyJones]] 20:39, 31 October 2008 (EDT)
:::The suggestion is that those who lie very frequently do so forr reasons of greed. Your denial of this self-evident fact, and your [[deceit]]ful twisting of Mr Schlafly's words, speak volumes of you, DavyJones. [[User:Bugler|Bugler]] 06:56, 1 November 2008 (EDT)

David Cameron

2008-11-01T01:15:25Z

DavyJones: /* Personal */

[[Image:674uyyhju.jpg|right|thumb]]
'''David Cameron''', born 9 October 1966, is the current leader of the British [[Conservative Party]]. According to the opinion polls, he is likely to be the next British [[Prime Minister]] after the next general election, which will probably be held in either 2009 or 2010.

==Personal==

Cameron spent his early years near Wantage in [[Oxfordshire]], [[England]], though his family's roots lie in [[Inverness]], [[Scotland]], and "Cameron" is well known in Britain as a Scottish name.

Cameron was educated at [[Eton College]], which is generally regarded as Britain's most prestigious private school, and at [[Brasenose College]], [[Oxford University|Oxford]].

Cameron is self-descibed as "upper middle class". His leadership and indeed his own party are supported by businesses, as opposed to the leftist Labour Party, led by the Scotsman [[Gordon Brown]]; who are backed overwhelmingly by the [[trade union]]s. Many intervening leaders have been middle-class ([[Edward Heath]], [[Margaret Thatcher]]) or even working-class ([[John Major]]).
His refusal to discuss his past, citing the right to a private life before politics<ref>http://news.bbc.co.uk/1/hi/uk_politics/4340328.stm</ref> has led to criticism from a small proportion of media sources and opposition MPs.

==Political career==

Cameron's pre-parliamentary career included spells as a staffer for controversial Conservative politician [[Norman Lamont]] and as a PR executive.

Cameron was elected to Parliament as MP for Witney in Oxfordshire at the 2001 general election.

Cameron was elected leader of the [[Conservative Party]] in December 2005, succeeding [[Michael Howard]].

In late June 2007, at the end of then-Prime Minister [[Tony Blair]]'s final Prime Minister's Questions session in the [[House of Commons]], David Cameron led his opposition party in giving the outgoing leader a standing ovation.<ref>[http://www.telegraph.co.uk/news/uknews/1555758/Tony-Blair-steps-down-to-a-standing-ovation.html Tony Blair steps down to standing ovation] - Daily Telegraph, June 27, 2007</ref>

==Policies==

Cameron has attempted to move the Conservative party towards what is perceived by some to be the centre ground of British politics. While the party under his leadership has expressed support for some traditional elements of Conservative policy, such as the importance of the [[family]], Cameron has also expressed a passionate concern about [[global warming]]. He has suggested a move towards [[privitisation]] within the strongly-socialist [[National Health Service]], in an attempt to combat the economic failures resulting from the flawed socialist ideas upon which the organisation is based. Designed and originated by the leftist [[Labour Party]], the organisation is notorious for its burocracy and the failure of its left-wing values in an economic sense. He garnered criticism from some sections of the press when when suggesting society try to breach the social divide caused by the [[Liberal media]]'s portrayal of all youths as criminals.

Some traditional Conservatives, particularly those on the [[Thatcherism|Thatcherite]] wing of the party, have criticized Cameron for moving the party too far to the left. They point to surveys showing that many voters feel they no longer know what the Conservative Party stands for.<ref>http://www.yougov.com/archives/pdf/TEL060101018_1.pdf</ref> However, he has stated that he is "certainly a big [[Margaret Thatcher|Thatcher]] fan, but I don't know whether that makes me a Thatcherite."<ref name="new identity">[http://news.bbc.co.uk/1/hi/uk_politics/4446864.stm "Cameron: Tories need new identity"], ''BBC News Online'', [[17 November]] [[2005]], accessed [[6 November]] [[2006]]</ref> He has also described himself as a "liberal Conservative" (though "liberal" in British English does not have the same meaning as in the United States, and instead has the meaning of "centrist" or "moderate").<ref name="Rawnsley">Andrew Rawnsley, [http://observer.guardian.co.uk/focus/story/0,,1669957,00.html "'I'm not a deeply ideological person. I'm a practical one'"], ''Guardian Unlimited'', [[18 December]] [[2005]], accessed [[6 November]] [[2006]]</ref> Some have gone so far as to claim that true conservatism is today represented in Britain not by the Conservative Party but by the [[UK Independence Party]]. On the other hand, the approval ratings of Cameron and his party continue to compare very favourably with those of the Labour Party and its leadership, which is undoubtedly unpopular.

Cameron has said: "My aim is to promote social justice, making sure that everyone has access to good schools, good healthcare and decent housing, take a lead in ending global poverty and do all we can to meet the great environmental threats of our age."<ref>http://www.conservatives.com/tile.do?def=david.cameron.about.page</ref> Some conservative politicians and commentators, notably [[Norman Tebbit]], have criticised him for prioritising issues of the environment and social justice over more traditionally Conservative policy areas, such as tax, immigration and foreign relations. Tebbit said: "Is he the party's [[Chairman Mao]] or [[Pol Pot]], intent on purging even the memory and name of [[Margaret Thatcher|Thatcherism]] before building a new modern compassionate green globally aware party somewhere on the left side of the middle?"<ref name="g1">[http://politics.guardian.co.uk/conservatives/story/0,,1698576,00.html Tories must retake centre ground says Cameron], ''Guardian Unlimited'', 31 January 2006</ref> However, Cameron has responded extensively to such criticisms by pointing out that the economic and social problems faced by modern-day Britain are radically different from those faced in the past; he has argued that the Conservative Party needs to re-take the [[centrist|centre ground]] of politics from the [[Labour Party]].<ref name="bbc1">[http://news.bbc.co.uk/1/hi/uk_politics/4661024.stm Cameron denies 'betraying' Tories], BBC News, 30 January 2006</ref> He argued: "The change is not a betrayal. It is a recognition that the challenges faced by Britain are not the challenges of the 1970s. Social justice and economic efficiency are the common ground of British politics. We have to find the means of succeeding where the government has failed."<ref name="g2"/>

On August 16, 2008, Cameron followed President [[George Bush]] in criticising [[Russia]]'s invasion of [[Georgia]] during a visit to the war-torn region.<ref>[http://afp.google.com/article/ALeqM5jl825geip9c65_-FTHTC_3wzMy0Q Cameron in Georgia slams 'invading' Russia]</ref>
==References==

<References/>

==See also==

* [[British politics]]
* [[Conservative Party]]

{{DEFAULTSORT: Cameron, David}}

[[category:British Politics]]

Talk:PNAS Response to Letter

2008-11-01T00:39:16Z

DavyJones: Point 5 is still refuted

Notice: misrepresentations are not going to be allowed on this page. Substantive comments only, please.

Note: earlier posts are archived [[Talk:PNAS_Response_to_Letter/Archive1|here]]. --[[User:BillA|BillA]] 17:05, 20 September 2008 (EDT)

== Point 5 Confirmed ==

I would like to contribute to this discussion because I have taught statistics to graduate biology students for 16 years.

The combination of data from several experiments is a specialist and sometimes difficult area of statistical theory but a simple example shows why Aschafly’s concern about combining the results of three different experiments is not justified and why this aspect of his criticism of Lenski’s recent paper in PNAS is not valid.

Suppose we want to conduct a test of whether or not men are taller than women on average. For the sake of the example, I generated random heights of people from a population in which men had an average height of 175cm (5’10’) and women of 165cm (5’6”). The standard deviations of height in both sexes were 7cm. I think these numbers are approximately correct for people in the UK but the details aren’t important.

Suppose we take 5 samples of 2 men and 2 women. Here are the numbers I generated:

{| class="wikitable"
|-
! Man1 !! Man2 !! Woman1 !! Woman2 !! Men mean !! Women mean !! Mean difference !! t !! P
|-
| 176 || 179 || 157 || 148 || 177.5 || 152.5 || 25 || 5.27 || 0.017
|-
| 180 || 176 || 160 || 164 || 178 || 162 || 16 || 5.66 || 0.015
|-
| 176 || 175 || 167 || 165 || 175.5 || 166 || 9.5 || 8.50 || 0.0068
|-
| 169 || 171 || 168 || 173 || 170 || 170.5 || -0.5 || -0.19 || 0.57
|-
| 179 || 175 || 166 || 178 || 177 || 172 || 5 || 0.79 || 0.26
|-
|}

P in the last column is the t-test probability for a one-side test of women being shorter than men. (Formally, it’s the probability of getting a value of t greater than that calculated from the data if women are in fact taller than men on average.)

Should the fact that, in the fourth sample, the average height of the women is taller than that of the men make us doubt that men are in fact taller on average? Should we be concerned about the last sample, in which the difference in height of the two sexes is rather small, though in the expected direction? No, in both cases. When we combine the data on all 10 men and all 10 women, we get this:

{| class="wikitable"
|-
! Men mean !! Women mean !! Mean difference !! t !! ''P''
|-
| 175.6 || 164.6 || 11 || 3.85 || 0.00058
|-
|}

Clearly, combining the data from several similar experiments strengthens the conclusions considerably, as shown by the fact that ''P'' is much smaller for the combined data than for any individual sample.

Although the combination of data from several experiments is a specialised area of statistics, I see nothing particularly incorrect about the approach used by Lenski and his colleagues. The general point is that it is valid to combine the results of different experiments if it is scientifically meaningful to do so. (For example: A. Combining the results of five samples of the heights of men and women is clearly valid. B. Combining three samples of heights of men and women with two samples of lengths of male and female squid clearly isn’t.) Generally speaking, the outcome of a combined analysis of several small experiments which all point in the same direction (or at least in a similar direction) will be more significant than that of any one of those experiments, as is shown in the larger table above.

I hope this clarifies the extensive discussion on this point and puts Aschafly’s mind at rest on this subject. [[User:KennyMac|KennyMac]] 08:20, 18 September 2008 (EDT)

:That's very nicely put, thanks. You should work on some of the stats pages here. Of course, technically any sample is ultimately just a combination of ''n'' samples of size 1. [[User:MikeR|MikeR]] 13:28, 18 September 2008 (EDT)

:I'll take a look at this Friday. It's not immediately obvious what the point is to your analysis above.--[[User:Aschlafly|Aschlafly]] 23:46, 18 September 2008 (EDT)
::"''The general point is that it is valid to combine the results of different experiments if it is scientifically meaningful to do so"''--[[User:KingOfNothing|KingOfNothing]] 00:57, 19 September 2008 (EDT)

:::This makes no sense as an argument. It may be true in this simple case that you can do one large or several small samples and get similar results - which is quite obvious and wouldn't need such a detailed rant. However, you provide no mathematical proof, just one example. [[User:Etc|Etc]] 01:08, 19 September 2008 (EDT)
:''"It's not immediately obvious what the point is to your analysis above"''. No surprise, Aschlafly, really. Maybe you should take your own advice: ''"I suggest you try harder with an open mind"''. --[[User:CrossC|CrossC]] 02:46, 19 September 2008 (EDT)

It is with great sadness that I note that the author of this - the only significant statistical explanation and discussion in this entire fiasco- has [http://www.conservapedia.com/index.php?title=Special%3ALog&type=block&user=DeanS&page=User%3AKennyMac just been blocked] for five years. Even his email is blocked, so he can't even appeal the action. I don't see such manouvers as having contributed to the much vaunted "open mind" of which various people here speak. [[User:BenHur|BenHur]] 10:27, 19 September 2008 (EDT)

'''REPLY''': I have now reviewed the above analysis, and it supports Point 5 rather than the PNAS paper. Point 5 stated, "The Third Experiment was erroneously combined with the other two experiments based on outcome rather than sample size, thereby yielding a false claim of overall statistical significance." The analysis above does nothing more than reinforce Point 5 by combining experiments based on sample size.

In Pavlovian manner, some Lenski types nod their head here in agreement at the above analysis, apparently unaware that it reinforces Point 5.

When combining results from samples that are vastly different in sample size, it is necessary to factor in the different sample sizes. Apparently the PNAS paper failed to do that, which helps explain why it refuses to provide a meaningful response to Point 5.--[[User:Aschlafly|Aschlafly]] 19:24, 19 September 2008 (EDT)

(rants below were deleted for being non-substantive in violation of this page's rules.)--[[User:Aschlafly|Aschlafly]] 19:24, 19 September 2008 (EDT)

:::I understand point 5 now, or at least I think I do. What we have as a "sample" is either:

::::1. Individual cultures (Schlafly)
::::2. Cultures that developed cit+. (Lenski)

:::Schlafly contends that the sample should be all the cultures and that Lenski has, improperly, filtered the sample by excluding the vast majority of it (i.e. all those cultures that did not become cit+). Am I right in thinking this is the argument? --[[User:Toffeeman|Toffeeman]] 19:57, 19 September 2008 (EDT)

:::: No, we're talking about how Lenski combined a large study (which did not really support Lenski's hypothesis) with small studies (which Lenski claims does support his hypothesis). The studies were not combined in a logical manner with proper weighting given to the much bigger size of the large study.--[[User:Aschlafly|Aschlafly]] 23:15, 19 September 2008 (EDT)
:::::Aschlafly, have you read the paper on z-transforms which explains the statistical technique used? You can download a .pdf copy of the paper for free [http://www3.interscience.wiley.com/journal/118663174/abstract here]. --[[User:BillA|BillA]] 06:30, 20 September 2008 (EDT)

:::::: You say "statistical technique used," but you should have said "statistical technique ''cited''." In fact, a close reading of the Z-transform paper provides more support for Point 5: combined studies must be weighted based on sample size:

::::::: "When there is variation in the sample size across studies, there can be a noticeable difference in the power of the two methods, with the weighted Z-approach being superior in all cases. As such, we should always prefer the weighted Z to the unweighted Z-approach when the independent studies test the same hypothesis."[http://www3.interscience.wiley.com/journal/118663174/abstract see p. 1371].

:::::: In other words, the cited paper actually ''supports'' Point 5.--[[User:Aschlafly|Aschlafly]] 09:34, 20 September 2008 (EDT)

(unindent)Lenski used the weighted method. See note 49 to the paper and the text around the combination. Of course there is the question of on what basis Lenski weighted the results. Lenski weighted the results on the basis of the Cit+ numbers and we may think it would have been better to weight on the basis of the number of replicates. I have below the calculations (not mine) of combined P-values based on 1) no weighting, 2) weighting on the basis of Cit+ and 3) weighting on the basis of replicates. The weighted Z-transformed = SUM(Weight x Z-score for each run)/SQRT(SUM(Weight^2 for each run))

{| class="wikitable"
|-
! Expt# !! p-value !! z-score !! #Cit+ muts !! #replicates
|-
| 1 || 0.0085 || 2.387 || 4 || 72
|-
| 2 || 0.0007 || 3.195 || 5 || 340
|-
| 3 || 0.0823 || 1.390 || 8 || 2800
|-
|}

Applying the formula described above..

{| class="wikitable"
|-
! Weighting !! Z transformed !! p
|-
| Equal || 4.025 || <0.001
|-
|By total Cit+|| 3.576 || <0.001
|-
|By total replicates|| 1.825 || 0.034
|-
|}

So weighting on the basis of the number of replicates considerably increases the P-value. It remains, however, well within the range of statistical significance (0<P<0.05). If we hold that Lenski should have weighted on the basis of replicates then he should have rejected the null hypothesis and reached exactly the same conclusions that he did. The entire paper would have been exactly the same except the sentence “the result is extremely significant (P<0.0001) whether or not….” Would read “the result is significant (P<0.04) whether or not”. Point 5 establishes one number and an “extremely”. Point 5, therefore, has no weight (excuse the pun).
--[[User:Toffeeman|Toffeeman]] 15:18, 20 September 2008 (EDT)

: Sorry, Toffeeman, a falsehood is still a falsehood. Based on your own posting, if Lenski had applied the Whitlock Z-transform paper in a logical manner, the results would not have been nearly as striking as Lenski claimed (his paper said the results were "extremely significant"). Moreover, I found Lenski's description of his application of the Whitlock paper to be particularly misleading. Lenski's use of "whether or not"<ref>"We also used the Z-transformation method (49) to combine the probabilities from our three experiments, and '''the result is extremely significant (P < 0.0001) whether or not''' the experiments are weighted by the number of independent Cit+ mutants observed in each one." (Lenski paper at 7902).</ref> obscures the basic error that he did not apply Whitlock's paper in the straightforward, correct manner. I think the wording in the Lenski paper deliberately obscures this falsehood from the reader.

: People have free will to embrace and defend falsehoods. I don't expect them to change quickly or admit they were wrong. But you'll find me defending and promoting the truth.

: Point 5 remains valid and the falsehood remains uncorrected by PNAS or Lenski. Four other points in higher priority remain uncorrected by them also.--[[User:Aschlafly|Aschlafly]] 16:47, 20 September 2008 (EDT)

::'''''"a falsehood is still a falsehood"'''''. Precisely, the null hypothesis should be considered false and the conclusions of the paper stand.

::Oh? Do you mean ''Lenski's falsehood''? And what falsehood is that? Lenski said that he had calculated the P-value without weighting and that had come out at <0.0001. That is true, not false. Lenski said he had calculated the P-value weighting on the basis of the Cit+ replicates and that had come out at <0.0001. That is true, not false. There is no falsehood. Lenski did not mention the results of weighting on the basis of replicate numbers. He thus made no claim about weighting on the basis of replicate numbers. If he made no claim he cannot have made a false claim.

::How do the words Lenski uses "mislead". If you read them as written what conclusion do you come to? You are lead to the conclusion that the mutation was not "rare-but-equal", instead it was contingent. That is the right conclusion. If Lenski had presented the data in a different manner (perhaps by including the results of weighting on the basis of replicate numbers) what conclusion do you come to? You are again lead to the conclusion that the mutation was not "rare-but-equal", instead it was contingent. That is the right conclusion. To mislead you must be lead to a conclusion that is incorrect. By Lenski's paper you are not lead to a conclusion that is incorrect. Thus is cannot be said to be "misleading".

::I shall not comment on your second paragraph, the temptation to ''"Tu Quoque"'' would be too great.

--[[User:Toffeeman|Toffeeman]] 17:13, 20 September 2008 (EDT)

::: The falsehood consists of pretending to apply the Whitlock Z-transform in a straightforward, logical and correct manner. I think the Lenski paper is intentionally misleading by using the "whether or not" wording, when both alternatives are nonsensical. Point 5 has been proven above to be correct in identify an error in the Lenski paper.

::: "Toffeeman", your blocking history suggests you have been less than straightforward yourself. Go elsewhere if you seek to be deceitful. You're not fooling anyone here.--[[User:Aschlafly|Aschlafly]] 17:54, 20 September 2008 (EDT)

::::Lenski did apply the Z-transformation correctly, both weighted and unweighted. The data points extracted from each replay are the ''generation numbers of those replicates that gave rise to Cit+ mutants''. Thus Replay 1 produced four data points: 30,500 31,500 32,500 32,500. Replay 2 produced five data points: 32,000 32,000 32,000 32,000 32,500. Replay 3 produced eight data points: 20,000 20,000 27,000 27,000 31,000 31,500 32,000 32,000. Thus the N for replay 1 is 4; replay 2 is 5 and replay 3 is 8. The fact that replay 3 used 38 times as many replicates as replay 1 does not mean that it should be weighted 38 times as much; it only produced twice as much data, not 38 times as much.

::::Suppose I want to find out what the average age of a murderer is in three cities. In L.A. I interview 72 random people and find that 4 of them were convicted of murder; I record the ages of the four. In Seattle I interview 340 people and find that 5 of them are convicted murderers; likewise in Singapore I interview 2800 and find 8 murderers. In the end, I have 4,5, and 8 data points from the three cities; the number of people I had to interview to obtain those data points doesn't factor into the analysis of what the average age of the murderers is.--[[User:Brossa|Brossa]] 00:06, 21 September 2008 (EDT)

::::: In your first paragraph you simply repeat the error underlying Lenski's paper. You, like the paper, incorrectly apply Whitlock's Z-transform.

::::: The quality and reliability of data is proportional to sample size, and when different studies are combined they need to be weighted accordingly. The results from a very large sample size would not be weighted equally with the results from a small sample size, as you and Lenski have done. That's basic logic, though I'm not optimistic that you or Lenski will admit it. Open-minded people who respect logic have no difficulty elevating logic over personal whim.-[[User:Aschlafly|Aschlafly]] 11:30, 21 September 2008 (EDT)

::::::Andy if you read Whitlock's paper you would see it say, and I quote, "Ideally each study is weighted proportional to the inverse of its error variance, that is, by the '''reciprocal of its squared standard error'''." It says nothing about weighting according to sample size, which is what you seem to be insisting should be done.
::::::Also Whitlock acknowledges in the paper that there is no preference for weighted versus equal weighting, so the fact that both equal weighting and weighting by the standard error give a statistically significant result shows that the 3 experiments combined support rejection of the null hypothesis. [[User:DanB|DanB]] 20:39, 21 September 2008 (EDT)

:::::::ASchlafly, you state that I incorrectly apply "Whitlock's Z-transform" (actually the test belongs to Mosteller & Bush<ref>Mosteller, F. & Bush, R.R. 1954. Selected quantitative techniques. In: ''Handbook of Social Psychology,'' Vol. 1 (G. Lindzey, ed.)</ref> and/or Liptak<ref>Liptak, T. 1958. On the combination of tests. ''Magyar Tud. Akad. Mat. Kutato Int. Kozl.'' '''3''': 171-197</ref>). Whitlock describes weighting by the reciprocal of the squared standard error. The standard error of the mean is proportional to 1/sqrt(N), so the reciprocal of the squared standard error is proportional to N. Thus larger studies ''are'' given more weight. I maintain that the sample sizes N of the three replays are 4, 5, and 8 respectively. Weighting based on those three N does not weight all three replays equally as you claim: it gives replay 2 25% more weight and replay 3 100% more weight than replay 1. Rather than simply repeating that I am wrong, will you please state what ''you'' think the sample sizes of the three replay experiments are, and, in your opinion, what the ''correct'' application of the Z-transformation would be?--[[User:Brossa|Brossa]] 18:00, 22 September 2008 (EDT)

:::::::: The Lenski paper states how it weighted the experiments, and that weighting is incorrect. Admit it. Moreover, the incorrect weighting in the Lenski paper was not likely an inadvertent error, as it inflated the significance of the results. I found the wording used by the Lenski paper to describe its (incorrect) weighting to be artfully misleading.

:::::::: Provide me with federal funding as Lenski received, and I'll write a paper for you. But I don't have to write an alternative paper to point out glaring errors in Lenski's paper.--[[User:Aschlafly|Aschlafly]] 08:35, 23 September 2008 (EDT)

::::::::: I've been following this discussion for a while and I have to agree with ASchlafly. It hardly seems fair that he should have to, in his spare time, replicate an experiment done by a professional just to "earn" the right to criticize it. I am unfamiliar with statistics, but if some complicated transform goes against common sense, common sense should prevail. After all, there are lies, damned lies, and statistics... [[User:AndyM|AndyM]] 10:57, 23 September 2008 (EDT)

(unindent)I'm not asking anyone to write a paper or replicate an experiment. I'm asking ASchlafly to support his statement "The results from a very large sample size would not be weighted equally with the results from a small sample size, '''as you and Lenski have done'''"(bolding mine). I have stated publicly, subject to challenge by others, that the sample sizes (n) of the three replays are four, five, and eight respectively. Furthermore, using n of 4, 5, and 8 in the weighted Z-method DOES NOT weight all the replay experiments equally - it weights replay 3 twice as much as replay 1 and 8/5 as much as replay 2. Tell you what: I'll drop all my questions about Monte Carlo and the Z-transform, and simply ask ASchlafly one question: '''what is the sample size, n, of the second replay experiment?''' He need not even do any calculations - a statement in words that will allow someone else to do the calculation will suffice. This is not a complicated question to answer; the paper states how many replicate cultures there were (340), how many cells there were in each replicate (3.9x10^8), how many replicates gave rise to Cit+ cells (5), and which generations those Cit+ replicates came from (4 from 32,000 and one from 32,500). I will even give ''my'' answer: '''five'''. Furthermore, I will say ''why'' I believe that, using the murderer/age analogy: performing the 340 replicates is the same as interviewing 340 people in order to find out if any of them are convicted murderers. Finding that five replicates gave rise to Cit+ mutants is the same as the survey finding that 5 of those 340 people were convicted murderers. Finding that the Cit+ mutants arose from 4 replicates from generation 32,000 and 1 from generation 32,500 is the same as finding the ages of the murderers. The five data points in the Lenski study allow one to calculate the 'mean generation of clones yielding Cit+': 32,100. This is the same as finding the mean age of the five murderers. If I want to compare this hypothetical murderer age study to some other study of the mean age of murderers, I would weight the studies based on how many murderers were in each study, not on how many non-murderers were included in the initial survey.

Surely ASchlafly can say ''what'' he thinks the n of the second replay is, even if he won't say ''why'' he thinks it. Is it five? 340? The number of replicates times the number of cells per replicate? Something else? No analysis need be performed on the resulting number.--[[User:Brossa|Brossa]] 15:54, 23 September 2008 (EDT)

:OK - would you care to put in writing that after ASchlafly gives you his response, you won't start obfuscating the issue with Monte Carlo and Z-transform issues? You understand: it is typical of liberals to, after being proven wrong, to start pretending that they were talking about an entirely different issue altogether. '''After ASchlafly states the sample size of the second replay experiment you will consider yourself answered.''' Correct?

:Brossa, your rant is misplaced. One cannot salvage an error in logic by questioning which of superior alternatives should be used instead. The sample size of an experiment is the number that comprises the underlying sample used in the experiment, not the number of a certain outcome from the experiment. Maybe you can debate yourself over what the correct underlying sample size is, but it is plainly not the number of a certain outcome from the experiment.--[[User:Aschlafly|Aschlafly]] 19:28, 23 September 2008 (EDT)

Maybe the Journal of Nature can be your next letter submission source. ''International Weekly Journal of Science'' -- [[Image:50 star flag.png|14px]] [[User:Jpatt|jp]] 21:17, 22 September 2008 (EDT)

==Point 5 Rejected==

ASchlafly and others: if you don't agree with me, present a reasoned argument against my points. Don't delete other people's comments on a Talk page and for goodness sake, don't be so spineless as to block me to prevent me from replying to you. I repeat what I wrote last week before you deleted my contribution to this discussion and blocked me.

I ''do'' have specialist knowledge of this area, despite Bugler's assertions to the contrary (made without any evidence whatsoever, may I say). But I repeat, it really doesn't matter whether I have particular qualifications or not. In science, what matters is what is said, not who says it. The most outstanding scientific discoveries of the 20th century were made by a patent clerk who had no academic position at the time.

I now repeat again my cut-and-paste from Longstop's contribution a couple of weeks ago. If you don't agree with it, discuss it, don't delete it.
"The main point he [Kennymac] makes is quite correct, that combining experiments will tend to give a more significant result (i.e. a lower P-value) than any single experiment on its own.
"The point that ASchlafly makes (headed '''REPLY''', shortly after KennyMac's example) is slightly misleading. You don't choose which experiments to combine on the basis of their outcomes - you either combine all relevant experiments or none. In this case, Professor Lenski chose to combine all the experiments and present a single analysis of them. That's fine.
"The issue of whether to weight the Z-test according to sample size is not a straightforward issue. Before Whitlock's recent paper, the consensus was that the P-value already depends on sample size so it should not be weighted according to sample size. (Basically, a high degree of significance, i.e. a low P-value, can be achieved by having either a large difference between the treatments or a large experiment or, of course, both.) Whitlock's work, based on computer simulations, is an interesting contribution but cannot be regarded as the last word on the subject because any computer simulation involves assumptions about the structure of the particular experiment simulated. I cannot imagine any editor of a scientific journal rejecting a paper because it used an unweighted Z-test rather than the weighted version (or vice-versa).
"The conclusion, therefore, is that while there is a quantitative difference in the level of significance obtained by weighted and unweighted Z-tests, there is undeniably a significant biological effect. ASchlafly and other contributors should not be concerned that there is anything incorrect about the biological conclusions of Professor Lenski and his students or that there was anything at all underhand about their analysis or presentation of their data." [[User:DavyJones|DavyJones]] 20:39, 31 October 2008 (EDT)

==Referring of Scientific Papers==

Another point that Aschlafly and others deleted was my explanation of why CP readers shouldn't be concerned about the fact that the Lenski paper was reviewed within 14 days. This is perfectly normal practice for a leading journal. If you're invited to review a paper for a leading journal and they give you 7/10/14/etc days, you only agree to review it if you're sure you're going to have time before the journal's deadline. So there's absolutely no reason to suppose the review wasn't done properly.

Again, if you disagree, discuss, don't delete and don't block. [[User:DavyJones|DavyJones]] 20:39, 31 October 2008 (EDT)

== References ==

<references/>

== Have we given up? ==

Not much activity here in the past few weeks. Have we given up on pursuing this matter further?
Conservapedia should work on continuing to keep the Lenski study and its flaws in the news.
Is there anything else we can do? Perhaps write to local officials about the misuse of public funds for studies like Lenski's, and also to complain about PNAS? --[[User:DRamon|DRamon]] 16:39, 31 October 2008 (EDT)

: We exposed five fundamental flaws in the study, and told the truth. The truth doesn't care whether some refuse to accept it. There will ''always'' be people who deny the truth, particularly when they stand to profit from falsehoods. For now, I've moved onto more pressing issues on this site.--[[User:Aschlafly|Aschlafly]] 16:56, 31 October 2008 (EDT)

:: What do you mean by "profit from falsehoods"? Are you seriously suggesting that everyone who has a different point of view from your own must have mercenary motives for disagreeing with you? That's a very bizarre point of view. [[User:DavyJones|DavyJones]] 20:39, 31 October 2008 (EDT)

Talk:PNAS Response to Letter

2008-10-20T20:36:33Z

DavyJones: Point 5 + reviewing

Notice: misrepresentations are not going to be allowed on this page. Substantive comments only, please.

Note: earlier posts are archived [[Talk:PNAS_Response_to_Letter/Archive1|here]]. --[[User:BillA|BillA]] 17:05, 20 September 2008 (EDT)

== Point 5 Confirmed ==

I would like to contribute to this discussion because I have taught statistics to graduate biology students for 16 years.

The combination of data from several experiments is a specialist and sometimes difficult area of statistical theory but a simple example shows why Aschafly’s concern about combining the results of three different experiments is not justified and why this aspect of his criticism of Lenski’s recent paper in PNAS is not valid.

Suppose we want to conduct a test of whether or not men are taller than women on average. For the sake of the example, I generated random heights of people from a population in which men had an average height of 175cm (5’10’) and women of 165cm (5’6”). The standard deviations of height in both sexes were 7cm. I think these numbers are approximately correct for people in the UK but the details aren’t important.

Suppose we take 5 samples of 2 men and 2 women. Here are the numbers I generated:

{| class="wikitable"
|-
! Man1 !! Man2 !! Woman1 !! Woman2 !! Men mean !! Women mean !! Mean difference !! t !! P
|-
| 176 || 179 || 157 || 148 || 177.5 || 152.5 || 25 || 5.27 || 0.017
|-
| 180 || 176 || 160 || 164 || 178 || 162 || 16 || 5.66 || 0.015
|-
| 176 || 175 || 167 || 165 || 175.5 || 166 || 9.5 || 8.50 || 0.0068
|-
| 169 || 171 || 168 || 173 || 170 || 170.5 || -0.5 || -0.19 || 0.57
|-
| 179 || 175 || 166 || 178 || 177 || 172 || 5 || 0.79 || 0.26
|-
|}

P in the last column is the t-test probability for a one-side test of women being shorter than men. (Formally, it’s the probability of getting a value of t greater than that calculated from the data if women are in fact taller than men on average.)

Should the fact that, in the fourth sample, the average height of the women is taller than that of the men make us doubt that men are in fact taller on average? Should we be concerned about the last sample, in which the difference in height of the two sexes is rather small, though in the expected direction? No, in both cases. When we combine the data on all 10 men and all 10 women, we get this:

{| class="wikitable"
|-
! Men mean !! Women mean !! Mean difference !! t !! ''P''
|-
| 175.6 || 164.6 || 11 || 3.85 || 0.00058
|-
|}

Clearly, combining the data from several similar experiments strengthens the conclusions considerably, as shown by the fact that ''P'' is much smaller for the combined data than for any individual sample.

Although the combination of data from several experiments is a specialised area of statistics, I see nothing particularly incorrect about the approach used by Lenski and his colleagues. The general point is that it is valid to combine the results of different experiments if it is scientifically meaningful to do so. (For example: A. Combining the results of five samples of the heights of men and women is clearly valid. B. Combining three samples of heights of men and women with two samples of lengths of male and female squid clearly isn’t.) Generally speaking, the outcome of a combined analysis of several small experiments which all point in the same direction (or at least in a similar direction) will be more significant than that of any one of those experiments, as is shown in the larger table above.

I hope this clarifies the extensive discussion on this point and puts Aschafly’s mind at rest on this subject. [[User:KennyMac|KennyMac]] 08:20, 18 September 2008 (EDT)

:That's very nicely put, thanks. You should work on some of the stats pages here. Of course, technically any sample is ultimately just a combination of ''n'' samples of size 1. [[User:MikeR|MikeR]] 13:28, 18 September 2008 (EDT)

:I'll take a look at this Friday. It's not immediately obvious what the point is to your analysis above.--[[User:Aschlafly|Aschlafly]] 23:46, 18 September 2008 (EDT)
::"''The general point is that it is valid to combine the results of different experiments if it is scientifically meaningful to do so"''--[[User:KingOfNothing|KingOfNothing]] 00:57, 19 September 2008 (EDT)

:::This makes no sense as an argument. It may be true in this simple case that you can do one large or several small samples and get similar results - which is quite obvious and wouldn't need such a detailed rant. However, you provide no mathematical proof, just one example. [[User:Etc|Etc]] 01:08, 19 September 2008 (EDT)
:''"It's not immediately obvious what the point is to your analysis above"''. No surprise, Aschlafly, really. Maybe you should take your own advice: ''"I suggest you try harder with an open mind"''. --[[User:CrossC|CrossC]] 02:46, 19 September 2008 (EDT)

It is with great sadness that I note that the author of this - the only significant statistical explanation and discussion in this entire fiasco- has [http://www.conservapedia.com/index.php?title=Special%3ALog&type=block&user=DeanS&page=User%3AKennyMac just been blocked] for five years. Even his email is blocked, so he can't even appeal the action. I don't see such manouvers as having contributed to the much vaunted "open mind" of which various people here speak. [[User:BenHur|BenHur]] 10:27, 19 September 2008 (EDT)

'''REPLY''': I have now reviewed the above analysis, and it supports Point 5 rather than the PNAS paper. Point 5 stated, "The Third Experiment was erroneously combined with the other two experiments based on outcome rather than sample size, thereby yielding a false claim of overall statistical significance." The analysis above does nothing more than reinforce Point 5 by combining experiments based on sample size.

In Pavlovian manner, some Lenski types nod their head here in agreement at the above analysis, apparently unaware that it reinforces Point 5.

When combining results from samples that are vastly different in sample size, it is necessary to factor in the different sample sizes. Apparently the PNAS paper failed to do that, which helps explain why it refuses to provide a meaningful response to Point 5.--[[User:Aschlafly|Aschlafly]] 19:24, 19 September 2008 (EDT)

(rants below were deleted for being non-substantive in violation of this page's rules.)--[[User:Aschlafly|Aschlafly]] 19:24, 19 September 2008 (EDT)

:::I understand point 5 now, or at least I think I do. What we have as a "sample" is either:

::::1. Individual cultures (Schlafly)
::::2. Cultures that developed cit+. (Lenski)

:::Schlafly contends that the sample should be all the cultures and that Lenski has, improperly, filtered the sample by excluding the vast majority of it (i.e. all those cultures that did not become cit+). Am I right in thinking this is the argument? --[[User:Toffeeman|Toffeeman]] 19:57, 19 September 2008 (EDT)

:::: No, we're talking about how Lenski combined a large study (which did not really support Lenski's hypothesis) with small studies (which Lenski claims does support his hypothesis). The studies were not combined in a logical manner with proper weighting given to the much bigger size of the large study.--[[User:Aschlafly|Aschlafly]] 23:15, 19 September 2008 (EDT)
:::::Aschlafly, have you read the paper on z-transforms which explains the statistical technique used? You can download a .pdf copy of the paper for free [http://www3.interscience.wiley.com/journal/118663174/abstract here]. --[[User:BillA|BillA]] 06:30, 20 September 2008 (EDT)

:::::: You say "statistical technique used," but you should have said "statistical technique ''cited''." In fact, a close reading of the Z-transform paper provides more support for Point 5: combined studies must be weighted based on sample size:

::::::: "When there is variation in the sample size across studies, there can be a noticeable difference in the power of the two methods, with the weighted Z-approach being superior in all cases. As such, we should always prefer the weighted Z to the unweighted Z-approach when the independent studies test the same hypothesis."[http://www3.interscience.wiley.com/journal/118663174/abstract see p. 1371].

:::::: In other words, the cited paper actually ''supports'' Point 5.--[[User:Aschlafly|Aschlafly]] 09:34, 20 September 2008 (EDT)

(unindent)Lenski used the weighted method. See note 49 to the paper and the text around the combination. Of course there is the question of on what basis Lenski weighted the results. Lenski weighted the results on the basis of the Cit+ numbers and we may think it would have been better to weight on the basis of the number of replicates. I have below the calculations (not mine) of combined P-values based on 1) no weighting, 2) weighting on the basis of Cit+ and 3) weighting on the basis of replicates. The weighted Z-transformed = SUM(Weight x Z-score for each run)/SQRT(SUM(Weight^2 for each run))

{| class="wikitable"
|-
! Expt# !! p-value !! z-score !! #Cit+ muts !! #replicates
|-
| 1 || 0.0085 || 2.387 || 4 || 72
|-
| 2 || 0.0007 || 3.195 || 5 || 340
|-
| 3 || 0.0823 || 1.390 || 8 || 2800
|-
|}

Applying the formula described above..

{| class="wikitable"
|-
! Weighting !! Z transformed !! p
|-
| Equal || 4.025 || <0.001
|-
|By total Cit+|| 3.576 || <0.001
|-
|By total replicates|| 1.825 || 0.034
|-
|}

So weighting on the basis of the number of replicates considerably increases the P-value. It remains, however, well within the range of statistical significance (0<P<0.05). If we hold that Lenski should have weighted on the basis of replicates then he should have rejected the null hypothesis and reached exactly the same conclusions that he did. The entire paper would have been exactly the same except the sentence “the result is extremely significant (P<0.0001) whether or not….” Would read “the result is significant (P<0.04) whether or not”. Point 5 establishes one number and an “extremely”. Point 5, therefore, has no weight (excuse the pun).
--[[User:Toffeeman|Toffeeman]] 15:18, 20 September 2008 (EDT)

: Sorry, Toffeeman, a falsehood is still a falsehood. Based on your own posting, if Lenski had applied the Whitlock Z-transform paper in a logical manner, the results would not have been nearly as striking as Lenski claimed (his paper said the results were "extremely significant"). Moreover, I found Lenski's description of his application of the Whitlock paper to be particularly misleading. Lenski's use of "whether or not"<ref>"We also used the Z-transformation method (49) to combine the probabilities from our three experiments, and '''the result is extremely significant (P < 0.0001) whether or not''' the experiments are weighted by the number of independent Cit+ mutants observed in each one." (Lenski paper at 7902).</ref> obscures the basic error that he did not apply Whitlock's paper in the straightforward, correct manner. I think the wording in the Lenski paper deliberately obscures this falsehood from the reader.

: People have free will to embrace and defend falsehoods. I don't expect them to change quickly or admit they were wrong. But you'll find me defending and promoting the truth.

: Point 5 remains valid and the falsehood remains uncorrected by PNAS or Lenski. Four other points in higher priority remain uncorrected by them also.--[[User:Aschlafly|Aschlafly]] 16:47, 20 September 2008 (EDT)

::'''''"a falsehood is still a falsehood"'''''. Precisely, the null hypothesis should be considered false and the conclusions of the paper stand.

::Oh? Do you mean ''Lenski's falsehood''? And what falsehood is that? Lenski said that he had calculated the P-value without weighting and that had come out at <0.0001. That is true, not false. Lenski said he had calculated the P-value weighting on the basis of the Cit+ replicates and that had come out at <0.0001. That is true, not false. There is no falsehood. Lenski did not mention the results of weighting on the basis of replicate numbers. He thus made no claim about weighting on the basis of replicate numbers. If he made no claim he cannot have made a false claim.

::How do the words Lenski uses "mislead". If you read them as written what conclusion do you come to? You are lead to the conclusion that the mutation was not "rare-but-equal", instead it was contingent. That is the right conclusion. If Lenski had presented the data in a different manner (perhaps by including the results of weighting on the basis of replicate numbers) what conclusion do you come to? You are again lead to the conclusion that the mutation was not "rare-but-equal", instead it was contingent. That is the right conclusion. To mislead you must be lead to a conclusion that is incorrect. By Lenski's paper you are not lead to a conclusion that is incorrect. Thus is cannot be said to be "misleading".

::I shall not comment on your second paragraph, the temptation to ''"Tu Quoque"'' would be too great.

--[[User:Toffeeman|Toffeeman]] 17:13, 20 September 2008 (EDT)

::: The falsehood consists of pretending to apply the Whitlock Z-transform in a straightforward, logical and correct manner. I think the Lenski paper is intentionally misleading by using the "whether or not" wording, when both alternatives are nonsensical. Point 5 has been proven above to be correct in identify an error in the Lenski paper.

::: "Toffeeman", your blocking history suggests you have been less than straightforward yourself. Go elsewhere if you seek to be deceitful. You're not fooling anyone here.--[[User:Aschlafly|Aschlafly]] 17:54, 20 September 2008 (EDT)

::::Lenski did apply the Z-transformation correctly, both weighted and unweighted. The data points extracted from each replay are the ''generation numbers of those replicates that gave rise to Cit+ mutants''. Thus Replay 1 produced four data points: 30,500 31,500 32,500 32,500. Replay 2 produced five data points: 32,000 32,000 32,000 32,000 32,500. Replay 3 produced eight data points: 20,000 20,000 27,000 27,000 31,000 31,500 32,000 32,000. Thus the N for replay 1 is 4; replay 2 is 5 and replay 3 is 8. The fact that replay 3 used 38 times as many replicates as replay 1 does not mean that it should be weighted 38 times as much; it only produced twice as much data, not 38 times as much.

::::Suppose I want to find out what the average age of a murderer is in three cities. In L.A. I interview 72 random people and find that 4 of them were convicted of murder; I record the ages of the four. In Seattle I interview 340 people and find that 5 of them are convicted murderers; likewise in Singapore I interview 2800 and find 8 murderers. In the end, I have 4,5, and 8 data points from the three cities; the number of people I had to interview to obtain those data points doesn't factor into the analysis of what the average age of the murderers is.--[[User:Brossa|Brossa]] 00:06, 21 September 2008 (EDT)

::::: In your first paragraph you simply repeat the error underlying Lenski's paper. You, like the paper, incorrectly apply Whitlock's Z-transform.

::::: The quality and reliability of data is proportional to sample size, and when different studies are combined they need to be weighted accordingly. The results from a very large sample size would not be weighted equally with the results from a small sample size, as you and Lenski have done. That's basic logic, though I'm not optimistic that you or Lenski will admit it. Open-minded people who respect logic have no difficulty elevating logic over personal whim.-[[User:Aschlafly|Aschlafly]] 11:30, 21 September 2008 (EDT)

::::::Andy if you read Whitlock's paper you would see it say, and I quote, "Ideally each study is weighted proportional to the inverse of its error variance, that is, by the '''reciprocal of its squared standard error'''." It says nothing about weighting according to sample size, which is what you seem to be insisting should be done.
::::::Also Whitlock acknowledges in the paper that there is no preference for weighted versus equal weighting, so the fact that both equal weighting and weighting by the standard error give a statistically significant result shows that the 3 experiments combined support rejection of the null hypothesis. [[User:DanB|DanB]] 20:39, 21 September 2008 (EDT)

:::::::ASchlafly, you state that I incorrectly apply "Whitlock's Z-transform" (actually the test belongs to Mosteller & Bush<ref>Mosteller, F. & Bush, R.R. 1954. Selected quantitative techniques. In: ''Handbook of Social Psychology,'' Vol. 1 (G. Lindzey, ed.)</ref> and/or Liptak<ref>Liptak, T. 1958. On the combination of tests. ''Magyar Tud. Akad. Mat. Kutato Int. Kozl.'' '''3''': 171-197</ref>). Whitlock describes weighting by the reciprocal of the squared standard error. The standard error of the mean is proportional to 1/sqrt(N), so the reciprocal of the squared standard error is proportional to N. Thus larger studies ''are'' given more weight. I maintain that the sample sizes N of the three replays are 4, 5, and 8 respectively. Weighting based on those three N does not weight all three replays equally as you claim: it gives replay 2 25% more weight and replay 3 100% more weight than replay 1. Rather than simply repeating that I am wrong, will you please state what ''you'' think the sample sizes of the three replay experiments are, and, in your opinion, what the ''correct'' application of the Z-transformation would be?--[[User:Brossa|Brossa]] 18:00, 22 September 2008 (EDT)

:::::::: The Lenski paper states how it weighted the experiments, and that weighting is incorrect. Admit it. Moreover, the incorrect weighting in the Lenski paper was not likely an inadvertent error, as it inflated the significance of the results. I found the wording used by the Lenski paper to describe its (incorrect) weighting to be artfully misleading.

:::::::: Provide me with federal funding as Lenski received, and I'll write a paper for you. But I don't have to write an alternative paper to point out glaring errors in Lenski's paper.--[[User:Aschlafly|Aschlafly]] 08:35, 23 September 2008 (EDT)

::::::::: I've been following this discussion for a while and I have to agree with ASchlafly. It hardly seems fair that he should have to, in his spare time, replicate an experiment done by a professional just to "earn" the right to criticize it. I am unfamiliar with statistics, but if some complicated transform goes against common sense, common sense should prevail. After all, there are lies, damned lies, and statistics... [[User:AndyM|AndyM]] 10:57, 23 September 2008 (EDT)

(unindent)I'm not asking anyone to write a paper or replicate an experiment. I'm asking ASchlafly to support his statement "The results from a very large sample size would not be weighted equally with the results from a small sample size, '''as you and Lenski have done'''"(bolding mine). I have stated publicly, subject to challenge by others, that the sample sizes (n) of the three replays are four, five, and eight respectively. Furthermore, using n of 4, 5, and 8 in the weighted Z-method DOES NOT weight all the replay experiments equally - it weights replay 3 twice as much as replay 1 and 8/5 as much as replay 2. Tell you what: I'll drop all my questions about Monte Carlo and the Z-transform, and simply ask ASchlafly one question: '''what is the sample size, n, of the second replay experiment?''' He need not even do any calculations - a statement in words that will allow someone else to do the calculation will suffice. This is not a complicated question to answer; the paper states how many replicate cultures there were (340), how many cells there were in each replicate (3.9x10^8), how many replicates gave rise to Cit+ cells (5), and which generations those Cit+ replicates came from (4 from 32,000 and one from 32,500). I will even give ''my'' answer: '''five'''. Furthermore, I will say ''why'' I believe that, using the murderer/age analogy: performing the 340 replicates is the same as interviewing 340 people in order to find out if any of them are convicted murderers. Finding that five replicates gave rise to Cit+ mutants is the same as the survey finding that 5 of those 340 people were convicted murderers. Finding that the Cit+ mutants arose from 4 replicates from generation 32,000 and 1 from generation 32,500 is the same as finding the ages of the murderers. The five data points in the Lenski study allow one to calculate the 'mean generation of clones yielding Cit+': 32,100. This is the same as finding the mean age of the five murderers. If I want to compare this hypothetical murderer age study to some other study of the mean age of murderers, I would weight the studies based on how many murderers were in each study, not on how many non-murderers were included in the initial survey.

Surely ASchlafly can say ''what'' he thinks the n of the second replay is, even if he won't say ''why'' he thinks it. Is it five? 340? The number of replicates times the number of cells per replicate? Something else? No analysis need be performed on the resulting number.--[[User:Brossa|Brossa]] 15:54, 23 September 2008 (EDT)

:OK - would you care to put in writing that after ASchlafly gives you his response, you won't start obfuscating the issue with Monte Carlo and Z-transform issues? You understand: it is typical of liberals to, after being proven wrong, to start pretending that they were talking about an entirely different issue altogether. '''After ASchlafly states the sample size of the second replay experiment you will consider yourself answered.''' Correct?

:Brossa, your rant is misplaced. One cannot salvage an error in logic by questioning which of superior alternatives should be used instead. The sample size of an experiment is the number that comprises the underlying sample used in the experiment, not the number of a certain outcome from the experiment. Maybe you can debate yourself over what the correct underlying sample size is, but it is plainly not the number of a certain outcome from the experiment.--[[User:Aschlafly|Aschlafly]] 19:28, 23 September 2008 (EDT)

Maybe the Journal of Nature can be your next letter submission source. ''International Weekly Journal of Science'' -- [[Image:50 star flag.png|14px]] [[User:Jpatt|jp]] 21:17, 22 September 2008 (EDT)

==Point 5 Rejected==

1. Before I make my main point, would either Aschlafly or Bugler like to comment on why they've repeatedly reverted my contributions to this Talk Page. I thought we weren't supposed to delete other people's stuff on Talk pages unless it's for a very good reason (obscenity, racism, etc). In this case, what are they embarrassed about?

2. I ''do'' have specialist knowledge of this area, despite Bugler's assertions to the contrary (made without any evidence whatsoever, may I say). But I repeat, it really doesn't matter whether I have particular qualifications or not. In science, what matters is what is said, not who says it. The most outstanding scientific discoveries of the 20th century were made by a patent clerk who had no academic position at the time.

3. I repeat my cut-and-paste from Longstop's contribution last week. If Aschlafly or Bugler don't agree, kindly discuss it on this page, don't just delete it with no explanation.
"The main point he [Kennymac] makes is quite correct, that combining experiments will tend to give a more significant result (i.e. a lower P-value) than any single experiment on its own.
"The point that ASchlafly makes (headed '''REPLY''', shortly after KennyMac's example) is slightly misleading. You don't choose which experiments to combine on the basis of their outcomes - you either combine all relevant experiments or none. In this case, Professor Lenski chose to combine all the experiments and present a single analysis of them. That's fine.
"The issue of whether to weight the Z-test according to sample size is not a straightforward issue. Before Whitlock's recent paper, the consensus was that the P-value already depends on sample size so it should not be weighted according to sample size. (Basically, a high degree of significance, i.e. a low P-value, can be achieved by having either a large difference between the treatments or a large experiment or, of course, both.) Whitlock's work, based on computer simulations, is an interesting contribution but cannot be regarded as the last word on the subject because any computer simulation involves assumptions about the structure of the particular experiment simulated. I cannot imagine any editor of a scientific journal rejecting a paper because it used an unweighted Z-test rather than the weighted version (or vice-versa).
"The conclusion, therefore, is that while there is a quantitative difference in the level of significance obtained by weighted and unweighted Z-tests, there is undeniably a significant biological effect. ASchlafly and other contributors should not be concerned that there is anything incorrect about the biological conclusions of Professor Lenski and his students or that there was anything at all underhand about their analysis or presentation of their data." [[User:DavyJones|DavyJones]] 16:36, 20 October 2008 (EDT)

==Referring of Scientific Papers==

Another point that Aschlafly and Bugler reverted with no explanation was the explanation of why CP readers shouldn't be concerned about the fact that the Lenski paper was reviewed within 14 days. This is perfectly normal practice for a leading journal. If you're invited to review a paper for a leading journal and they give you 7/10/14/etc days, you only agree to review it if you're sure you're going to have time before the journal's deadline. So there's absolutely no reason to suppose the review wasn't done properly.

Again, if Aschlafly or Bugler disagrees, please explain why, on this page. Don't just delete what I've written with no explanation. [[User:DavyJones|DavyJones]] 16:36, 20 October 2008 (EDT)

== References ==

<references/>

Talk:PNAS Response to Letter

2008-10-18T03:19:43Z

DavyJones: Undo revision 538133 by Aschlafly (Talk) Please explain reasons for reversion

Notice: misrepresentations are not going to be allowed on this page. Substantive comments only, please.

Note: earlier posts are archived [[Talk:PNAS_Response_to_Letter/Archive1|here]]. --[[User:BillA|BillA]] 17:05, 20 September 2008 (EDT)

== Point 5 Not Confirmed ==

''See end of this article to understand 'Not' in the above.'' [[User:DavyJones|DavyJones]] 17:12, 17 October 2008 (EDT)

I would like to contribute to this discussion because I have taught statistics to graduate biology students for 16 years.

The combination of data from several experiments is a specialist and sometimes difficult area of statistical theory but a simple example shows why Aschafly’s concern about combining the results of three different experiments is not justified and why this aspect of his criticism of Lenski’s recent paper in PNAS is not valid.

Suppose we want to conduct a test of whether or not men are taller than women on average. For the sake of the example, I generated random heights of people from a population in which men had an average height of 175cm (5’10’) and women of 165cm (5’6”). The standard deviations of height in both sexes were 7cm. I think these numbers are approximately correct for people in the UK but the details aren’t important.

Suppose we take 5 samples of 2 men and 2 women. Here are the numbers I generated:

{| class="wikitable"
|-
! Man1 !! Man2 !! Woman1 !! Woman2 !! Men mean !! Women mean !! Mean difference !! t !! P
|-
| 176 || 179 || 157 || 148 || 177.5 || 152.5 || 25 || 5.27 || 0.017
|-
| 180 || 176 || 160 || 164 || 178 || 162 || 16 || 5.66 || 0.015
|-
| 176 || 175 || 167 || 165 || 175.5 || 166 || 9.5 || 8.50 || 0.0068
|-
| 169 || 171 || 168 || 173 || 170 || 170.5 || -0.5 || -0.19 || 0.57
|-
| 179 || 175 || 166 || 178 || 177 || 172 || 5 || 0.79 || 0.26
|-
|}

P in the last column is the t-test probability for a one-side test of women being shorter than men. (Formally, it’s the probability of getting a value of t greater than that calculated from the data if women are in fact taller than men on average.)

Should the fact that, in the fourth sample, the average height of the women is taller than that of the men make us doubt that men are in fact taller on average? Should we be concerned about the last sample, in which the difference in height of the two sexes is rather small, though in the expected direction? No, in both cases. When we combine the data on all 10 men and all 10 women, we get this:

{| class="wikitable"
|-
! Men mean !! Women mean !! Mean difference !! t !! ''P''
|-
| 175.6 || 164.6 || 11 || 3.85 || 0.00058
|-
|}

Clearly, combining the data from several similar experiments strengthens the conclusions considerably, as shown by the fact that ''P'' is much smaller for the combined data than for any individual sample.

Although the combination of data from several experiments is a specialised area of statistics, I see nothing particularly incorrect about the approach used by Lenski and his colleagues. The general point is that it is valid to combine the results of different experiments if it is scientifically meaningful to do so. (For example: A. Combining the results of five samples of the heights of men and women is clearly valid. B. Combining three samples of heights of men and women with two samples of lengths of male and female squid clearly isn’t.) Generally speaking, the outcome of a combined analysis of several small experiments which all point in the same direction (or at least in a similar direction) will be more significant than that of any one of those experiments, as is shown in the larger table above.

I hope this clarifies the extensive discussion on this point and puts Aschafly’s mind at rest on this subject. [[User:KennyMac|KennyMac]] 08:20, 18 September 2008 (EDT)

:That's very nicely put, thanks. You should work on some of the stats pages here. Of course, technically any sample is ultimately just a combination of ''n'' samples of size 1. [[User:MikeR|MikeR]] 13:28, 18 September 2008 (EDT)

:I'll take a look at this Friday. It's not immediately obvious what the point is to your analysis above.--[[User:Aschlafly|Aschlafly]] 23:46, 18 September 2008 (EDT)
::"''The general point is that it is valid to combine the results of different experiments if it is scientifically meaningful to do so"''--[[User:KingOfNothing|KingOfNothing]] 00:57, 19 September 2008 (EDT)

:::This makes no sense as an argument. It may be true in this simple case that you can do one large or several small samples and get similar results - which is quite obvious and wouldn't need such a detailed rant. However, you provide no mathematical proof, just one example. [[User:Etc|Etc]] 01:08, 19 September 2008 (EDT)
:''"It's not immediately obvious what the point is to your analysis above"''. No surprise, Aschlafly, really. Maybe you should take your own advice: ''"I suggest you try harder with an open mind"''. --[[User:CrossC|CrossC]] 02:46, 19 September 2008 (EDT)

It is with great sadness that I note that the author of this - the only significant statistical explanation and discussion in this entire fiasco- has [http://www.conservapedia.com/index.php?title=Special%3ALog&type=block&user=DeanS&page=User%3AKennyMac just been blocked] for five years. Even his email is blocked, so he can't even appeal the action. I don't see such manouvers as having contributed to the much vaunted "open mind" of which various people here speak. [[User:BenHur|BenHur]] 10:27, 19 September 2008 (EDT)

'''REPLY''': I have now reviewed the above analysis, and it supports Point 5 rather than the PNAS paper. Point 5 stated, "The Third Experiment was erroneously combined with the other two experiments based on outcome rather than sample size, thereby yielding a false claim of overall statistical significance." The analysis above does nothing more than reinforce Point 5 by combining experiments based on sample size.

In Pavlovian manner, some Lenski types nod their head here in agreement at the above analysis, apparently unaware that it reinforces Point 5.

When combining results from samples that are vastly different in sample size, it is necessary to factor in the different sample sizes. Apparently the PNAS paper failed to do that, which helps explain why it refuses to provide a meaningful response to Point 5.--[[User:Aschlafly|Aschlafly]] 19:24, 19 September 2008 (EDT)

(rants below were deleted for being non-substantive in violation of this page's rules.)--[[User:Aschlafly|Aschlafly]] 19:24, 19 September 2008 (EDT)

:::I understand point 5 now, or at least I think I do. What we have as a "sample" is either:

::::1. Individual cultures (Schlafly)
::::2. Cultures that developed cit+. (Lenski)

:::Schlafly contends that the sample should be all the cultures and that Lenski has, improperly, filtered the sample by excluding the vast majority of it (i.e. all those cultures that did not become cit+). Am I right in thinking this is the argument? --[[User:Toffeeman|Toffeeman]] 19:57, 19 September 2008 (EDT)

:::: No, we're talking about how Lenski combined a large study (which did not really support Lenski's hypothesis) with small studies (which Lenski claims does support his hypothesis). The studies were not combined in a logical manner with proper weighting given to the much bigger size of the large study.--[[User:Aschlafly|Aschlafly]] 23:15, 19 September 2008 (EDT)
:::::Aschlafly, have you read the paper on z-transforms which explains the statistical technique used? You can download a .pdf copy of the paper for free [http://www3.interscience.wiley.com/journal/118663174/abstract here]. --[[User:BillA|BillA]] 06:30, 20 September 2008 (EDT)

:::::: You say "statistical technique used," but you should have said "statistical technique ''cited''." In fact, a close reading of the Z-transform paper provides more support for Point 5: combined studies must be weighted based on sample size:

::::::: "When there is variation in the sample size across studies, there can be a noticeable difference in the power of the two methods, with the weighted Z-approach being superior in all cases. As such, we should always prefer the weighted Z to the unweighted Z-approach when the independent studies test the same hypothesis."[http://www3.interscience.wiley.com/journal/118663174/abstract see p. 1371].

:::::: In other words, the cited paper actually ''supports'' Point 5.--[[User:Aschlafly|Aschlafly]] 09:34, 20 September 2008 (EDT)

(unindent)Lenski used the weighted method. See note 49 to the paper and the text around the combination. Of course there is the question of on what basis Lenski weighted the results. Lenski weighted the results on the basis of the Cit+ numbers and we may think it would have been better to weight on the basis of the number of replicates. I have below the calculations (not mine) of combined P-values based on 1) no weighting, 2) weighting on the basis of Cit+ and 3) weighting on the basis of replicates. The weighted Z-transformed = SUM(Weight x Z-score for each run)/SQRT(SUM(Weight^2 for each run))

{| class="wikitable"
|-
! Expt# !! p-value !! z-score !! #Cit+ muts !! #replicates
|-
| 1 || 0.0085 || 2.387 || 4 || 72
|-
| 2 || 0.0007 || 3.195 || 5 || 340
|-
| 3 || 0.0823 || 1.390 || 8 || 2800
|-
|}

Applying the formula described above..

{| class="wikitable"
|-
! Weighting !! Z transformed !! p
|-
| Equal || 4.025 || <0.001
|-
|By total Cit+|| 3.576 || <0.001
|-
|By total replicates|| 1.825 || 0.034
|-
|}

So weighting on the basis of the number of replicates considerably increases the P-value. It remains, however, well within the range of statistical significance (0<P<0.05). If we hold that Lenski should have weighted on the basis of replicates then he should have rejected the null hypothesis and reached exactly the same conclusions that he did. The entire paper would have been exactly the same except the sentence “the result is extremely significant (P<0.0001) whether or not….” Would read “the result is significant (P<0.04) whether or not”. Point 5 establishes one number and an “extremely”. Point 5, therefore, has no weight (excuse the pun).
--[[User:Toffeeman|Toffeeman]] 15:18, 20 September 2008 (EDT)

: Sorry, Toffeeman, a falsehood is still a falsehood. Based on your own posting, if Lenski had applied the Whitlock Z-transform paper in a logical manner, the results would not have been nearly as striking as Lenski claimed (his paper said the results were "extremely significant"). Moreover, I found Lenski's description of his application of the Whitlock paper to be particularly misleading. Lenski's use of "whether or not"<ref>"We also used the Z-transformation method (49) to combine the probabilities from our three experiments, and '''the result is extremely significant (P < 0.0001) whether or not''' the experiments are weighted by the number of independent Cit+ mutants observed in each one." (Lenski paper at 7902).</ref> obscures the basic error that he did not apply Whitlock's paper in the straightforward, correct manner. I think the wording in the Lenski paper deliberately obscures this falsehood from the reader.

: People have free will to embrace and defend falsehoods. I don't expect them to change quickly or admit they were wrong. But you'll find me defending and promoting the truth.

: Point 5 remains valid and the falsehood remains uncorrected by PNAS or Lenski. Four other points in higher priority remain uncorrected by them also.--[[User:Aschlafly|Aschlafly]] 16:47, 20 September 2008 (EDT)

::'''''"a falsehood is still a falsehood"'''''. Precisely, the null hypothesis should be considered false and the conclusions of the paper stand.

::Oh? Do you mean ''Lenski's falsehood''? And what falsehood is that? Lenski said that he had calculated the P-value without weighting and that had come out at <0.0001. That is true, not false. Lenski said he had calculated the P-value weighting on the basis of the Cit+ replicates and that had come out at <0.0001. That is true, not false. There is no falsehood. Lenski did not mention the results of weighting on the basis of replicate numbers. He thus made no claim about weighting on the basis of replicate numbers. If he made no claim he cannot have made a false claim.

::How do the words Lenski uses "mislead". If you read them as written what conclusion do you come to? You are lead to the conclusion that the mutation was not "rare-but-equal", instead it was contingent. That is the right conclusion. If Lenski had presented the data in a different manner (perhaps by including the results of weighting on the basis of replicate numbers) what conclusion do you come to? You are again lead to the conclusion that the mutation was not "rare-but-equal", instead it was contingent. That is the right conclusion. To mislead you must be lead to a conclusion that is incorrect. By Lenski's paper you are not lead to a conclusion that is incorrect. Thus is cannot be said to be "misleading".

::I shall not comment on your second paragraph, the temptation to ''"Tu Quoque"'' would be too great.

--[[User:Toffeeman|Toffeeman]] 17:13, 20 September 2008 (EDT)

::: The falsehood consists of pretending to apply the Whitlock Z-transform in a straightforward, logical and correct manner. I think the Lenski paper is intentionally misleading by using the "whether or not" wording, when both alternatives are nonsensical. Point 5 has been proven above to be correct in identify an error in the Lenski paper.

::: "Toffeeman", your blocking history suggests you have been less than straightforward yourself. Go elsewhere if you seek to be deceitful. You're not fooling anyone here.--[[User:Aschlafly|Aschlafly]] 17:54, 20 September 2008 (EDT)

::::Lenski did apply the Z-transformation correctly, both weighted and unweighted. The data points extracted from each replay are the ''generation numbers of those replicates that gave rise to Cit+ mutants''. Thus Replay 1 produced four data points: 30,500 31,500 32,500 32,500. Replay 2 produced five data points: 32,000 32,000 32,000 32,000 32,500. Replay 3 produced eight data points: 20,000 20,000 27,000 27,000 31,000 31,500 32,000 32,000. Thus the N for replay 1 is 4; replay 2 is 5 and replay 3 is 8. The fact that replay 3 used 38 times as many replicates as replay 1 does not mean that it should be weighted 38 times as much; it only produced twice as much data, not 38 times as much.

::::Suppose I want to find out what the average age of a murderer is in three cities. In L.A. I interview 72 random people and find that 4 of them were convicted of murder; I record the ages of the four. In Seattle I interview 340 people and find that 5 of them are convicted murderers; likewise in Singapore I interview 2800 and find 8 murderers. In the end, I have 4,5, and 8 data points from the three cities; the number of people I had to interview to obtain those data points doesn't factor into the analysis of what the average age of the murderers is.--[[User:Brossa|Brossa]] 00:06, 21 September 2008 (EDT)

::::: In your first paragraph you simply repeat the error underlying Lenski's paper. You, like the paper, incorrectly apply Whitlock's Z-transform.

::::: The quality and reliability of data is proportional to sample size, and when different studies are combined they need to be weighted accordingly. The results from a very large sample size would not be weighted equally with the results from a small sample size, as you and Lenski have done. That's basic logic, though I'm not optimistic that you or Lenski will admit it. Open-minded people who respect logic have no difficulty elevating logic over personal whim.-[[User:Aschlafly|Aschlafly]] 11:30, 21 September 2008 (EDT)

::::::Andy if you read Whitlock's paper you would see it say, and I quote, "Ideally each study is weighted proportional to the inverse of its error variance, that is, by the '''reciprocal of its squared standard error'''." It says nothing about weighting according to sample size, which is what you seem to be insisting should be done.
::::::Also Whitlock acknowledges in the paper that there is no preference for weighted versus equal weighting, so the fact that both equal weighting and weighting by the standard error give a statistically significant result shows that the 3 experiments combined support rejection of the null hypothesis. [[User:DanB|DanB]] 20:39, 21 September 2008 (EDT)

:::::::ASchlafly, you state that I incorrectly apply "Whitlock's Z-transform" (actually the test belongs to Mosteller & Bush<ref>Mosteller, F. & Bush, R.R. 1954. Selected quantitative techniques. In: ''Handbook of Social Psychology,'' Vol. 1 (G. Lindzey, ed.)</ref> and/or Liptak<ref>Liptak, T. 1958. On the combination of tests. ''Magyar Tud. Akad. Mat. Kutato Int. Kozl.'' '''3''': 171-197</ref>). Whitlock describes weighting by the reciprocal of the squared standard error. The standard error of the mean is proportional to 1/sqrt(N), so the reciprocal of the squared standard error is proportional to N. Thus larger studies ''are'' given more weight. I maintain that the sample sizes N of the three replays are 4, 5, and 8 respectively. Weighting based on those three N does not weight all three replays equally as you claim: it gives replay 2 25% more weight and replay 3 100% more weight than replay 1. Rather than simply repeating that I am wrong, will you please state what ''you'' think the sample sizes of the three replay experiments are, and, in your opinion, what the ''correct'' application of the Z-transformation would be?--[[User:Brossa|Brossa]] 18:00, 22 September 2008 (EDT)

:::::::: The Lenski paper states how it weighted the experiments, and that weighting is incorrect. Admit it. Moreover, the incorrect weighting in the Lenski paper was not likely an inadvertent error, as it inflated the significance of the results. I found the wording used by the Lenski paper to describe its (incorrect) weighting to be artfully misleading.

:::::::: Provide me with federal funding as Lenski received, and I'll write a paper for you. But I don't have to write an alternative paper to point out glaring errors in Lenski's paper.--[[User:Aschlafly|Aschlafly]] 08:35, 23 September 2008 (EDT)

::::::::: I've been following this discussion for a while and I have to agree with ASchlafly. It hardly seems fair that he should have to, in his spare time, replicate an experiment done by a professional just to "earn" the right to criticize it. I am unfamiliar with statistics, but if some complicated transform goes against common sense, common sense should prevail. After all, there are lies, damned lies, and statistics... [[User:AndyM|AndyM]] 10:57, 23 September 2008 (EDT)

(unindent)I'm not asking anyone to write a paper or replicate an experiment. I'm asking ASchlafly to support his statement "The results from a very large sample size would not be weighted equally with the results from a small sample size, '''as you and Lenski have done'''"(bolding mine). I have stated publicly, subject to challenge by others, that the sample sizes (n) of the three replays are four, five, and eight respectively. Furthermore, using n of 4, 5, and 8 in the weighted Z-method DOES NOT weight all the replay experiments equally - it weights replay 3 twice as much as replay 1 and 8/5 as much as replay 2. Tell you what: I'll drop all my questions about Monte Carlo and the Z-transform, and simply ask ASchlafly one question: '''what is the sample size, n, of the second replay experiment?''' He need not even do any calculations - a statement in words that will allow someone else to do the calculation will suffice. This is not a complicated question to answer; the paper states how many replicate cultures there were (340), how many cells there were in each replicate (3.9x10^8), how many replicates gave rise to Cit+ cells (5), and which generations those Cit+ replicates came from (4 from 32,000 and one from 32,500). I will even give ''my'' answer: '''five'''. Furthermore, I will say ''why'' I believe that, using the murderer/age analogy: performing the 340 replicates is the same as interviewing 340 people in order to find out if any of them are convicted murderers. Finding that five replicates gave rise to Cit+ mutants is the same as the survey finding that 5 of those 340 people were convicted murderers. Finding that the Cit+ mutants arose from 4 replicates from generation 32,000 and 1 from generation 32,500 is the same as finding the ages of the murderers. The five data points in the Lenski study allow one to calculate the 'mean generation of clones yielding Cit+': 32,100. This is the same as finding the mean age of the five murderers. If I want to compare this hypothetical murderer age study to some other study of the mean age of murderers, I would weight the studies based on how many murderers were in each study, not on how many non-murderers were included in the initial survey.

Surely ASchlafly can say ''what'' he thinks the n of the second replay is, even if he won't say ''why'' he thinks it. Is it five? 340? The number of replicates times the number of cells per replicate? Something else? No analysis need be performed on the resulting number.--[[User:Brossa|Brossa]] 15:54, 23 September 2008 (EDT)

:OK - would you care to put in writing that after ASchlafly gives you his response, you won't start obfuscating the issue with Monte Carlo and Z-transform issues? You understand: it is typical of liberals to, after being proven wrong, to start pretending that they were talking about an entirely different issue altogether. '''After ASchlafly states the sample size of the second replay experiment you will consider yourself answered.''' Correct?

:Brossa, your rant is misplaced. One cannot salvage an error in logic by questioning which of superior alternatives should be used instead. The sample size of an experiment is the number that comprises the underlying sample used in the experiment, not the number of a certain outcome from the experiment. Maybe you can debate yourself over what the correct underlying sample size is, but it is plainly not the number of a certain outcome from the experiment.--[[User:Aschlafly|Aschlafly]] 19:28, 23 September 2008 (EDT)

Maybe the Journal of Nature can be your next letter submission source. ''International Weekly Journal of Science'' -- [[Image:50 star flag.png|14px]] [[User:Jpatt|jp]] 21:17, 22 September 2008 (EDT)

=== ''Not'' confirmed ===

Like Kennymac and Longstop, I have some qualifications in this area because I have taught statistics to researchers (not mathematicians) - actually for even longer than Kennymac. I've read the contribution from Longstop and I've decided that the best thing I can do is to replace it in its entirety because it makes the point quite well. (Actually both points - the statistical point and the one about reviewing scientific papers.) But my qualifications are really unimportant - as Longstop said, it doesn't matter who says something in science, it's '''what''' they say that matters. After all, the most important discoveries in science in the 20th century were made by a patent clerk who wasn't an academic at the time and hadn't even been a particularly outstanding student.

The rest of this posting is cut-and-pasted from Longstop's contribution earlier this week.

'''''Start of quote''''' The main point he [Kennymac] makes is quite correct, that combining experiments will tend to give a more significant result (i.e. a lower P-value) than any single experiment on its own.

The point that ASchlafly makes (headed '''REPLY''', shortly after KennyMac's example) is slightly misleading. You don't choose which experiments to combine on the basis of their outcomes - you either combine all relevant experiments or none. In this case, Professor Lenski chose to combine all the experiments and present a single analysis of them. That's fine.

The issue of whether to weight the Z-test according to sample size is not a straightforward issue. Before Whitlock's recent paper, the consensus was that the P-value already depends on sample size so it should not be weighted according to sample size. (Basically, a high degree of significance, i.e. a low P-value, can be achieved by having either a large difference between the treatments or a large experiment or, of course, both.) Whitlock's work, based on computer simulations, is an interesting contribution but cannot be regarded as the last word on the subject because any computer simulation involves assumptions about the structure of the particular experiment simulated. I cannot imagine any editor of a scientific journal rejecting a paper because it used an unweighted Z-test rather than the weighted version (or vice-versa).

The conclusion, therefore, is that while there is a quantitative difference in the level of significance obtained by weighted and unweighted Z-tests, there is undeniably a significant biological effect. ASchlafly and other contributors should not be concerned that there is anything incorrect about the biological conclusions of Professor Lenski and his students or that there was anything at all underhand about their analysis or presentation of their data.

On a different point, please would CP readers note that there's nothing at all suspicious about a paper being peer-reviewed in only 14 days. Editors of scientific journals ask reviewers beforehand if they are free to edit a paper within a certain period of time. If an academic agrees to review a paper for a prestigious journal such as PNAS within 2 weeks, they will generally ensure they have time during that period to read and comment on the paper thoroughly. '''''End of quote''''' [[User:DavyJones|DavyJones]] 17:55, 17 October 2008 (EDT)

== References ==

<references/>

Gordon Brown

2008-10-17T22:32:45Z

DavyJones: October 2008

{{Prime Minister
|image=Gordon Brown.jpg
|seq=74
|term_start=June 27 2007
|term_end=present
|previous=Tony Blair
|party=Labour Party
|birth_date=February 20 1951
|birth_place=Glasgow
|spouse=Sarah Brown
|religion=[[Church of Scotland]]
}}
'''Dr. James Gordon Brown''', generally known as '''Gordon Brown''', is the current [[Prime Minister]] of the [[United Kingdom]] and leader of the British [[Labour Party]]. He succeeded [[Tony Blair]] in these positions in June 2007.

A Scottish [[Labour Party|Labour]] politician, Brown served as Britain's [[Chancellor of the Exchequer]] for ten years. His mutual enmity with former Prime Minister Blair was a consistent feature of British political life for a number of years.

In Britain, Brown is seen as being a more sombre, sober and serious figure in contrast to Tony Blair, who is regarded as charismatic and has at times been perceived as lightweight and as an overly "slick" media performer (not unlike [[Bill Clinton]]). This resonates with a stereotype that many English people have of Scottish people being humorless and dour. Brown's father was a Minister in the [[Presbyterianism|Presbyterian]] [[Church of Scotland]], and it is thought that Brown's religious beliefs have influenced his serious, sober style. On the negative side, some believe that he is insufficiently likeable and sunny to appeal to voters. He has also been criticized for secretiveness, control-freakery and an awkward personal style. However, his communication skills, especially reading from autocues and being interviewed under bright lights in television students, may be adversely affected by the fact that his eyesight is extremely poor. He is blind in one eye and his vision in the other is weak, owing to a sporting injury sustained when he was a teenager.

Brown was one of the longest serving Chancellors in history, and took credit for the consistently healthy state of the British economy during his tenure - credit which many are reassessing in light of the current (as of October 2008) perilous condition of the British economy. He is a passionate advocate of reducing poverty in the [[Third World]]. He has made speeches in which he has praised the concept of "Britishness" and suggested that the British should display the British flag outside their houses, as many Americans do with the US flag. However, his patriotic convictions are expected to have consequences in foreign policy which are arguably negative: it is widely believed that he will be zealous in defending British interests (narrowly defined), but that he will neglect broader elements of Tony Blair's foreign policy such as support for the United States and the [[War on Terror]].

During Brown's tenure as Chancellor, the UK enjoyed sustained economic growth and generally positive reports from the [[International Monetary Fund]], although there were concerns at extreme inflationary pressures in the housing market. These concerns were more than borne out by the collapse in the housing market and credit crunch of 2007-2008.

Brown followed a generally redistributionary policy, increasing spending in the [[National Health Service]] and [[education]], and giving tax breaks to some poorer families whilst significantly increasing taxes on many others. His most significant achievement in the early days of the Labour Government was to grant fiscal independence to the Bank of England.

Just two days after the Brown ministry began, Islamic terrorists initiated several [[June 2007 UK terror attacks|attempted attacks]] against the UK, consisting of two car bombs in [[London]] on June 29 and a suicide-bomb attack at Glasgow International Airport on June 30.

By the Fall of 2008, Brown's premiership was increasingly seen as catastrophic by the country as a whole and his own party. Labour's opinion poll ratings dropped to historic lows, with widepread predictions of a Conservative landslide at the next General Election. The events of early October 2008, gained him new respect, though not necessarily popularity, as he exercised cool, firm international leadership in the midst of the banking crisis.

==See also==

* [[British politics]]
* [[Labour Party]]

==References==

http://www.imf.org/external/country/GBR/index.htm
{{DEFAULTSORT:Brown, Gordon}}

[[Category:United Kingdom Prime Ministers|Brown, Gordon]]
[[category:Scottish People|Brown, Gordon]]

Gordon Brown

2008-10-17T22:31:21Z

DavyJones: Eyesight

{{Prime Minister
|image=Gordon Brown.jpg
|seq=74
|term_start=June 27 2007
|term_end=present
|previous=Tony Blair
|party=Labour Party
|birth_date=February 20 1951
|birth_place=Glasgow
|spouse=Sarah Brown
|religion=[[Church of Scotland]]
}}
'''Dr. James Gordon Brown''', generally known as '''Gordon Brown''', is the current [[Prime Minister]] of the [[United Kingdom]] and leader of the British [[Labour Party]]. He succeeded [[Tony Blair]] in these positions in June 2007.

A Scottish [[Labour Party|Labour]] politician, Brown served as Britain's [[Chancellor of the Exchequer]] for ten years. His mutual enmity with former Prime Minister Blair was a consistent feature of British political life for a number of years.

In Britain, Brown is seen as being a more sombre, sober and serious figure in contrast to Tony Blair, who is regarded as charismatic and has at times been perceived as lightweight and as an overly "slick" media performer (not unlike [[Bill Clinton]]). This resonates with a stereotype that many English people have of Scottish people being humorless and dour. Brown's father was a Minister in the [[Presbyterianism|Presbyterian]] [[Church of Scotland]], and it is thought that Brown's religious beliefs have influenced his serious, sober style. On the negative side, some believe that he is insufficiently likeable and sunny to appeal to voters. He has also been criticized for secretiveness, control-freakery and an awkward personal style. However, his communication skills, especially reading from autocues and being interviewed under bright lights in television students, may be adversely affected by the fact that his eyesight is extremely poor. He is blind in one eye and his vision in the other is weak, owing to a sporting injury sustained when he was a teenager.

Brown was one of the longest serving Chancellors in history, and took credit for the consistently healthy state of the British economy during his tenure - credit which many are reassessing in light of the current (as of October 2008) perilous condition of the British economy. He is a passionate advocate of reducing poverty in the [[Third World]]. He has made speeches in which he has praised the concept of "Britishness" and suggested that the British should display the British flag outside their houses, as many Americans do with the US flag. However, his patriotic convictions are expected to have consequences in foreign policy which are arguably negative: it is widely believed that he will be zealous in defending British interests (narrowly defined), but that he will neglect broader elements of Tony Blair's foreign policy such as support for the United States and the [[War on Terror]].

During Brown's tenure as Chancellor, the UK enjoyed sustained economic growth and generally positive reports from the [[International Monetary Fund]], although there were concerns at extreme inflationary pressures in the housing market. These concerns were more than borne out by the collapse in the housing market and credit crunch of 2007-2008.

Brown followed a generally redistributionary policy, increasing spending in the [[National Health Service]] and [[education]], and giving tax breaks to some poorer families whilst significantly increasing taxes on many others. His most significant achievement in the early days of the Labour Government was to grant fiscal independence to the Bank of England.

Just two days after the Brown ministry began, Islamic terrorists initiated several [[June 2007 UK terror attacks|attempted attacks]] against the UK, consisting of two car bombs in [[London]] on June 29 and a suicide-bomb attack at Glasgow International Airport on June 30.

By the Fall of 2008, Brown's premiership was increasingly seen as catastrophic by the country as a whole and his own party. Labour's opinion poll ratings dropped to historic lows, with widepread predictions of a Conservative landslide at the next General Election.

==See also==

* [[British politics]]
* [[Labour Party]]

==References==

http://www.imf.org/external/country/GBR/index.htm
{{DEFAULTSORT:Brown, Gordon}}

[[Category:United Kingdom Prime Ministers|Brown, Gordon]]
[[category:Scottish People|Brown, Gordon]]

Scotland

2008-10-17T22:27:44Z

DavyJones: /* Religion */ Episcopalian

{{Country
|name =''Scotland''
|map =Scotland-map.jpg
|flag =Flag of Scotland.png
|arms =Lion rampant.png
|capital =Edinburgh
|capital-raw =
|government =Devolved parliamentary democracy
|government-raw =
|language =English, Gaelic
|king =
|queen =Elizabeth II
|monarch-raw =
|president =
|president-raw =
|chancellor =
|chancellor-raw =
|pm =Gordon Brown
|pm-raw =
|area =
|pop =
|pop-basis =
|gdp =
|gdp-year =
|gdp-pc =
|currency =
|idd =
|tld =
}}
'''Scotland''' is the second-largest and northern-most of the four countries in the [[United Kingdom]].
It is about three-eighths the size of its southern neighbour England, but is much less populous; most of the population lives in the ''central belt'', a band across central Scotland between the capital [[Edinburgh]] and the city of [[Glasgow]]. Other cities are [[Aberdeen]] and [[Dundee]]. [[Inverness]] and [[Stirling]] were granted city status recently but are in fact smaller than some of the larger Scottish towns like Paisley and Perth.

The symbol of Scotland is the [[thistle]]. The Scottish flag is the Cross of St. Andrew, a white diagonal cross on a dark blue background. The design originated in the 9th century and it is the oldest national flag still in use anywhere in the world.
Scotland's motto is ''Nemo Me Impune Lacessit'' ("No one provokes me with impunity")<ref>http://www.scotland-guide.co.uk/ALL_AREAS_IN_SCOTLAND/Glasgow/Areas/Centre/Mercat_Cross.htm </ref>

==Geography==
Scotland is split into three distinct geographical regions; the mountainous Highlands to the north, the rolling countryside of the Central Lowlands (where the major urban centres are located) and the hilly Southern Uplands that lie next to the English border. Scotland also includes the island groups of [[Orkney]], [[Shetland]], the [[Inner Hebrides|Inner]] and [[Outer Hebrides]], the islands of the [[Firth of Clyde]] including [[Arran]], [[Bute]], [[Cumbrae]] & [[Wee Cumbrae]], the [[St. Kilda]] archipelago, [[Rockall]] and various other smaller islands.

[[Ben Nevis]], the highest mountain in the [[United Kingdom]], is in the Scottish [[Highlands of Scotland|Highlands]], as are most of the nation's highest mountains. Those with heights above 3000 feet are eponymously named [[Munro| Munros]] after Sir Hector Munro, the first person to compile a list of such mountains.<ref> for a complete list of Munros see http://www.sol.co.uk/d/dickwall/munroes.htm</ref>

Scotland has some 2,300 miles of coastline, much of it in broad or narrow bays called ''firths''. Major rivers include the Tay, Tweed, Clyde, and Forth. Freshwater lakes (or ''lochs'') are abundant; Lochs Lomond, Morar, and Ness are the largest in the British Isles and well-known for their picturesque beauty, with Loch Ness having additional fame as the home of a legendary monster.

==People==

====Religion====
Scotland is historically Christian; the national church is the [[Church of Scotland]]. Scotland was traditionally a fiercely Protestant nation and was at the vanguard of the Reformation. Notable figures from that time include John Knox and George Wishart. However, from the mid 19th century until the interwar period, there were large scale immigrations of Irish Catholics to Scotland's industrial urban centres and this had a profound effect on the religious demography of Scotland. Today there are a similar number of communicants of both the Roman Catholic Church and the Presbyterian Church of Scotland although both religions have suffered considerable declines in church going attendances. The Episcopalian Church is predominant in the north-east. There are also significant populations of Muslims, Jews and Sikhs in Glasgow and Edinburgh.

====Culture and sports====

Scotland has given the English speaking world many of the languages finest writers, poets and philosophers. Among these are Adam Smith, David Hume, Sir Walter Scott, Robert Burns, Frances Hutcheson, James Hogg, Robert Louis Stevenson, Arthur Conan Doyle, J.M Barrie and Hugh Macdairmid. The Scottish intellectual and cultural tradition can be traced back to the Scottish Enlightenment, a remarkable period in the 18th century characterized by an outpouring of intellectual and scientific accomplishments. Indeed it was Voltaire who said "we look to Scotland for all our ideas of civilisation." Scotland is also famous for its disproportionate amount of inventors and scientists such as Alexander Graham Bell (telephone), Lord Kelvin (the Kelvin si unit of temperature), James Watt (condensed steam power), John Napier (logarithms and the decimal point), Joseph Lister (pioneer of antiseptics), Alexander Fleming (penicillin) James Clark Maxwell (electro-magnetism), Robert Watson Watt (radar) and John Logie Baird (television). It is home to ancient world class universities such as Edinburgh, Glasgow and St Andrews Universities and being one of the first industrialised and urbanised nations in the world.

The national preoccupation, indeed obsession, is [[football (soccer)]]. Other diversions include [[rugby]], [[lawn bowls]], [[motorsports]], [[horseracing]], [[shinty]] (similar to hockey), [[curling]], sports of the [[Highland Games]] - such as tossing the [[caber]] and, of course, [[golf]]. Scotland is the home of golf. The Royal and Ancient Golf Club at [[St Andrews]] is the governing body of world golf.

Other things associated with the country are [[kilt]]s ([[tartan]] skirtlike garments worn by Scotsmen), and the haunting music of the [[bagpipes]]. Famous Scottish products include [[pie]]s, [[haggis]] and Scotch [[whisky]].

==Government==
Scotland has its own [[Scottish Parliament]] comprising 129 members (MSPs) as well as sending 59 Members of Parliament (MPs) to represent its interests in the [[United Kingdom]] parliament which sits in [[London]]. Scottish MPs have historically been recognized for their political skills and appointed to the Cabinet in larger numbers than is proportionate. The current Prime Minister [[Gordon Brown]], is Scottish, and formerly he was [[Chancellor of the Exchequer]].

The '''Scottish Government''' (formerly known as the Scottish Executive) is the government in Scotland for devolved matters. Responsibility for all devolved matters was passed to the Scottish Executive from the
'''Scottish Office''' and other UK Government departments in 1999. The members of the Scottish Government are chosen from the party or parties holding most seats in the Parliament. The Scottish Government is led by the First Minister, who forms a ministerial team of Cabinet Secretaries. In the election on May 3 2007, the [[Scottish National Party]] won the largest number of seats, but not enough for an absolute majority. At the moment the party forms a minority government.

===Principal Government Officials===

===Relations with England===
Relationships between Scottish and English MPs before [[devolution]] were sometimes tense because of what the former [[Conservative|Conservative Party]] MP, by then an [[Ulster Unionist]], [[Enoch Powell]] dubbed ''The West Lothian question''. The name arose in 1977 after [[Tam Dalyell]], Labour MP for West Lothian in Scotland, asked during a debate in the [[Houses of Parliament]] over Scottish and Welsh [[devolution]]:

<blockquote>''For how long will English constituencies and English Honourable members tolerate... at least 119 Honourable Members from Scotland, Wales and Northern Ireland exercising an important, and probably often decisive, effect on British politics while they themselves have no say in the same matters in Scotland, Wales and Northern Ireland?''</blockquote>

He pointed out that he as MP for West Lothian could vote on matters affecting English constituencies but not his own constituency.

==Economy==
Scotland's position at the forefront of the industrial revolution in the 19th century bequeathed a legacy of heavy engineering and manufacturing that lasted well into the 20th century. However with de-industrialisation from the 1970s onwards and latterly the relocation of manufacturing jobs to countries with lower labour costs (eg. Eastern Europe) the Scottish economy is now heavily dependant on tourism, the oil industry, agriculture, the service industry and public sector jobs.

==History==
Scotland has been inhabited since the first [[Mesolithic]] hunter-gatherers are thought to have migrated to Scotland.<ref>At least 8500 years before recorded history dealt with Britain, according to the uniformitarian timescale. [http://www.scotlandhistory.net/ Scotland History], Wormland, Jenny. Scotland: a History. 2005, Oxford: Oxford University Press. p.1</ref>
These inhabitants showed advanced knowledge of astronomy, creating several [[Stonehenge]]-like monuments.

At the time of the [[Romans]] the tribes in what became Scotland were similar to those further south, and can be considered to be [[Celtic]] peoples. Those from the North-East were called ‘Picti’ (Picts) by Roman writers, which could mean ‘painted people' and refer to tattoos. The Romans never subdued these northern tribes, and after a brief period when the Antonine Wall between the Firths of Forth and Clyde was the Roman Empire’s northern frontier, they drew back and had [[Hadrian’s Wall]] as the frontier. They did try and influence the tribes between the two Walls, and when kingdoms like Strathclyde emerged in the early [[Dark Ages]], their rulers often bore Roman names or titles, the dynasties having been founded by Roman officials. The Scots themselves began arriving as settlers in the West of Scotland at this time (AD 400-500). They were from a part of the north of [[Ireland]] and spoke Old Irish, which changed to become Scottish [[Gaelic]], and eventually replaced Pictish. They sometimes warred with the Picts and [[Briton]]s and sometimes allied with them, but a unified kingdom under the Scottish king Kenneth Mac Alpin was established in AD 843, called ‘Alba’ (still the [[Gaelic]] name for Scotland). This kingdom took over Strathclyde in the early 11th century to form the basis of Mediaeval Scotland. [[Normans]] and their decscendents such as Robert the Bruce ('de Brus' was a Norman surname) became important nobles in Scotland.

====Union with England====
After the death of Queen [[Elizabeth I]] of England in 1603, James VI of Scotland ascended to the Throne of England, becoming [[James I]] of England. He was the first monarch to call himself King of Great Britain. This is referred to as the Union of the Crowns. James was also at this time King of [[Ireland]].

The Parliaments of Scotland and [[England]] were not united until 1707 and it is this date that is recognized as the formation of [[Great Britain]]. This is referred to as the Union of the Parliaments. (The [[United Kingdom]] was to come into being with the addition of [[Ireland]] in 1801.) The formation of the Irish Free State in 1922 resulted in the current name of the United Kingdom of Great Britain and Northern Ireland.

==External Links==
*[http://www.n-cyclopedia.com/scottish-history/index.htm A Brief History of Scotland]

==References==
<references/>

[[Category:Scotland]]
[[Category:United Kingdom]]
[[Category:Scottish Culture]]

User talk:DavyJones

2008-10-17T22:19:34Z

DavyJones: Reply to ASchlafly

==PNAS==
The talk page is for substantive contributions, not for Liberal obfuscation. I doubt that you have greater statistical expertise than Mr Schlafly; certainly not on this issue, to which he has devoted considerable expert attention. I see that my initial impulse to send you to the deeps was correct. Be very careful. [[User:Bugler|Bugler]] 17:19, 17 October 2008 (EDT)
:Mr Ugler, please direct your friendly fire at the issue, not the person. It doesn't matter if it's me who's wrong and Mr Schlafly who's right (or vice-versa), what matters is which statement is wrong and which is right. [[User:DavyJones|DavyJones]] 17:53, 17 October 2008 (EDT)

:: Change to your real name and stop claiming expertise and reverting settled matters, or your account will be blocked, "Davy".--[[User:Aschlafly|Aschlafly]] 18:13, 17 October 2008 (EDT)

:::Mr Schlafly, (i) my real name's Davy Jones (ii) I have expertise in the area in question (iii) I don't regard the matter as settled (and I thought you were opposed to "last-word-ism"). [[User:DavyJones|DavyJones]] 18:19, 17 October 2008 (EDT)

Talk:PNAS Response to Letter

2008-10-17T21:55:21Z

DavyJones: Undo revision 538025 by Bugler (Talk) Please address the issue, not the person - see my talk page.

Notice: misrepresentations are not going to be allowed on this page. Substantive comments only, please.

Note: earlier posts are archived [[Talk:PNAS_Response_to_Letter/Archive1|here]]. --[[User:BillA|BillA]] 17:05, 20 September 2008 (EDT)

== Point 5 Not Confirmed ==

''See end of this article to understand 'Not' in the above.'' [[User:DavyJones|DavyJones]] 17:12, 17 October 2008 (EDT)

I would like to contribute to this discussion because I have taught statistics to graduate biology students for 16 years.

The combination of data from several experiments is a specialist and sometimes difficult area of statistical theory but a simple example shows why Aschafly’s concern about combining the results of three different experiments is not justified and why this aspect of his criticism of Lenski’s recent paper in PNAS is not valid.

Suppose we want to conduct a test of whether or not men are taller than women on average. For the sake of the example, I generated random heights of people from a population in which men had an average height of 175cm (5’10’) and women of 165cm (5’6”). The standard deviations of height in both sexes were 7cm. I think these numbers are approximately correct for people in the UK but the details aren’t important.

Suppose we take 5 samples of 2 men and 2 women. Here are the numbers I generated:

{| class="wikitable"
|-
! Man1 !! Man2 !! Woman1 !! Woman2 !! Men mean !! Women mean !! Mean difference !! t !! P
|-
| 176 || 179 || 157 || 148 || 177.5 || 152.5 || 25 || 5.27 || 0.017
|-
| 180 || 176 || 160 || 164 || 178 || 162 || 16 || 5.66 || 0.015
|-
| 176 || 175 || 167 || 165 || 175.5 || 166 || 9.5 || 8.50 || 0.0068
|-
| 169 || 171 || 168 || 173 || 170 || 170.5 || -0.5 || -0.19 || 0.57
|-
| 179 || 175 || 166 || 178 || 177 || 172 || 5 || 0.79 || 0.26
|-
|}

P in the last column is the t-test probability for a one-side test of women being shorter than men. (Formally, it’s the probability of getting a value of t greater than that calculated from the data if women are in fact taller than men on average.)

Should the fact that, in the fourth sample, the average height of the women is taller than that of the men make us doubt that men are in fact taller on average? Should we be concerned about the last sample, in which the difference in height of the two sexes is rather small, though in the expected direction? No, in both cases. When we combine the data on all 10 men and all 10 women, we get this:

{| class="wikitable"
|-
! Men mean !! Women mean !! Mean difference !! t !! ''P''
|-
| 175.6 || 164.6 || 11 || 3.85 || 0.00058
|-
|}

Clearly, combining the data from several similar experiments strengthens the conclusions considerably, as shown by the fact that ''P'' is much smaller for the combined data than for any individual sample.

Although the combination of data from several experiments is a specialised area of statistics, I see nothing particularly incorrect about the approach used by Lenski and his colleagues. The general point is that it is valid to combine the results of different experiments if it is scientifically meaningful to do so. (For example: A. Combining the results of five samples of the heights of men and women is clearly valid. B. Combining three samples of heights of men and women with two samples of lengths of male and female squid clearly isn’t.) Generally speaking, the outcome of a combined analysis of several small experiments which all point in the same direction (or at least in a similar direction) will be more significant than that of any one of those experiments, as is shown in the larger table above.

I hope this clarifies the extensive discussion on this point and puts Aschafly’s mind at rest on this subject. [[User:KennyMac|KennyMac]] 08:20, 18 September 2008 (EDT)

:That's very nicely put, thanks. You should work on some of the stats pages here. Of course, technically any sample is ultimately just a combination of ''n'' samples of size 1. [[User:MikeR|MikeR]] 13:28, 18 September 2008 (EDT)

:I'll take a look at this Friday. It's not immediately obvious what the point is to your analysis above.--[[User:Aschlafly|Aschlafly]] 23:46, 18 September 2008 (EDT)
::"''The general point is that it is valid to combine the results of different experiments if it is scientifically meaningful to do so"''--[[User:KingOfNothing|KingOfNothing]] 00:57, 19 September 2008 (EDT)

:::This makes no sense as an argument. It may be true in this simple case that you can do one large or several small samples and get similar results - which is quite obvious and wouldn't need such a detailed rant. However, you provide no mathematical proof, just one example. [[User:Etc|Etc]] 01:08, 19 September 2008 (EDT)
:''"It's not immediately obvious what the point is to your analysis above"''. No surprise, Aschlafly, really. Maybe you should take your own advice: ''"I suggest you try harder with an open mind"''. --[[User:CrossC|CrossC]] 02:46, 19 September 2008 (EDT)

It is with great sadness that I note that the author of this - the only significant statistical explanation and discussion in this entire fiasco- has [http://www.conservapedia.com/index.php?title=Special%3ALog&type=block&user=DeanS&page=User%3AKennyMac just been blocked] for five years. Even his email is blocked, so he can't even appeal the action. I don't see such manouvers as having contributed to the much vaunted "open mind" of which various people here speak. [[User:BenHur|BenHur]] 10:27, 19 September 2008 (EDT)

'''REPLY''': I have now reviewed the above analysis, and it supports Point 5 rather than the PNAS paper. Point 5 stated, "The Third Experiment was erroneously combined with the other two experiments based on outcome rather than sample size, thereby yielding a false claim of overall statistical significance." The analysis above does nothing more than reinforce Point 5 by combining experiments based on sample size.

In Pavlovian manner, some Lenski types nod their head here in agreement at the above analysis, apparently unaware that it reinforces Point 5.

When combining results from samples that are vastly different in sample size, it is necessary to factor in the different sample sizes. Apparently the PNAS paper failed to do that, which helps explain why it refuses to provide a meaningful response to Point 5.--[[User:Aschlafly|Aschlafly]] 19:24, 19 September 2008 (EDT)

(rants below were deleted for being non-substantive in violation of this page's rules.)--[[User:Aschlafly|Aschlafly]] 19:24, 19 September 2008 (EDT)

:::I understand point 5 now, or at least I think I do. What we have as a "sample" is either:

::::1. Individual cultures (Schlafly)
::::2. Cultures that developed cit+. (Lenski)

:::Schlafly contends that the sample should be all the cultures and that Lenski has, improperly, filtered the sample by excluding the vast majority of it (i.e. all those cultures that did not become cit+). Am I right in thinking this is the argument? --[[User:Toffeeman|Toffeeman]] 19:57, 19 September 2008 (EDT)

:::: No, we're talking about how Lenski combined a large study (which did not really support Lenski's hypothesis) with small studies (which Lenski claims does support his hypothesis). The studies were not combined in a logical manner with proper weighting given to the much bigger size of the large study.--[[User:Aschlafly|Aschlafly]] 23:15, 19 September 2008 (EDT)
:::::Aschlafly, have you read the paper on z-transforms which explains the statistical technique used? You can download a .pdf copy of the paper for free [http://www3.interscience.wiley.com/journal/118663174/abstract here]. --[[User:BillA|BillA]] 06:30, 20 September 2008 (EDT)

:::::: You say "statistical technique used," but you should have said "statistical technique ''cited''." In fact, a close reading of the Z-transform paper provides more support for Point 5: combined studies must be weighted based on sample size:

::::::: "When there is variation in the sample size across studies, there can be a noticeable difference in the power of the two methods, with the weighted Z-approach being superior in all cases. As such, we should always prefer the weighted Z to the unweighted Z-approach when the independent studies test the same hypothesis."[http://www3.interscience.wiley.com/journal/118663174/abstract see p. 1371].

:::::: In other words, the cited paper actually ''supports'' Point 5.--[[User:Aschlafly|Aschlafly]] 09:34, 20 September 2008 (EDT)

(unindent)Lenski used the weighted method. See note 49 to the paper and the text around the combination. Of course there is the question of on what basis Lenski weighted the results. Lenski weighted the results on the basis of the Cit+ numbers and we may think it would have been better to weight on the basis of the number of replicates. I have below the calculations (not mine) of combined P-values based on 1) no weighting, 2) weighting on the basis of Cit+ and 3) weighting on the basis of replicates. The weighted Z-transformed = SUM(Weight x Z-score for each run)/SQRT(SUM(Weight^2 for each run))

{| class="wikitable"
|-
! Expt# !! p-value !! z-score !! #Cit+ muts !! #replicates
|-
| 1 || 0.0085 || 2.387 || 4 || 72
|-
| 2 || 0.0007 || 3.195 || 5 || 340
|-
| 3 || 0.0823 || 1.390 || 8 || 2800
|-
|}

Applying the formula described above..

{| class="wikitable"
|-
! Weighting !! Z transformed !! p
|-
| Equal || 4.025 || <0.001
|-
|By total Cit+|| 3.576 || <0.001
|-
|By total replicates|| 1.825 || 0.034
|-
|}

So weighting on the basis of the number of replicates considerably increases the P-value. It remains, however, well within the range of statistical significance (0<P<0.05). If we hold that Lenski should have weighted on the basis of replicates then he should have rejected the null hypothesis and reached exactly the same conclusions that he did. The entire paper would have been exactly the same except the sentence “the result is extremely significant (P<0.0001) whether or not….” Would read “the result is significant (P<0.04) whether or not”. Point 5 establishes one number and an “extremely”. Point 5, therefore, has no weight (excuse the pun).
--[[User:Toffeeman|Toffeeman]] 15:18, 20 September 2008 (EDT)

: Sorry, Toffeeman, a falsehood is still a falsehood. Based on your own posting, if Lenski had applied the Whitlock Z-transform paper in a logical manner, the results would not have been nearly as striking as Lenski claimed (his paper said the results were "extremely significant"). Moreover, I found Lenski's description of his application of the Whitlock paper to be particularly misleading. Lenski's use of "whether or not"<ref>"We also used the Z-transformation method (49) to combine the probabilities from our three experiments, and '''the result is extremely significant (P < 0.0001) whether or not''' the experiments are weighted by the number of independent Cit+ mutants observed in each one." (Lenski paper at 7902).</ref> obscures the basic error that he did not apply Whitlock's paper in the straightforward, correct manner. I think the wording in the Lenski paper deliberately obscures this falsehood from the reader.

: People have free will to embrace and defend falsehoods. I don't expect them to change quickly or admit they were wrong. But you'll find me defending and promoting the truth.

: Point 5 remains valid and the falsehood remains uncorrected by PNAS or Lenski. Four other points in higher priority remain uncorrected by them also.--[[User:Aschlafly|Aschlafly]] 16:47, 20 September 2008 (EDT)

::'''''"a falsehood is still a falsehood"'''''. Precisely, the null hypothesis should be considered false and the conclusions of the paper stand.

::Oh? Do you mean ''Lenski's falsehood''? And what falsehood is that? Lenski said that he had calculated the P-value without weighting and that had come out at <0.0001. That is true, not false. Lenski said he had calculated the P-value weighting on the basis of the Cit+ replicates and that had come out at <0.0001. That is true, not false. There is no falsehood. Lenski did not mention the results of weighting on the basis of replicate numbers. He thus made no claim about weighting on the basis of replicate numbers. If he made no claim he cannot have made a false claim.

::How do the words Lenski uses "mislead". If you read them as written what conclusion do you come to? You are lead to the conclusion that the mutation was not "rare-but-equal", instead it was contingent. That is the right conclusion. If Lenski had presented the data in a different manner (perhaps by including the results of weighting on the basis of replicate numbers) what conclusion do you come to? You are again lead to the conclusion that the mutation was not "rare-but-equal", instead it was contingent. That is the right conclusion. To mislead you must be lead to a conclusion that is incorrect. By Lenski's paper you are not lead to a conclusion that is incorrect. Thus is cannot be said to be "misleading".

::I shall not comment on your second paragraph, the temptation to ''"Tu Quoque"'' would be too great.

--[[User:Toffeeman|Toffeeman]] 17:13, 20 September 2008 (EDT)

::: The falsehood consists of pretending to apply the Whitlock Z-transform in a straightforward, logical and correct manner. I think the Lenski paper is intentionally misleading by using the "whether or not" wording, when both alternatives are nonsensical. Point 5 has been proven above to be correct in identify an error in the Lenski paper.

::: "Toffeeman", your blocking history suggests you have been less than straightforward yourself. Go elsewhere if you seek to be deceitful. You're not fooling anyone here.--[[User:Aschlafly|Aschlafly]] 17:54, 20 September 2008 (EDT)

::::Lenski did apply the Z-transformation correctly, both weighted and unweighted. The data points extracted from each replay are the ''generation numbers of those replicates that gave rise to Cit+ mutants''. Thus Replay 1 produced four data points: 30,500 31,500 32,500 32,500. Replay 2 produced five data points: 32,000 32,000 32,000 32,000 32,500. Replay 3 produced eight data points: 20,000 20,000 27,000 27,000 31,000 31,500 32,000 32,000. Thus the N for replay 1 is 4; replay 2 is 5 and replay 3 is 8. The fact that replay 3 used 38 times as many replicates as replay 1 does not mean that it should be weighted 38 times as much; it only produced twice as much data, not 38 times as much.

::::Suppose I want to find out what the average age of a murderer is in three cities. In L.A. I interview 72 random people and find that 4 of them were convicted of murder; I record the ages of the four. In Seattle I interview 340 people and find that 5 of them are convicted murderers; likewise in Singapore I interview 2800 and find 8 murderers. In the end, I have 4,5, and 8 data points from the three cities; the number of people I had to interview to obtain those data points doesn't factor into the analysis of what the average age of the murderers is.--[[User:Brossa|Brossa]] 00:06, 21 September 2008 (EDT)

::::: In your first paragraph you simply repeat the error underlying Lenski's paper. You, like the paper, incorrectly apply Whitlock's Z-transform.

::::: The quality and reliability of data is proportional to sample size, and when different studies are combined they need to be weighted accordingly. The results from a very large sample size would not be weighted equally with the results from a small sample size, as you and Lenski have done. That's basic logic, though I'm not optimistic that you or Lenski will admit it. Open-minded people who respect logic have no difficulty elevating logic over personal whim.-[[User:Aschlafly|Aschlafly]] 11:30, 21 September 2008 (EDT)

::::::Andy if you read Whitlock's paper you would see it say, and I quote, "Ideally each study is weighted proportional to the inverse of its error variance, that is, by the '''reciprocal of its squared standard error'''." It says nothing about weighting according to sample size, which is what you seem to be insisting should be done.
::::::Also Whitlock acknowledges in the paper that there is no preference for weighted versus equal weighting, so the fact that both equal weighting and weighting by the standard error give a statistically significant result shows that the 3 experiments combined support rejection of the null hypothesis. [[User:DanB|DanB]] 20:39, 21 September 2008 (EDT)

:::::::ASchlafly, you state that I incorrectly apply "Whitlock's Z-transform" (actually the test belongs to Mosteller & Bush<ref>Mosteller, F. & Bush, R.R. 1954. Selected quantitative techniques. In: ''Handbook of Social Psychology,'' Vol. 1 (G. Lindzey, ed.)</ref> and/or Liptak<ref>Liptak, T. 1958. On the combination of tests. ''Magyar Tud. Akad. Mat. Kutato Int. Kozl.'' '''3''': 171-197</ref>). Whitlock describes weighting by the reciprocal of the squared standard error. The standard error of the mean is proportional to 1/sqrt(N), so the reciprocal of the squared standard error is proportional to N. Thus larger studies ''are'' given more weight. I maintain that the sample sizes N of the three replays are 4, 5, and 8 respectively. Weighting based on those three N does not weight all three replays equally as you claim: it gives replay 2 25% more weight and replay 3 100% more weight than replay 1. Rather than simply repeating that I am wrong, will you please state what ''you'' think the sample sizes of the three replay experiments are, and, in your opinion, what the ''correct'' application of the Z-transformation would be?--[[User:Brossa|Brossa]] 18:00, 22 September 2008 (EDT)

:::::::: The Lenski paper states how it weighted the experiments, and that weighting is incorrect. Admit it. Moreover, the incorrect weighting in the Lenski paper was not likely an inadvertent error, as it inflated the significance of the results. I found the wording used by the Lenski paper to describe its (incorrect) weighting to be artfully misleading.

:::::::: Provide me with federal funding as Lenski received, and I'll write a paper for you. But I don't have to write an alternative paper to point out glaring errors in Lenski's paper.--[[User:Aschlafly|Aschlafly]] 08:35, 23 September 2008 (EDT)

::::::::: I've been following this discussion for a while and I have to agree with ASchlafly. It hardly seems fair that he should have to, in his spare time, replicate an experiment done by a professional just to "earn" the right to criticize it. I am unfamiliar with statistics, but if some complicated transform goes against common sense, common sense should prevail. After all, there are lies, damned lies, and statistics... [[User:AndyM|AndyM]] 10:57, 23 September 2008 (EDT)

(unindent)I'm not asking anyone to write a paper or replicate an experiment. I'm asking ASchlafly to support his statement "The results from a very large sample size would not be weighted equally with the results from a small sample size, '''as you and Lenski have done'''"(bolding mine). I have stated publicly, subject to challenge by others, that the sample sizes (n) of the three replays are four, five, and eight respectively. Furthermore, using n of 4, 5, and 8 in the weighted Z-method DOES NOT weight all the replay experiments equally - it weights replay 3 twice as much as replay 1 and 8/5 as much as replay 2. Tell you what: I'll drop all my questions about Monte Carlo and the Z-transform, and simply ask ASchlafly one question: '''what is the sample size, n, of the second replay experiment?''' He need not even do any calculations - a statement in words that will allow someone else to do the calculation will suffice. This is not a complicated question to answer; the paper states how many replicate cultures there were (340), how many cells there were in each replicate (3.9x10^8), how many replicates gave rise to Cit+ cells (5), and which generations those Cit+ replicates came from (4 from 32,000 and one from 32,500). I will even give ''my'' answer: '''five'''. Furthermore, I will say ''why'' I believe that, using the murderer/age analogy: performing the 340 replicates is the same as interviewing 340 people in order to find out if any of them are convicted murderers. Finding that five replicates gave rise to Cit+ mutants is the same as the survey finding that 5 of those 340 people were convicted murderers. Finding that the Cit+ mutants arose from 4 replicates from generation 32,000 and 1 from generation 32,500 is the same as finding the ages of the murderers. The five data points in the Lenski study allow one to calculate the 'mean generation of clones yielding Cit+': 32,100. This is the same as finding the mean age of the five murderers. If I want to compare this hypothetical murderer age study to some other study of the mean age of murderers, I would weight the studies based on how many murderers were in each study, not on how many non-murderers were included in the initial survey.

Surely ASchlafly can say ''what'' he thinks the n of the second replay is, even if he won't say ''why'' he thinks it. Is it five? 340? The number of replicates times the number of cells per replicate? Something else? No analysis need be performed on the resulting number.--[[User:Brossa|Brossa]] 15:54, 23 September 2008 (EDT)

:OK - would you care to put in writing that after ASchlafly gives you his response, you won't start obfuscating the issue with Monte Carlo and Z-transform issues? You understand: it is typical of liberals to, after being proven wrong, to start pretending that they were talking about an entirely different issue altogether. '''After ASchlafly states the sample size of the second replay experiment you will consider yourself answered.''' Correct?

:Brossa, your rant is misplaced. One cannot salvage an error in logic by questioning which of superior alternatives should be used instead. The sample size of an experiment is the number that comprises the underlying sample used in the experiment, not the number of a certain outcome from the experiment. Maybe you can debate yourself over what the correct underlying sample size is, but it is plainly not the number of a certain outcome from the experiment.--[[User:Aschlafly|Aschlafly]] 19:28, 23 September 2008 (EDT)

Maybe the Journal of Nature can be your next letter submission source. ''International Weekly Journal of Science'' -- [[Image:50 star flag.png|14px]] [[User:Jpatt|jp]] 21:17, 22 September 2008 (EDT)

=== ''Not'' confirmed ===

Like Kennymac and Longstop, I have some qualifications in this area because I have taught statistics to researchers (not mathematicians) - actually for even longer than Kennymac. I've read the contribution from Longstop and I've decided that the best thing I can do is to replace it in its entirety because it makes the point quite well. (Actually both points - the statistical point and the one about reviewing scientific papers.) But my qualifications are really unimportant - as Longstop said, it doesn't matter who says something in science, it's '''what''' they say that matters. After all, the most important discoveries in science in the 20th century were made by a patent clerk who wasn't an academic at the time and hadn't even been a particularly outstanding student.

The rest of this posting is cut-and-pasted from Longstop's contribution earlier this week.

'''''Start of quote''''' The main point he [Kennymac] makes is quite correct, that combining experiments will tend to give a more significant result (i.e. a lower P-value) than any single experiment on its own.

The point that ASchlafly makes (headed '''REPLY''', shortly after KennyMac's example) is slightly misleading. You don't choose which experiments to combine on the basis of their outcomes - you either combine all relevant experiments or none. In this case, Professor Lenski chose to combine all the experiments and present a single analysis of them. That's fine.

The issue of whether to weight the Z-test according to sample size is not a straightforward issue. Before Whitlock's recent paper, the consensus was that the P-value already depends on sample size so it should not be weighted according to sample size. (Basically, a high degree of significance, i.e. a low P-value, can be achieved by having either a large difference between the treatments or a large experiment or, of course, both.) Whitlock's work, based on computer simulations, is an interesting contribution but cannot be regarded as the last word on the subject because any computer simulation involves assumptions about the structure of the particular experiment simulated. I cannot imagine any editor of a scientific journal rejecting a paper because it used an unweighted Z-test rather than the weighted version (or vice-versa).

The conclusion, therefore, is that while there is a quantitative difference in the level of significance obtained by weighted and unweighted Z-tests, there is undeniably a significant biological effect. ASchlafly and other contributors should not be concerned that there is anything incorrect about the biological conclusions of Professor Lenski and his students or that there was anything at all underhand about their analysis or presentation of their data.

On a different point, please would CP readers note that there's nothing at all suspicious about a paper being peer-reviewed in only 14 days. Editors of scientific journals ask reviewers beforehand if they are free to edit a paper within a certain period of time. If an academic agrees to review a paper for a prestigious journal such as PNAS within 2 weeks, they will generally ensure they have time during that period to read and comment on the paper thoroughly. '''''End of quote''''' [[User:DavyJones|DavyJones]] 17:55, 17 October 2008 (EDT)

== References ==

<references/>

User talk:DavyJones

2008-10-17T21:53:20Z

DavyJones: Reply to Bugler

Talk:PNAS Response to Letter

2008-10-17T21:14:50Z

DavyJones:

Notice: misrepresentations are not going to be allowed on this page. Substantive comments only, please.

Note: earlier posts are archived [[Talk:PNAS_Response_to_Letter/Archive1|here]]. --[[User:BillA|BillA]] 17:05, 20 September 2008 (EDT)

== Point 5 Not Confirmed ==

''See end of this article to understand 'Not' in the above.'' [[User:DavyJones|DavyJones]] 17:12, 17 October 2008 (EDT)

I would like to contribute to this discussion because I have taught statistics to graduate biology students for 16 years.

The combination of data from several experiments is a specialist and sometimes difficult area of statistical theory but a simple example shows why Aschafly’s concern about combining the results of three different experiments is not justified and why this aspect of his criticism of Lenski’s recent paper in PNAS is not valid.

Suppose we want to conduct a test of whether or not men are taller than women on average. For the sake of the example, I generated random heights of people from a population in which men had an average height of 175cm (5’10’) and women of 165cm (5’6”). The standard deviations of height in both sexes were 7cm. I think these numbers are approximately correct for people in the UK but the details aren’t important.

Suppose we take 5 samples of 2 men and 2 women. Here are the numbers I generated:

{| class="wikitable"
|-
! Man1 !! Man2 !! Woman1 !! Woman2 !! Men mean !! Women mean !! Mean difference !! t !! P
|-
| 176 || 179 || 157 || 148 || 177.5 || 152.5 || 25 || 5.27 || 0.017
|-
| 180 || 176 || 160 || 164 || 178 || 162 || 16 || 5.66 || 0.015
|-
| 176 || 175 || 167 || 165 || 175.5 || 166 || 9.5 || 8.50 || 0.0068
|-
| 169 || 171 || 168 || 173 || 170 || 170.5 || -0.5 || -0.19 || 0.57
|-
| 179 || 175 || 166 || 178 || 177 || 172 || 5 || 0.79 || 0.26
|-
|}

P in the last column is the t-test probability for a one-side test of women being shorter than men. (Formally, it’s the probability of getting a value of t greater than that calculated from the data if women are in fact taller than men on average.)

Should the fact that, in the fourth sample, the average height of the women is taller than that of the men make us doubt that men are in fact taller on average? Should we be concerned about the last sample, in which the difference in height of the two sexes is rather small, though in the expected direction? No, in both cases. When we combine the data on all 10 men and all 10 women, we get this:

{| class="wikitable"
|-
! Men mean !! Women mean !! Mean difference !! t !! ''P''
|-
| 175.6 || 164.6 || 11 || 3.85 || 0.00058
|-
|}

Clearly, combining the data from several similar experiments strengthens the conclusions considerably, as shown by the fact that ''P'' is much smaller for the combined data than for any individual sample.

Although the combination of data from several experiments is a specialised area of statistics, I see nothing particularly incorrect about the approach used by Lenski and his colleagues. The general point is that it is valid to combine the results of different experiments if it is scientifically meaningful to do so. (For example: A. Combining the results of five samples of the heights of men and women is clearly valid. B. Combining three samples of heights of men and women with two samples of lengths of male and female squid clearly isn’t.) Generally speaking, the outcome of a combined analysis of several small experiments which all point in the same direction (or at least in a similar direction) will be more significant than that of any one of those experiments, as is shown in the larger table above.

I hope this clarifies the extensive discussion on this point and puts Aschafly’s mind at rest on this subject. [[User:KennyMac|KennyMac]] 08:20, 18 September 2008 (EDT)

:That's very nicely put, thanks. You should work on some of the stats pages here. Of course, technically any sample is ultimately just a combination of ''n'' samples of size 1. [[User:MikeR|MikeR]] 13:28, 18 September 2008 (EDT)

:I'll take a look at this Friday. It's not immediately obvious what the point is to your analysis above.--[[User:Aschlafly|Aschlafly]] 23:46, 18 September 2008 (EDT)
::"''The general point is that it is valid to combine the results of different experiments if it is scientifically meaningful to do so"''--[[User:KingOfNothing|KingOfNothing]] 00:57, 19 September 2008 (EDT)

:::This makes no sense as an argument. It may be true in this simple case that you can do one large or several small samples and get similar results - which is quite obvious and wouldn't need such a detailed rant. However, you provide no mathematical proof, just one example. [[User:Etc|Etc]] 01:08, 19 September 2008 (EDT)
:''"It's not immediately obvious what the point is to your analysis above"''. No surprise, Aschlafly, really. Maybe you should take your own advice: ''"I suggest you try harder with an open mind"''. --[[User:CrossC|CrossC]] 02:46, 19 September 2008 (EDT)

It is with great sadness that I note that the author of this - the only significant statistical explanation and discussion in this entire fiasco- has [http://www.conservapedia.com/index.php?title=Special%3ALog&type=block&user=DeanS&page=User%3AKennyMac just been blocked] for five years. Even his email is blocked, so he can't even appeal the action. I don't see such manouvers as having contributed to the much vaunted "open mind" of which various people here speak. [[User:BenHur|BenHur]] 10:27, 19 September 2008 (EDT)

'''REPLY''': I have now reviewed the above analysis, and it supports Point 5 rather than the PNAS paper. Point 5 stated, "The Third Experiment was erroneously combined with the other two experiments based on outcome rather than sample size, thereby yielding a false claim of overall statistical significance." The analysis above does nothing more than reinforce Point 5 by combining experiments based on sample size.

In Pavlovian manner, some Lenski types nod their head here in agreement at the above analysis, apparently unaware that it reinforces Point 5.

When combining results from samples that are vastly different in sample size, it is necessary to factor in the different sample sizes. Apparently the PNAS paper failed to do that, which helps explain why it refuses to provide a meaningful response to Point 5.--[[User:Aschlafly|Aschlafly]] 19:24, 19 September 2008 (EDT)

(rants below were deleted for being non-substantive in violation of this page's rules.)--[[User:Aschlafly|Aschlafly]] 19:24, 19 September 2008 (EDT)

:::I understand point 5 now, or at least I think I do. What we have as a "sample" is either:

::::1. Individual cultures (Schlafly)
::::2. Cultures that developed cit+. (Lenski)

:::Schlafly contends that the sample should be all the cultures and that Lenski has, improperly, filtered the sample by excluding the vast majority of it (i.e. all those cultures that did not become cit+). Am I right in thinking this is the argument? --[[User:Toffeeman|Toffeeman]] 19:57, 19 September 2008 (EDT)

:::: No, we're talking about how Lenski combined a large study (which did not really support Lenski's hypothesis) with small studies (which Lenski claims does support his hypothesis). The studies were not combined in a logical manner with proper weighting given to the much bigger size of the large study.--[[User:Aschlafly|Aschlafly]] 23:15, 19 September 2008 (EDT)
:::::Aschlafly, have you read the paper on z-transforms which explains the statistical technique used? You can download a .pdf copy of the paper for free [http://www3.interscience.wiley.com/journal/118663174/abstract here]. --[[User:BillA|BillA]] 06:30, 20 September 2008 (EDT)

:::::: You say "statistical technique used," but you should have said "statistical technique ''cited''." In fact, a close reading of the Z-transform paper provides more support for Point 5: combined studies must be weighted based on sample size:

::::::: "When there is variation in the sample size across studies, there can be a noticeable difference in the power of the two methods, with the weighted Z-approach being superior in all cases. As such, we should always prefer the weighted Z to the unweighted Z-approach when the independent studies test the same hypothesis."[http://www3.interscience.wiley.com/journal/118663174/abstract see p. 1371].

:::::: In other words, the cited paper actually ''supports'' Point 5.--[[User:Aschlafly|Aschlafly]] 09:34, 20 September 2008 (EDT)

(unindent)Lenski used the weighted method. See note 49 to the paper and the text around the combination. Of course there is the question of on what basis Lenski weighted the results. Lenski weighted the results on the basis of the Cit+ numbers and we may think it would have been better to weight on the basis of the number of replicates. I have below the calculations (not mine) of combined P-values based on 1) no weighting, 2) weighting on the basis of Cit+ and 3) weighting on the basis of replicates. The weighted Z-transformed = SUM(Weight x Z-score for each run)/SQRT(SUM(Weight^2 for each run))

{| class="wikitable"
|-
! Expt# !! p-value !! z-score !! #Cit+ muts !! #replicates
|-
| 1 || 0.0085 || 2.387 || 4 || 72
|-
| 2 || 0.0007 || 3.195 || 5 || 340
|-
| 3 || 0.0823 || 1.390 || 8 || 2800
|-
|}

Applying the formula described above..

{| class="wikitable"
|-
! Weighting !! Z transformed !! p
|-
| Equal || 4.025 || <0.001
|-
|By total Cit+|| 3.576 || <0.001
|-
|By total replicates|| 1.825 || 0.034
|-
|}

So weighting on the basis of the number of replicates considerably increases the P-value. It remains, however, well within the range of statistical significance (0<P<0.05). If we hold that Lenski should have weighted on the basis of replicates then he should have rejected the null hypothesis and reached exactly the same conclusions that he did. The entire paper would have been exactly the same except the sentence “the result is extremely significant (P<0.0001) whether or not….” Would read “the result is significant (P<0.04) whether or not”. Point 5 establishes one number and an “extremely”. Point 5, therefore, has no weight (excuse the pun).
--[[User:Toffeeman|Toffeeman]] 15:18, 20 September 2008 (EDT)

: Sorry, Toffeeman, a falsehood is still a falsehood. Based on your own posting, if Lenski had applied the Whitlock Z-transform paper in a logical manner, the results would not have been nearly as striking as Lenski claimed (his paper said the results were "extremely significant"). Moreover, I found Lenski's description of his application of the Whitlock paper to be particularly misleading. Lenski's use of "whether or not"<ref>"We also used the Z-transformation method (49) to combine the probabilities from our three experiments, and '''the result is extremely significant (P < 0.0001) whether or not''' the experiments are weighted by the number of independent Cit+ mutants observed in each one." (Lenski paper at 7902).</ref> obscures the basic error that he did not apply Whitlock's paper in the straightforward, correct manner. I think the wording in the Lenski paper deliberately obscures this falsehood from the reader.

: People have free will to embrace and defend falsehoods. I don't expect them to change quickly or admit they were wrong. But you'll find me defending and promoting the truth.

: Point 5 remains valid and the falsehood remains uncorrected by PNAS or Lenski. Four other points in higher priority remain uncorrected by them also.--[[User:Aschlafly|Aschlafly]] 16:47, 20 September 2008 (EDT)

::'''''"a falsehood is still a falsehood"'''''. Precisely, the null hypothesis should be considered false and the conclusions of the paper stand.

::Oh? Do you mean ''Lenski's falsehood''? And what falsehood is that? Lenski said that he had calculated the P-value without weighting and that had come out at <0.0001. That is true, not false. Lenski said he had calculated the P-value weighting on the basis of the Cit+ replicates and that had come out at <0.0001. That is true, not false. There is no falsehood. Lenski did not mention the results of weighting on the basis of replicate numbers. He thus made no claim about weighting on the basis of replicate numbers. If he made no claim he cannot have made a false claim.

::How do the words Lenski uses "mislead". If you read them as written what conclusion do you come to? You are lead to the conclusion that the mutation was not "rare-but-equal", instead it was contingent. That is the right conclusion. If Lenski had presented the data in a different manner (perhaps by including the results of weighting on the basis of replicate numbers) what conclusion do you come to? You are again lead to the conclusion that the mutation was not "rare-but-equal", instead it was contingent. That is the right conclusion. To mislead you must be lead to a conclusion that is incorrect. By Lenski's paper you are not lead to a conclusion that is incorrect. Thus is cannot be said to be "misleading".

::I shall not comment on your second paragraph, the temptation to ''"Tu Quoque"'' would be too great.

--[[User:Toffeeman|Toffeeman]] 17:13, 20 September 2008 (EDT)

::: The falsehood consists of pretending to apply the Whitlock Z-transform in a straightforward, logical and correct manner. I think the Lenski paper is intentionally misleading by using the "whether or not" wording, when both alternatives are nonsensical. Point 5 has been proven above to be correct in identify an error in the Lenski paper.

::: "Toffeeman", your blocking history suggests you have been less than straightforward yourself. Go elsewhere if you seek to be deceitful. You're not fooling anyone here.--[[User:Aschlafly|Aschlafly]] 17:54, 20 September 2008 (EDT)

::::Lenski did apply the Z-transformation correctly, both weighted and unweighted. The data points extracted from each replay are the ''generation numbers of those replicates that gave rise to Cit+ mutants''. Thus Replay 1 produced four data points: 30,500 31,500 32,500 32,500. Replay 2 produced five data points: 32,000 32,000 32,000 32,000 32,500. Replay 3 produced eight data points: 20,000 20,000 27,000 27,000 31,000 31,500 32,000 32,000. Thus the N for replay 1 is 4; replay 2 is 5 and replay 3 is 8. The fact that replay 3 used 38 times as many replicates as replay 1 does not mean that it should be weighted 38 times as much; it only produced twice as much data, not 38 times as much.

::::Suppose I want to find out what the average age of a murderer is in three cities. In L.A. I interview 72 random people and find that 4 of them were convicted of murder; I record the ages of the four. In Seattle I interview 340 people and find that 5 of them are convicted murderers; likewise in Singapore I interview 2800 and find 8 murderers. In the end, I have 4,5, and 8 data points from the three cities; the number of people I had to interview to obtain those data points doesn't factor into the analysis of what the average age of the murderers is.--[[User:Brossa|Brossa]] 00:06, 21 September 2008 (EDT)

::::: In your first paragraph you simply repeat the error underlying Lenski's paper. You, like the paper, incorrectly apply Whitlock's Z-transform.

::::: The quality and reliability of data is proportional to sample size, and when different studies are combined they need to be weighted accordingly. The results from a very large sample size would not be weighted equally with the results from a small sample size, as you and Lenski have done. That's basic logic, though I'm not optimistic that you or Lenski will admit it. Open-minded people who respect logic have no difficulty elevating logic over personal whim.-[[User:Aschlafly|Aschlafly]] 11:30, 21 September 2008 (EDT)

::::::Andy if you read Whitlock's paper you would see it say, and I quote, "Ideally each study is weighted proportional to the inverse of its error variance, that is, by the '''reciprocal of its squared standard error'''." It says nothing about weighting according to sample size, which is what you seem to be insisting should be done.
::::::Also Whitlock acknowledges in the paper that there is no preference for weighted versus equal weighting, so the fact that both equal weighting and weighting by the standard error give a statistically significant result shows that the 3 experiments combined support rejection of the null hypothesis. [[User:DanB|DanB]] 20:39, 21 September 2008 (EDT)

:::::::ASchlafly, you state that I incorrectly apply "Whitlock's Z-transform" (actually the test belongs to Mosteller & Bush<ref>Mosteller, F. & Bush, R.R. 1954. Selected quantitative techniques. In: ''Handbook of Social Psychology,'' Vol. 1 (G. Lindzey, ed.)</ref> and/or Liptak<ref>Liptak, T. 1958. On the combination of tests. ''Magyar Tud. Akad. Mat. Kutato Int. Kozl.'' '''3''': 171-197</ref>). Whitlock describes weighting by the reciprocal of the squared standard error. The standard error of the mean is proportional to 1/sqrt(N), so the reciprocal of the squared standard error is proportional to N. Thus larger studies ''are'' given more weight. I maintain that the sample sizes N of the three replays are 4, 5, and 8 respectively. Weighting based on those three N does not weight all three replays equally as you claim: it gives replay 2 25% more weight and replay 3 100% more weight than replay 1. Rather than simply repeating that I am wrong, will you please state what ''you'' think the sample sizes of the three replay experiments are, and, in your opinion, what the ''correct'' application of the Z-transformation would be?--[[User:Brossa|Brossa]] 18:00, 22 September 2008 (EDT)

:::::::: The Lenski paper states how it weighted the experiments, and that weighting is incorrect. Admit it. Moreover, the incorrect weighting in the Lenski paper was not likely an inadvertent error, as it inflated the significance of the results. I found the wording used by the Lenski paper to describe its (incorrect) weighting to be artfully misleading.

:::::::: Provide me with federal funding as Lenski received, and I'll write a paper for you. But I don't have to write an alternative paper to point out glaring errors in Lenski's paper.--[[User:Aschlafly|Aschlafly]] 08:35, 23 September 2008 (EDT)

::::::::: I've been following this discussion for a while and I have to agree with ASchlafly. It hardly seems fair that he should have to, in his spare time, replicate an experiment done by a professional just to "earn" the right to criticize it. I am unfamiliar with statistics, but if some complicated transform goes against common sense, common sense should prevail. After all, there are lies, damned lies, and statistics... [[User:AndyM|AndyM]] 10:57, 23 September 2008 (EDT)

(unindent)I'm not asking anyone to write a paper or replicate an experiment. I'm asking ASchlafly to support his statement "The results from a very large sample size would not be weighted equally with the results from a small sample size, '''as you and Lenski have done'''"(bolding mine). I have stated publicly, subject to challenge by others, that the sample sizes (n) of the three replays are four, five, and eight respectively. Furthermore, using n of 4, 5, and 8 in the weighted Z-method DOES NOT weight all the replay experiments equally - it weights replay 3 twice as much as replay 1 and 8/5 as much as replay 2. Tell you what: I'll drop all my questions about Monte Carlo and the Z-transform, and simply ask ASchlafly one question: '''what is the sample size, n, of the second replay experiment?''' He need not even do any calculations - a statement in words that will allow someone else to do the calculation will suffice. This is not a complicated question to answer; the paper states how many replicate cultures there were (340), how many cells there were in each replicate (3.9x10^8), how many replicates gave rise to Cit+ cells (5), and which generations those Cit+ replicates came from (4 from 32,000 and one from 32,500). I will even give ''my'' answer: '''five'''. Furthermore, I will say ''why'' I believe that, using the murderer/age analogy: performing the 340 replicates is the same as interviewing 340 people in order to find out if any of them are convicted murderers. Finding that five replicates gave rise to Cit+ mutants is the same as the survey finding that 5 of those 340 people were convicted murderers. Finding that the Cit+ mutants arose from 4 replicates from generation 32,000 and 1 from generation 32,500 is the same as finding the ages of the murderers. The five data points in the Lenski study allow one to calculate the 'mean generation of clones yielding Cit+': 32,100. This is the same as finding the mean age of the five murderers. If I want to compare this hypothetical murderer age study to some other study of the mean age of murderers, I would weight the studies based on how many murderers were in each study, not on how many non-murderers were included in the initial survey.

Surely ASchlafly can say ''what'' he thinks the n of the second replay is, even if he won't say ''why'' he thinks it. Is it five? 340? The number of replicates times the number of cells per replicate? Something else? No analysis need be performed on the resulting number.--[[User:Brossa|Brossa]] 15:54, 23 September 2008 (EDT)

:OK - would you care to put in writing that after ASchlafly gives you his response, you won't start obfuscating the issue with Monte Carlo and Z-transform issues? You understand: it is typical of liberals to, after being proven wrong, to start pretending that they were talking about an entirely different issue altogether. '''After ASchlafly states the sample size of the second replay experiment you will consider yourself answered.''' Correct?

:Brossa, your rant is misplaced. One cannot salvage an error in logic by questioning which of superior alternatives should be used instead. The sample size of an experiment is the number that comprises the underlying sample used in the experiment, not the number of a certain outcome from the experiment. Maybe you can debate yourself over what the correct underlying sample size is, but it is plainly not the number of a certain outcome from the experiment.--[[User:Aschlafly|Aschlafly]] 19:28, 23 September 2008 (EDT)

Maybe the Journal of Nature can be your next letter submission source. ''International Weekly Journal of Science'' -- [[Image:50 star flag.png|14px]] [[User:Jpatt|jp]] 21:17, 22 September 2008 (EDT)

=== ''Not'' confirmed ===

Like Kennymac and Longstop, I have some qualifications in this area because I have taught statistics to researchers (not mathematicians) - actually for even longer than Kennymac. I've read the contribution from Longstop and I've decided that the best thing I can do is to replace it in its entirety because it makes the point quite well. (Actually both points - the statistical point and the one about reviewing scientific papers.) But my qualifications are really unimportant - as Longstop said, it doesn't matter who says something in science, it's '''what''' they say that matters. After all, the most important discoveries in science in the 20th century were made by a patent clerk who wasn't an academic at the time and hadn't even been a particularly outstanding student.

The rest of this posting is cut-and-pasted from Longstop's contribution earlier this week.

''Quote starts here.'' The main point he [Kennymac] makes is quite correct, that combining experiments will tend to give a more significant result (i.e. a lower P-value) than any single experiment on its own.

The point that ASchlafly makes (headed '''REPLY''', shortly after KennyMac's example) is slightly misleading. You don't choose which experiments to combine on the basis of their outcomes - you either combine all relevant experiments or none. In this case, Professor Lenski chose to combine all the experiments and present a single analysis of them. That's fine.

The issue of whether to weight the Z-test according to sample size is not a straightforward issue. Before Whitlock's recent paper, the consensus was that the P-value already depends on sample size so it should not be weighted according to sample size. (Basically, a high degree of significance, i.e. a low P-value, can be achieved by having either a large difference between the treatments or a large experiment or, of course, both.) Whitlock's work, based on computer simulations, is an interesting contribution but cannot be regarded as the last word on the subject because any computer simulation involves assumptions about the structure of the particular experiment simulated. I cannot imagine any editor of a scientific journal rejecting a paper because it used an unweighted Z-test rather than the weighted version (or vice-versa).

The conclusion, therefore, is that while there is a quantitative difference in the level of significance obtained by weighted and unweighted Z-tests, there is undeniably a significant biological effect. ASchlafly and other contributors should not be concerned that there is anything incorrect about the biological conclusions of Professor Lenski and his students or that there was anything at all underhand about their analysis or presentation of their data.

On a different point, please would CP readers note that there's nothing at all suspicious about a paper being peer-reviewed in only 14 days. Editors of scientific journals ask reviewers beforehand if they are free to edit a paper within a certain period of time. If an academic agrees to review a paper for a prestigious journal such as PNAS within 2 weeks, they will generally ensure they have time during that period to read and comment on the paper thoroughly. ''Quote ends here'' [[User:DavyJones|DavyJones]] 17:12, 17 October 2008 (EDT)

== References ==

<references/>

Talk:PNAS Response to Letter

2008-10-17T21:12:03Z

DavyJones: Point 5 not confirmed

Notice: misrepresentations are not going to be allowed on this page. Substantive comments only, please.

Note: earlier posts are archived [[Talk:PNAS_Response_to_Letter/Archive1|here]]. --[[User:BillA|BillA]] 17:05, 20 September 2008 (EDT)

== Point 5 Not Confirmed ==

''See end of this article to understand 'Not' in the above.'' [[User:DavyJones|DavyJones]] 17:12, 17 October 2008 (EDT)

I would like to contribute to this discussion because I have taught statistics to graduate biology students for 16 years.

The combination of data from several experiments is a specialist and sometimes difficult area of statistical theory but a simple example shows why Aschafly’s concern about combining the results of three different experiments is not justified and why this aspect of his criticism of Lenski’s recent paper in PNAS is not valid.

Suppose we want to conduct a test of whether or not men are taller than women on average. For the sake of the example, I generated random heights of people from a population in which men had an average height of 175cm (5’10’) and women of 165cm (5’6”). The standard deviations of height in both sexes were 7cm. I think these numbers are approximately correct for people in the UK but the details aren’t important.

Suppose we take 5 samples of 2 men and 2 women. Here are the numbers I generated:

{| class="wikitable"
|-
! Man1 !! Man2 !! Woman1 !! Woman2 !! Men mean !! Women mean !! Mean difference !! t !! P
|-
| 176 || 179 || 157 || 148 || 177.5 || 152.5 || 25 || 5.27 || 0.017
|-
| 180 || 176 || 160 || 164 || 178 || 162 || 16 || 5.66 || 0.015
|-
| 176 || 175 || 167 || 165 || 175.5 || 166 || 9.5 || 8.50 || 0.0068
|-
| 169 || 171 || 168 || 173 || 170 || 170.5 || -0.5 || -0.19 || 0.57
|-
| 179 || 175 || 166 || 178 || 177 || 172 || 5 || 0.79 || 0.26
|-
|}

P in the last column is the t-test probability for a one-side test of women being shorter than men. (Formally, it’s the probability of getting a value of t greater than that calculated from the data if women are in fact taller than men on average.)

Should the fact that, in the fourth sample, the average height of the women is taller than that of the men make us doubt that men are in fact taller on average? Should we be concerned about the last sample, in which the difference in height of the two sexes is rather small, though in the expected direction? No, in both cases. When we combine the data on all 10 men and all 10 women, we get this:

{| class="wikitable"
|-
! Men mean !! Women mean !! Mean difference !! t !! ''P''
|-
| 175.6 || 164.6 || 11 || 3.85 || 0.00058
|-
|}

Clearly, combining the data from several similar experiments strengthens the conclusions considerably, as shown by the fact that ''P'' is much smaller for the combined data than for any individual sample.

Although the combination of data from several experiments is a specialised area of statistics, I see nothing particularly incorrect about the approach used by Lenski and his colleagues. The general point is that it is valid to combine the results of different experiments if it is scientifically meaningful to do so. (For example: A. Combining the results of five samples of the heights of men and women is clearly valid. B. Combining three samples of heights of men and women with two samples of lengths of male and female squid clearly isn’t.) Generally speaking, the outcome of a combined analysis of several small experiments which all point in the same direction (or at least in a similar direction) will be more significant than that of any one of those experiments, as is shown in the larger table above.

I hope this clarifies the extensive discussion on this point and puts Aschafly’s mind at rest on this subject. [[User:KennyMac|KennyMac]] 08:20, 18 September 2008 (EDT)

:That's very nicely put, thanks. You should work on some of the stats pages here. Of course, technically any sample is ultimately just a combination of ''n'' samples of size 1. [[User:MikeR|MikeR]] 13:28, 18 September 2008 (EDT)

:I'll take a look at this Friday. It's not immediately obvious what the point is to your analysis above.--[[User:Aschlafly|Aschlafly]] 23:46, 18 September 2008 (EDT)
::"''The general point is that it is valid to combine the results of different experiments if it is scientifically meaningful to do so"''--[[User:KingOfNothing|KingOfNothing]] 00:57, 19 September 2008 (EDT)

:::This makes no sense as an argument. It may be true in this simple case that you can do one large or several small samples and get similar results - which is quite obvious and wouldn't need such a detailed rant. However, you provide no mathematical proof, just one example. [[User:Etc|Etc]] 01:08, 19 September 2008 (EDT)
:''"It's not immediately obvious what the point is to your analysis above"''. No surprise, Aschlafly, really. Maybe you should take your own advice: ''"I suggest you try harder with an open mind"''. --[[User:CrossC|CrossC]] 02:46, 19 September 2008 (EDT)

It is with great sadness that I note that the author of this - the only significant statistical explanation and discussion in this entire fiasco- has [http://www.conservapedia.com/index.php?title=Special%3ALog&type=block&user=DeanS&page=User%3AKennyMac just been blocked] for five years. Even his email is blocked, so he can't even appeal the action. I don't see such manouvers as having contributed to the much vaunted "open mind" of which various people here speak. [[User:BenHur|BenHur]] 10:27, 19 September 2008 (EDT)

'''REPLY''': I have now reviewed the above analysis, and it supports Point 5 rather than the PNAS paper. Point 5 stated, "The Third Experiment was erroneously combined with the other two experiments based on outcome rather than sample size, thereby yielding a false claim of overall statistical significance." The analysis above does nothing more than reinforce Point 5 by combining experiments based on sample size.

In Pavlovian manner, some Lenski types nod their head here in agreement at the above analysis, apparently unaware that it reinforces Point 5.

When combining results from samples that are vastly different in sample size, it is necessary to factor in the different sample sizes. Apparently the PNAS paper failed to do that, which helps explain why it refuses to provide a meaningful response to Point 5.--[[User:Aschlafly|Aschlafly]] 19:24, 19 September 2008 (EDT)

(rants below were deleted for being non-substantive in violation of this page's rules.)--[[User:Aschlafly|Aschlafly]] 19:24, 19 September 2008 (EDT)

:::I understand point 5 now, or at least I think I do. What we have as a "sample" is either:

::::1. Individual cultures (Schlafly)
::::2. Cultures that developed cit+. (Lenski)

:::Schlafly contends that the sample should be all the cultures and that Lenski has, improperly, filtered the sample by excluding the vast majority of it (i.e. all those cultures that did not become cit+). Am I right in thinking this is the argument? --[[User:Toffeeman|Toffeeman]] 19:57, 19 September 2008 (EDT)

:::: No, we're talking about how Lenski combined a large study (which did not really support Lenski's hypothesis) with small studies (which Lenski claims does support his hypothesis). The studies were not combined in a logical manner with proper weighting given to the much bigger size of the large study.--[[User:Aschlafly|Aschlafly]] 23:15, 19 September 2008 (EDT)
:::::Aschlafly, have you read the paper on z-transforms which explains the statistical technique used? You can download a .pdf copy of the paper for free [http://www3.interscience.wiley.com/journal/118663174/abstract here]. --[[User:BillA|BillA]] 06:30, 20 September 2008 (EDT)

:::::: You say "statistical technique used," but you should have said "statistical technique ''cited''." In fact, a close reading of the Z-transform paper provides more support for Point 5: combined studies must be weighted based on sample size:

::::::: "When there is variation in the sample size across studies, there can be a noticeable difference in the power of the two methods, with the weighted Z-approach being superior in all cases. As such, we should always prefer the weighted Z to the unweighted Z-approach when the independent studies test the same hypothesis."[http://www3.interscience.wiley.com/journal/118663174/abstract see p. 1371].

:::::: In other words, the cited paper actually ''supports'' Point 5.--[[User:Aschlafly|Aschlafly]] 09:34, 20 September 2008 (EDT)

(unindent)Lenski used the weighted method. See note 49 to the paper and the text around the combination. Of course there is the question of on what basis Lenski weighted the results. Lenski weighted the results on the basis of the Cit+ numbers and we may think it would have been better to weight on the basis of the number of replicates. I have below the calculations (not mine) of combined P-values based on 1) no weighting, 2) weighting on the basis of Cit+ and 3) weighting on the basis of replicates. The weighted Z-transformed = SUM(Weight x Z-score for each run)/SQRT(SUM(Weight^2 for each run))

{| class="wikitable"
|-
! Expt# !! p-value !! z-score !! #Cit+ muts !! #replicates
|-
| 1 || 0.0085 || 2.387 || 4 || 72
|-
| 2 || 0.0007 || 3.195 || 5 || 340
|-
| 3 || 0.0823 || 1.390 || 8 || 2800
|-
|}

Applying the formula described above..

{| class="wikitable"
|-
! Weighting !! Z transformed !! p
|-
| Equal || 4.025 || <0.001
|-
|By total Cit+|| 3.576 || <0.001
|-
|By total replicates|| 1.825 || 0.034
|-
|}

So weighting on the basis of the number of replicates considerably increases the P-value. It remains, however, well within the range of statistical significance (0<P<0.05). If we hold that Lenski should have weighted on the basis of replicates then he should have rejected the null hypothesis and reached exactly the same conclusions that he did. The entire paper would have been exactly the same except the sentence “the result is extremely significant (P<0.0001) whether or not….” Would read “the result is significant (P<0.04) whether or not”. Point 5 establishes one number and an “extremely”. Point 5, therefore, has no weight (excuse the pun).
--[[User:Toffeeman|Toffeeman]] 15:18, 20 September 2008 (EDT)

: Sorry, Toffeeman, a falsehood is still a falsehood. Based on your own posting, if Lenski had applied the Whitlock Z-transform paper in a logical manner, the results would not have been nearly as striking as Lenski claimed (his paper said the results were "extremely significant"). Moreover, I found Lenski's description of his application of the Whitlock paper to be particularly misleading. Lenski's use of "whether or not"<ref>"We also used the Z-transformation method (49) to combine the probabilities from our three experiments, and '''the result is extremely significant (P < 0.0001) whether or not''' the experiments are weighted by the number of independent Cit+ mutants observed in each one." (Lenski paper at 7902).</ref> obscures the basic error that he did not apply Whitlock's paper in the straightforward, correct manner. I think the wording in the Lenski paper deliberately obscures this falsehood from the reader.

: People have free will to embrace and defend falsehoods. I don't expect them to change quickly or admit they were wrong. But you'll find me defending and promoting the truth.

: Point 5 remains valid and the falsehood remains uncorrected by PNAS or Lenski. Four other points in higher priority remain uncorrected by them also.--[[User:Aschlafly|Aschlafly]] 16:47, 20 September 2008 (EDT)

::'''''"a falsehood is still a falsehood"'''''. Precisely, the null hypothesis should be considered false and the conclusions of the paper stand.

::Oh? Do you mean ''Lenski's falsehood''? And what falsehood is that? Lenski said that he had calculated the P-value without weighting and that had come out at <0.0001. That is true, not false. Lenski said he had calculated the P-value weighting on the basis of the Cit+ replicates and that had come out at <0.0001. That is true, not false. There is no falsehood. Lenski did not mention the results of weighting on the basis of replicate numbers. He thus made no claim about weighting on the basis of replicate numbers. If he made no claim he cannot have made a false claim.

::How do the words Lenski uses "mislead". If you read them as written what conclusion do you come to? You are lead to the conclusion that the mutation was not "rare-but-equal", instead it was contingent. That is the right conclusion. If Lenski had presented the data in a different manner (perhaps by including the results of weighting on the basis of replicate numbers) what conclusion do you come to? You are again lead to the conclusion that the mutation was not "rare-but-equal", instead it was contingent. That is the right conclusion. To mislead you must be lead to a conclusion that is incorrect. By Lenski's paper you are not lead to a conclusion that is incorrect. Thus is cannot be said to be "misleading".

::I shall not comment on your second paragraph, the temptation to ''"Tu Quoque"'' would be too great.

--[[User:Toffeeman|Toffeeman]] 17:13, 20 September 2008 (EDT)

::: The falsehood consists of pretending to apply the Whitlock Z-transform in a straightforward, logical and correct manner. I think the Lenski paper is intentionally misleading by using the "whether or not" wording, when both alternatives are nonsensical. Point 5 has been proven above to be correct in identify an error in the Lenski paper.

::: "Toffeeman", your blocking history suggests you have been less than straightforward yourself. Go elsewhere if you seek to be deceitful. You're not fooling anyone here.--[[User:Aschlafly|Aschlafly]] 17:54, 20 September 2008 (EDT)

::::Lenski did apply the Z-transformation correctly, both weighted and unweighted. The data points extracted from each replay are the ''generation numbers of those replicates that gave rise to Cit+ mutants''. Thus Replay 1 produced four data points: 30,500 31,500 32,500 32,500. Replay 2 produced five data points: 32,000 32,000 32,000 32,000 32,500. Replay 3 produced eight data points: 20,000 20,000 27,000 27,000 31,000 31,500 32,000 32,000. Thus the N for replay 1 is 4; replay 2 is 5 and replay 3 is 8. The fact that replay 3 used 38 times as many replicates as replay 1 does not mean that it should be weighted 38 times as much; it only produced twice as much data, not 38 times as much.

::::Suppose I want to find out what the average age of a murderer is in three cities. In L.A. I interview 72 random people and find that 4 of them were convicted of murder; I record the ages of the four. In Seattle I interview 340 people and find that 5 of them are convicted murderers; likewise in Singapore I interview 2800 and find 8 murderers. In the end, I have 4,5, and 8 data points from the three cities; the number of people I had to interview to obtain those data points doesn't factor into the analysis of what the average age of the murderers is.--[[User:Brossa|Brossa]] 00:06, 21 September 2008 (EDT)

::::: In your first paragraph you simply repeat the error underlying Lenski's paper. You, like the paper, incorrectly apply Whitlock's Z-transform.

::::: The quality and reliability of data is proportional to sample size, and when different studies are combined they need to be weighted accordingly. The results from a very large sample size would not be weighted equally with the results from a small sample size, as you and Lenski have done. That's basic logic, though I'm not optimistic that you or Lenski will admit it. Open-minded people who respect logic have no difficulty elevating logic over personal whim.-[[User:Aschlafly|Aschlafly]] 11:30, 21 September 2008 (EDT)

::::::Andy if you read Whitlock's paper you would see it say, and I quote, "Ideally each study is weighted proportional to the inverse of its error variance, that is, by the '''reciprocal of its squared standard error'''." It says nothing about weighting according to sample size, which is what you seem to be insisting should be done.
::::::Also Whitlock acknowledges in the paper that there is no preference for weighted versus equal weighting, so the fact that both equal weighting and weighting by the standard error give a statistically significant result shows that the 3 experiments combined support rejection of the null hypothesis. [[User:DanB|DanB]] 20:39, 21 September 2008 (EDT)

:::::::ASchlafly, you state that I incorrectly apply "Whitlock's Z-transform" (actually the test belongs to Mosteller & Bush<ref>Mosteller, F. & Bush, R.R. 1954. Selected quantitative techniques. In: ''Handbook of Social Psychology,'' Vol. 1 (G. Lindzey, ed.)</ref> and/or Liptak<ref>Liptak, T. 1958. On the combination of tests. ''Magyar Tud. Akad. Mat. Kutato Int. Kozl.'' '''3''': 171-197</ref>). Whitlock describes weighting by the reciprocal of the squared standard error. The standard error of the mean is proportional to 1/sqrt(N), so the reciprocal of the squared standard error is proportional to N. Thus larger studies ''are'' given more weight. I maintain that the sample sizes N of the three replays are 4, 5, and 8 respectively. Weighting based on those three N does not weight all three replays equally as you claim: it gives replay 2 25% more weight and replay 3 100% more weight than replay 1. Rather than simply repeating that I am wrong, will you please state what ''you'' think the sample sizes of the three replay experiments are, and, in your opinion, what the ''correct'' application of the Z-transformation would be?--[[User:Brossa|Brossa]] 18:00, 22 September 2008 (EDT)

:::::::: The Lenski paper states how it weighted the experiments, and that weighting is incorrect. Admit it. Moreover, the incorrect weighting in the Lenski paper was not likely an inadvertent error, as it inflated the significance of the results. I found the wording used by the Lenski paper to describe its (incorrect) weighting to be artfully misleading.

:::::::: Provide me with federal funding as Lenski received, and I'll write a paper for you. But I don't have to write an alternative paper to point out glaring errors in Lenski's paper.--[[User:Aschlafly|Aschlafly]] 08:35, 23 September 2008 (EDT)

::::::::: I've been following this discussion for a while and I have to agree with ASchlafly. It hardly seems fair that he should have to, in his spare time, replicate an experiment done by a professional just to "earn" the right to criticize it. I am unfamiliar with statistics, but if some complicated transform goes against common sense, common sense should prevail. After all, there are lies, damned lies, and statistics... [[User:AndyM|AndyM]] 10:57, 23 September 2008 (EDT)

(unindent)I'm not asking anyone to write a paper or replicate an experiment. I'm asking ASchlafly to support his statement "The results from a very large sample size would not be weighted equally with the results from a small sample size, '''as you and Lenski have done'''"(bolding mine). I have stated publicly, subject to challenge by others, that the sample sizes (n) of the three replays are four, five, and eight respectively. Furthermore, using n of 4, 5, and 8 in the weighted Z-method DOES NOT weight all the replay experiments equally - it weights replay 3 twice as much as replay 1 and 8/5 as much as replay 2. Tell you what: I'll drop all my questions about Monte Carlo and the Z-transform, and simply ask ASchlafly one question: '''what is the sample size, n, of the second replay experiment?''' He need not even do any calculations - a statement in words that will allow someone else to do the calculation will suffice. This is not a complicated question to answer; the paper states how many replicate cultures there were (340), how many cells there were in each replicate (3.9x10^8), how many replicates gave rise to Cit+ cells (5), and which generations those Cit+ replicates came from (4 from 32,000 and one from 32,500). I will even give ''my'' answer: '''five'''. Furthermore, I will say ''why'' I believe that, using the murderer/age analogy: performing the 340 replicates is the same as interviewing 340 people in order to find out if any of them are convicted murderers. Finding that five replicates gave rise to Cit+ mutants is the same as the survey finding that 5 of those 340 people were convicted murderers. Finding that the Cit+ mutants arose from 4 replicates from generation 32,000 and 1 from generation 32,500 is the same as finding the ages of the murderers. The five data points in the Lenski study allow one to calculate the 'mean generation of clones yielding Cit+': 32,100. This is the same as finding the mean age of the five murderers. If I want to compare this hypothetical murderer age study to some other study of the mean age of murderers, I would weight the studies based on how many murderers were in each study, not on how many non-murderers were included in the initial survey.

Surely ASchlafly can say ''what'' he thinks the n of the second replay is, even if he won't say ''why'' he thinks it. Is it five? 340? The number of replicates times the number of cells per replicate? Something else? No analysis need be performed on the resulting number.--[[User:Brossa|Brossa]] 15:54, 23 September 2008 (EDT)

:OK - would you care to put in writing that after ASchlafly gives you his response, you won't start obfuscating the issue with Monte Carlo and Z-transform issues? You understand: it is typical of liberals to, after being proven wrong, to start pretending that they were talking about an entirely different issue altogether. '''After ASchlafly states the sample size of the second replay experiment you will consider yourself answered.''' Correct?

:Brossa, your rant is misplaced. One cannot salvage an error in logic by questioning which of superior alternatives should be used instead. The sample size of an experiment is the number that comprises the underlying sample used in the experiment, not the number of a certain outcome from the experiment. Maybe you can debate yourself over what the correct underlying sample size is, but it is plainly not the number of a certain outcome from the experiment.--[[User:Aschlafly|Aschlafly]] 19:28, 23 September 2008 (EDT)

Maybe the Journal of Nature can be your next letter submission source. ''International Weekly Journal of Science'' -- [[Image:50 star flag.png|14px]] [[User:Jpatt|jp]] 21:17, 22 September 2008 (EDT)

=== ''Not'' confirmed ===

Like Kennymac and Longstop, I have some qualifications in this area because I have taught statistics to researchers (not mathematicians) - actually for even longer than Kennymac. I've read the contribution from Longstop and I've decided that the best thing I can do is to replace it in its entirety because it makes the point quite well. (Actually both points - the statistical point and the one about reviewing scientific papers.) But my qualifications are really unimportant - as Longstop said, it doesn't matter who says something in science, it's '''what''' they say that matters. After all, the most important discoveries in science in the 20th century were made by a patent clerk who wasn't an academic at the time and hadn't even been a particularly outstanding student.

The rest of this posting is cut-and-pasted from Longstop's contribution earlier this week.

The main point he [Kennymac] makes is quite correct, that combining experiments will tend to give a more significant result (i.e. a lower P-value) than any single experiment on its own.

The point that ASchlafly makes (headed '''REPLY''', shortly after KennyMac's example) is slightly misleading. You don't choose which experiments to combine on the basis of their outcomes - you either combine all relevant experiments or none. In this case, Professor Lenski chose to combine all the experiments and present a single analysis of them. That's fine.

The issue of whether to weight the Z-test according to sample size is not a straightforward issue. Before Whitlock's recent paper, the consensus was that the P-value already depends on sample size so it should not be weighted according to sample size. (Basically, a high degree of significance, i.e. a low P-value, can be achieved by having either a large difference between the treatments or a large experiment or, of course, both.) Whitlock's work, based on computer simulations, is an interesting contribution but cannot be regarded as the last word on the subject because any computer simulation involves assumptions about the structure of the particular experiment simulated. I cannot imagine any editor of a scientific journal rejecting a paper because it used an unweighted Z-test rather than the weighted version (or vice-versa).

The conclusion, therefore, is that while there is a quantitative difference in the level of significance obtained by weighted and unweighted Z-tests, there is undeniably a significant biological effect. ASchlafly and other contributors should not be concerned that there is anything incorrect about the biological conclusions of Professor Lenski and his students or that there was anything at all underhand about their analysis or presentation of their data.

On a different point, please would CP readers note that there's nothing at all suspicious about a paper being peer-reviewed in only 14 days. Editors of scientific journals ask reviewers beforehand if they are free to edit a paper within a certain period of time. If an academic agrees to review a paper for a prestigious journal such as PNAS within 2 weeks, they will generally ensure they have time during that period to read and comment on the paper thoroughly. [[User:DavyJones|DavyJones]] 17:12, 17 October 2008 (EDT)

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