Correlation - Revision history

DavidB4-bot: /* Example */Spelling, Grammar, and General Cleanup

2017-09-01T12:59:16Z

Example: Spelling, Grammar, and General Cleanup

JDano: /* Example */ round up

2017-06-05T11:12:27Z

Example: round up

JDano: /* Example */ typo

2017-06-05T11:07:05Z

Example: typo

JDano: /* Example */ typos

2017-06-05T10:40:13Z

Example: typos

JDano: /* Correlation and Causation */ an example

2017-06-05T10:32:05Z

Correlation and Causation: an example

DavidB4-bot: /* top */Spelling/Grammar Check, typos fixed: a another → an another

2016-07-15T13:55:28Z

top: Spelling/Grammar Check, typos fixed: a another → an another

DavidB4-bot: clean up & uniformity

2016-07-13T06:57:10Z

clean up & uniformity

Ed Poor: What is causal inference?

2010-10-26T17:52:54Z

What is causal inference?

Ed Poor: correlation does not imply causation. This is the most frequent mistake made by people

2010-10-26T17:52:19Z

correlation does not imply causation. This is the most frequent mistake made by people

Dasonk: /* Formal definition */ Added paragraph on independence with Normal random variables

2010-04-13T00:45:23Z

Formal definition: Added paragraph on independence with Normal random variables

@@ Line 94: / Line 94: @@
 |correlation coeff||0.75||1||0.73||0.42
 |}
-Whether the person voted for Trump is the dependent variable, and each of the other questions are independent variables.  The correlation coefficient can then be computed comparing the column of each dependent variable with the Trump column.  What this data tells us is that being blue collar is a perfect predictor of voting for Trump -- the correlation coefficient is 1.  The next best predictive factor would be whether the voter was a Republican, where they match 6 out of 7 times. Then comes gender and West Virginia residence.  Assuming that the data sample was large enough to be statistically significant, we could build a model to predict whether other voters would vote for Trump by asking the same questions and computing a score using the formula:
+Whether the person voted for Trump is the dependent variable, and each of the other questions are independent variables.  The correlation coefficient can then be computed comparing the column of each dependent variable with the Trump column.  What this data tells us is that being blue collar is a perfect predictor of voting for Trump—the correlation coefficient is 1.  The next best predictive factor would be whether the voter was a Republican, where they match 6 out of 7 times. Then comes gender and West Virginia residence.  Assuming that the data sample was large enough to be statistically significant, we could build a model to predict whether other voters would vote for Trump by asking the same questions and computing a score using the formula:
   .75*Republican + 1*Blue collar + .73*Male + .42*WVa
 A perfect score would be 2.897, and someone with a 0 score would be most unlikely to vote for Trump.  Of course, the polling firm would be using many more questions and would experiment to fine-tune the questions to get the best predictive scores.  They would also use much larger data samples.

@@ Line 96: / Line 96: @@
 Whether the person voted for Trump is the dependent variable, and each of the other questions are independent variables.  The correlation coefficient can then be computed comparing the column of each dependent variable with the Trump column.  What this data tells us is that being blue collar is a perfect predictor of voting for Trump -- the correlation coefficient is 1.  The next best predictive factor would be whether the voter was a Republican, where they match 6 out of 7 times. Then comes gender and West Virginia residence.  Assuming that the data sample was large enough to be statistically significant, we could build a model to predict whether other voters would vote for Trump by asking the same questions and computing a score using the formula:
   .75*Republican + 1*Blue collar + .73*Male + .42*WVa
-A perfect score would be 2.896, and someone with a 0 score would be most unlikely to vote for Trump.  Of course, the polling firm would be using many more questions and would experiment to fine-tune the questions to get the best predictive scores.  They would also use much larger data samples.
+A perfect score would be 2.897, and someone with a 0 score would be most unlikely to vote for Trump.  Of course, the polling firm would be using many more questions and would experiment to fine-tune the questions to get the best predictive scores.  They would also use much larger data samples.
 This fine-tuning process is a form of learning.  When a computer does this by itself it is called [[machine learning]].

@@ Line 94: / Line 94: @@
 |correlation coeff||0.75||1||0.73||0.42
 |}
-Whether the person voted for Trump is the independent variable, and each of the other questions are dependent variables.  The correlation coefficient can then be computed comparing the column of each dependent variable with the Trump column.  What this data tells us is that being blue collar is a perfect predictor of voting for Trump -- the correlation coefficient is 1.  The next best predictive factor would be whether the voter was a Republican, where they match 6 out of 7 times. Then comes gender and West Virginia residence.  Assuming that the data sample was large enough to be statistically significant, we could build a model to predict whether other voters would vote for Trump by asking the same questions and computing a score using the formula:
+Whether the person voted for Trump is the dependent variable, and each of the other questions are independent variables.  The correlation coefficient can then be computed comparing the column of each dependent variable with the Trump column.  What this data tells us is that being blue collar is a perfect predictor of voting for Trump -- the correlation coefficient is 1.  The next best predictive factor would be whether the voter was a Republican, where they match 6 out of 7 times. Then comes gender and West Virginia residence.  Assuming that the data sample was large enough to be statistically significant, we could build a model to predict whether other voters would vote for Trump by asking the same questions and computing a score using the formula:
   .75*Republican + 1*Blue collar + .73*Male + .42*WVa
 A perfect score would be 2.896, and someone with a 0 score would be most unlikely to vote for Trump.  Of course, the polling firm would be using many more questions and would experiment to fine-tune the questions to get the best predictive scores.  They would also use much larger data samples.

@@ Line 76: / Line 76: @@
 Suppose a polling firm was hired to talk to voters as they voted.  Each voter was asked "Are you a Republican?", "Are you a blue collar worker?", "Are you male?", "Do you live in West Virginia?", and "Did you vote for Donald Trump?"  We can record that data on a spreadsheet using one for yes and zero for no:
 {| class="wikitable"
-|Person||Republican?||Blue collar?||Male?||Wva?||Trump?
+|Person||Republican?||Blue collar?||Male?||WVa?||Trump?
 |-
 |A||1||1||1||1||1
@@ Line 95: / Line 95: @@
 |}
 Whether the person voted for Trump is the independent variable, and each of the other questions are dependent variables.  The correlation coefficient can then be computed comparing the column of each dependent variable with the Trump column.  What this data tells us is that being blue collar is a perfect predictor of voting for Trump -- the correlation coefficient is 1.  The next best predictive factor would be whether the voter was a Republican, where they match 6 out of 7 times. Then comes gender and West Virginia residence.  Assuming that the data sample was large enough to be statistically significant, we could build a model to predict whether other voters would vote for Trump by asking the same questions and computing a score using the formula:
-  .75*Republican + Blue collar + .73*Male + .42WVa
+  .75*Republican + 1*Blue collar + .73*Male + .42*WVa
 A perfect score would be 2.896, and someone with a 0 score would be most unlikely to vote for Trump.  Of course, the polling firm would be using many more questions and would experiment to fine-tune the questions to get the best predictive scores.  They would also use much larger data samples.

← Older revision		Revision as of 10:32, June 5, 2017
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	Additionally, correlation estimates a linear relationship between X and Y. Thus, an increase in variable X is assumed to exert the same influence on Y across all values of X and Y.		Additionally, correlation estimates a linear relationship between X and Y. Thus, an increase in variable X is assumed to exert the same influence on Y across all values of X and Y.
		+
		+	===Example===
		+	Suppose a polling firm was hired to talk to voters as they voted. Each voter was asked "Are you a Republican?", "Are you a blue collar worker?", "Are you male?", "Do you live in West Virginia?", and "Did you vote for Donald Trump?" We can record that data on a spreadsheet using one for yes and zero for no:
		+	{\| class="wikitable"
		+	\|Person\|\|Republican?\|\|Blue collar?\|\|Male?\|\|Wva?\|\|Trump?
		+	\|-
		+	\|A\|\|1\|\|1\|\|1\|\|1\|\|1
		+	\|-
		+	\|B\|\|1\|\|1\|\|1\|\|1\|\|1
		+	\|-
		+	\|C\|\|1\|\|1\|\|1\|\|0\|\|1
		+	\|-
		+	\|D\|\|0\|\|1\|\|1\|\|1\|\|1
		+	\|-
		+	\|E\|\|0\|\|0\|\|1\|\|0\|\|0
		+	\|-
		+	\|F\|\|0\|\|0\|\|0\|\|0\|\|0
		+	\|-
		+	\|G\|\|0\|\|0\|\|0\|\|1\|\|0
		+	\|-
		+	\|correlation coeff\|\|0.75\|\|1\|\|0.73\|\|0.42
		+	\|}
		+	Whether the person voted for Trump is the independent variable, and each of the other questions are dependent variables. The correlation coefficient can then be computed comparing the column of each dependent variable with the Trump column. What this data tells us is that being blue collar is a perfect predictor of voting for Trump -- the correlation coefficient is 1. The next best predictive factor would be whether the voter was a Republican, where they match 6 out of 7 times. Then comes gender and West Virginia residence. Assuming that the data sample was large enough to be statistically significant, we could build a model to predict whether other voters would vote for Trump by asking the same questions and computing a score using the formula:
		+	.75Republican + Blue collar + .73Male + .42WVa
		+	A perfect score would be 2.896, and someone with a 0 score would be most unlikely to vote for Trump. Of course, the polling firm would be using many more questions and would experiment to fine-tune the questions to get the best predictive scores. They would also use much larger data samples.
		+
		+	This fine-tuning process is a form of learning. When a computer does this by itself it is called [[machine learning]].

	==Correlation and Causation==		==Correlation and Causation==

← Older revision		Revision as of 13:55, July 15, 2016
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−	'''Correlation''' describes the relationship of two factors to one another (see [[cause and effect]]). When two factors are found to go together, there are only three explanations. First, the two things may be entirely unrelated. Second, they may both be caused by a another factor. Third, one of the factors might be causing the other. It is the task of [[statistics]] to point out the existence of a correlation, but it is the task of science to discover what relationship, if any, exists.	+	'''Correlation''' describes the relationship of two factors to one another (see [[cause and effect]]). When two factors are found to go together, there are only three explanations. First, the two things may be entirely unrelated. Second, they may both be caused by another factor. Third, one of the factors might be causing the other. It is the task of [[statistics]] to point out the existence of a correlation, but it is the task of science to discover what relationship, if any, exists.

	* correlation '''does not imply causation'''. This is the most frequent mistake made by people. There are set of principles of [[causal inference]] that need to be satisfied in order to imply cause and effect. [http://www.math.sfu.ca/~cschwarz/Stat-301/Handouts/node46.html]		* correlation '''does not imply causation'''. This is the most frequent mistake made by people. There are set of principles of [[causal inference]] that need to be satisfied in order to imply cause and effect. [http://www.math.sfu.ca/~cschwarz/Stat-301/Handouts/node46.html]

@@ Line 75: / Line 75: @@
 ==Correlation and Causation==
-''Main article: [[Correlation is not causation]]''
+{{Main|Correlation is not causation}}
 Correlation is a linear statistic and makes no mathematical distinction between [[independent variable|independent]] and [[dependent variable]]s. As a consequence, it is impossible to assert [[causation]] based on a correlation even if that correlation is statistically significant. Therefore, when a significant correlation has been identified it is possible that X -> Y (i.e. X causes Y), Y -> X (i.e. Y causes X), or that X <- Z -> Y (i.e. Both X and Y are caused by an additional variable, Z). Caution must be exercised in asserting causation using correlation and claims to this effect must be viewed with considerable skepticism.
@@ Line 83: / Line 83: @@
 Aron, Arthur, Elaine N. Aron and Elliot J. Coups. 2008. ''Statistics for the Behavioral and Social Sciences: A Brief Course.'' 4/e. Upper Saddle River, New Jersey: Prentice Hall.
-[[Category:statistics]]
+[[Category:Statistics]]

← Older revision		Revision as of 17:52, October 26, 2010
Line 1:		Line 1:
	'''Correlation''' describes the relationship of two factors to one another (see [[cause and effect]]). When two factors are found to go together, there are only three explanations. First, the two things may be entirely unrelated. Second, they may both be caused by a another factor. Third, one of the factors might be causing the other. It is the task of [[statistics]] to point out the existence of a correlation, but it is the task of science to discover what relationship, if any, exists.		'''Correlation''' describes the relationship of two factors to one another (see [[cause and effect]]). When two factors are found to go together, there are only three explanations. First, the two things may be entirely unrelated. Second, they may both be caused by a another factor. Third, one of the factors might be causing the other. It is the task of [[statistics]] to point out the existence of a correlation, but it is the task of science to discover what relationship, if any, exists.

−	* correlation '''does not imply causation'''. This is the most frequent mistake made by people. There are set of principles of causal inference that need to be satisfied in order to imply cause and effect. [http://www.math.sfu.ca/~cschwarz/Stat-301/Handouts/node46.html]	+	* correlation '''does not imply causation'''. This is the most frequent mistake made by people. There are set of principles of [[causal inference]] that need to be satisfied in order to imply cause and effect. [http://www.math.sfu.ca/~cschwarz/Stat-301/Handouts/node46.html]

← Older revision		Revision as of 00:45, April 13, 2010
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	The results of this test should be evaluated against the standard t-distribution with degrees of freedom equal to n-2. As usual in significance tests, a result described as significant (i.e. a low value of ''P'' in the ''t'' test) means that the chance of getting a correlation coefficient at least as large (whichever the direction) as that observed, if there is in fact no correlation, is small. A statistically significant result can therefore arise if the actual correlation is strong, even if the dataset is small, or if the actual correlation is weak but many data are observed.		The results of this test should be evaluated against the standard t-distribution with degrees of freedom equal to n-2. As usual in significance tests, a result described as significant (i.e. a low value of ''P'' in the ''t'' test) means that the chance of getting a correlation coefficient at least as large (whichever the direction) as that observed, if there is in fact no correlation, is small. A statistically significant result can therefore arise if the actual correlation is strong, even if the dataset is small, or if the actual correlation is weak but many data are observed.
		+
		+	One should note that for most random variables a correlation of 0 does not imply that they are independent. However, if the two variables come from the [[Normal Distribution]] then it can be claimed that a correlation of 0 implies independence.

	It is important to note that the correlation coefficient should not be calculated when either of the variables is not continuous. That is, when they do not vary continuously and have a meaningful zero. As such, correlating a dichotomous variable (e.g. sex) with a ratio variable (e.g. IQ) is inappropriate and will return uninterpretable results.		It is important to note that the correlation coefficient should not be calculated when either of the variables is not continuous. That is, when they do not vary continuously and have a meaningful zero. As such, correlating a dichotomous variable (e.g. sex) with a ratio variable (e.g. IQ) is inappropriate and will return uninterpretable results.