User:Brossa

Z-transformation: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Z_s=\frac{\sum_{i=1}^k Z_n}{\sqrt{k}}}

Weighted Z-method: $Z_{W}={\frac {\sum _{i=1}^{k}w_{i}Z_{i}}{\sqrt {\sum _{i=1}^{k}w_{i}^{2}}}}$

where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle w = \frac{1}{(SE_{\overline x})^2}}

for $SE_{\overline {x}}={\frac {s}{\sqrt {n}}}$

where $s={\sqrt {{\frac {1}{N-1}}\sum _{i=1}^{N}(x_{i}-{\overline {x}})^{2}}}$

therefore $w={\frac {n}{s^{2}}}$

where $s^{2}={\frac {1}{N-1}}\sum _{i=1}^{N}(x_{i}-{\overline {x}})^{2}$

If $s$ of all trials is similar, then Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle SE_{\overline x} \propto \frac {1}{\sqrt n}}

andFailed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle w \propto n}