User:Brossa

Z-transformation: <math>Z_s=\frac{\sum_{i=1}^k Z_n}{\sqrt{k}}</math>

Weighted Z-method: <math>Z_W=\frac{\sum_{i=1}^k w_i Z_i}{\sqrt{\sum_{i=1}^k w_i^2}}</math>

where <math>w = \frac{1}{(SE_{\overline x})^2}</math>

for <math>SE_{\overline x} = \frac{s}{\sqrt n}</math>

where <math>s=\sqrt{\frac{1}{N-1} \sum_{i=1}^N (x_i - \overline{x})^2}</math>

therefore <math>w = \frac{n}{s^2}</math>

where <math>s^2=\frac{1}{N-1} \sum_{i=1}^N (x_i - \overline{x})^2</math>

If <math>s</math> of all trials is similar, then <math>SE_{\overline x} \propto \frac {1}{\sqrt n}</math>

and<math>w \propto n</math>