# User:Brossa

Z-transformation: $Z_s=\frac{\sum_{i=1}^k Z_n}{\sqrt{k}}$

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

where $w = \frac{1}{(SE_{\overline x})^2}$

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 $SE_{\overline x} \propto \frac {1}{\sqrt n}$

and$w \propto n$