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User:Martin Arrowsmith/maths

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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} \varpropto \frac {1}{\sqrt n}

andw \varpropto n