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Merge pull request #41 from egouldo/egouldo-patch-1
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fix #40 correct equation
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egouldo authored Jul 29, 2024
2 parents 9a12006 + d4b1dbb commit 91ca56a
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Expand Up @@ -2061,13 +2061,13 @@ This is because the same t-statistic value will be obtained by the same sample s
We see this by first examining the formula for the standard error, SE for variance, ($\tau^{2}$) or SE($\tau^{2}$) assuming normality in an underlying distribution of effect sizes [@knight2000]:

$$
SE({{τ}^2})=\sqrt{\frac{{t}^4}{n-1}}
SE({{\tau}^2})=\sqrt{\frac{{2\tau}^4}{n-1}}
$$ {#eq-SE-tau}
and then rearranging the above formula to show how the t-statistic is independent of $\tau^2$, as seen below.
$$
t=\frac{{τ}^2}{SE({{τ}^2})}=\sqrt{\frac{n-1}{2}}
t=\frac{{\tau}^2}{SE({{\tau}^2})}=\sqrt{\frac{n-1}{2}}
$$ {#eq-t-tau}
We then find a minimum n = 12 according to this formula.
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