Editing Effect size (section)

==== Distribution of effect sizes based on means ====
Provided that the data is [[Gaussian distribution|Gaussian]] distributed a scaled Hedges' ''g'', <math display="inline">\sqrt{n_1 n_2/(n_1+n_2)}\,g</math>, follows a [[noncentral t-distribution|noncentral ''t''-distribution]] with the [[noncentrality parameter]] <math display="inline">\sqrt{n_1 n_2/(n_1+n_2)}\theta</math> and {{math|(''n''<sub>1</sub> + ''n''<sub>2</sub> − 2)}} degrees of freedom.  Likewise, the scaled Glass' Δ is distributed with {{math|''n''<sub>2</sub> − 1}} degrees of freedom.

From the distribution it is possible to compute the [[Expected value|expectation]] and variance of the effect sizes.

In some cases large sample approximations for the variance are used. One suggestion for the variance of Hedges' unbiased estimator is<ref name="HedgesL1985Statistical"/> {{Rp|p=86|date=November 2012}}
<math display="block">\hat{\sigma}^2(g^*) = \frac{n_1+n_2}{n_1 n_2} + \frac{(g^*)^2}{2(n_1 + n_2)}.</math>