The sampling variance of a *d* value is:

$$\left(\frac{n-1}{n-3}\right)\left(\frac{n_{1}+n_{2}}{n_{1}n_{2}}+\frac{d^{2}}{2(n_{1}+n_{2})}\right)$$

When groups 1 and 2 are of equal size, this reduces to

$$var_{e}=\left(\frac{n-1}{n-3}\right)\left(\frac{4}{n}\right)\left(1+\frac{d^{2}}{8}\right)$$

This can be corrected for bias by first correcting the *d* value (see `correct_d_bias`

) prior to estimating the error variance.