# Formula for the standard error of a Cohen's d

According to p238 of standard text on meta-analysis in social science The Handbook of Research Synthesis, the variance of Cohen's d is

( [(n1 + n2)/(n1*n2)] + d^{2 } / 2*(n1 + n2 − 2) )*([n1 + n2] / [n1 + n2 − 2] ),

where n1 and n2 are the sample sizes of the two groups being compared and d is Cohen's d .

Taking the square-root of this variance gives the standard error of d , needed as input by several of the user-written meta-analysis packages for Stata. (Some of them also accept confidence intervals as input, but they simply convert them to standard errors internally anyway.)

See also equation 4.20 here and here which also gives standard error formulae for d.