# Obtaining a pooled SD from a weighted difference in means for working Cohen's d for power analysis

Some meta-analyses quote the difference between two group means (e.g. between patient and control groups) and weight these to obtain an overall measure of this raw group difference. If a confidence interval is given for the pooled raw difference in group means this can be used to obtain a rough estimate of the pooled (study) sd so that Cohen's d can then be calculated from these published studies for use in power calculations for future work looking at similar groups.

Cohen's d = weighted pooled study difference in group means / pooled study sd of the difference between groups

We use the fact that half the width of a confidence interval (05CI) of the difference between two independent sample means equals z(0.05/2) x standard error of the difference in means. Since the standard error equals [(1/n1) + (1/n2)] x (sd pooled over study of difference in group means) and we can average the sample sizes of the groups using the harmonic mean equal to number of samples / sum of 1/(sample sizes) = nh we have

sd from pooled study CI of raw difference in group means = (05CI / 2) / sqrt(2/nh).