Effect size comparison for populations with an application in psychology

Effect size estimates are now widely reported in various behavioural studies. In precise estimation or power analysis studies, sample size planning revolves around the standard error (or variance) of the effect size. Note these studies are carried out under sampling-budget constraints. Hence, the optimum allocation of resources to populations with different inherent population variances is paramount as this affects the effect size variance. In this paper, a general effect size meant to compare two population characteristics is defined, and under budget constraints, we aim to optimize the variance of the general effect size. In the process, we use sequential theory to arrive at optimum sample sizes of the corresponding populations to achieve minimum variance. The sequential method we developed is a distribution-free method and does not need knowledge of population parameters. Mathematical justification of the characteristics enjoyed by our sequential method is laid out along with simulation studies. Thus, our work has wide applicability in the effect size comparison context.