Effect size standard errors for the non-normal non-identically distributed case

ABSTRACT. Suppose there are k independent studies and for each study the experi-mental and control groups have been sampled from independent but essentially arbi-trary populations. The problem is to construct a plausible standard error of the effect size mean (effect sizes are standardized experimental-control group mean differences) when given only minimal sample statistic information. Standard errors based on the sample standard error, or bootstrap, will typically be much too large and have very large variance. A normal theory estimator may prove practically useful in more general settings. Asymptotic distribution-free estimators are provided for two cases. This paper is concerned with the construction of effect size standard errors in situations where the effect sizes are independent but the data have likely been sampled from non-normal distributions, and possibly for different stud-ies, from different families of non-normal distributions. Define effect size Dj for study / as Dj(XEj, Xq, Sj) = {XEj- XQ)ISh / = 1,..., * , (1) all random variables where XE and Xc will be referred to generically a