miesize: Effect-size calculation in imputed data

Abstract

In this article, I describe the miesize command for the calculation of effect sizes in imputed data. There may be situations where an effect size needs to be estimated for an intervention, an exposure, or a group membership variable but data on the independent or dependent variable are missing. Such missing data are commonly dealt with by multiply imputing plausible values. However, in this circumstance, the estimated effect size and associated standard errors will need to be pooled and estimated from the imputed dataset. The miesize command automates this process and calculates effect sizes for a binary variable from multiply imputed data in wide format. The estimates and standard errors (used to calculate the confidence intervals) are recombined using Rubin’s (1987, Multiple Imputation for Nonresponse in Surveys [Wiley]) rules. These rules are applied such that the average point estimate for the effect size is calculated from the imputed datasets. The pooled standard error, and hence confidence intervals, is calculated to account for both the variance between the imputed datasets and the variance within them. Pooled effect sizes and confidence intervals for Cohen’s (1988, Statistical Power Analysis for the Behavioral Sciences, 2nd ed. [Lawrence Erlbaum]) d, Hedges’s (1981, Journal of Educational Statistics 6: 107-128) g, and Glass’s (Smith and Glass, 1977, American Psychologist 32: 752-760) delta are provided by miesize.