Inference on effect size indices from several two-armed experiments

Abstract

The statistical inference problem on effect size indices is addressed using a series of independent two-armed experiments from k arbitrary populations. The effect size parameter simply quantifies the difference between two groups. It is a meaningful index to be used when data are measured on different scales. In the context of bivariate statistical models, we define estimators of the effect size indices and propose large sample testing procedures to test the homogeneity of these indices. The null and non-null distributions of the proposed testing procedures are derived and their performance is evaluated via Monte Carlo simulation. Further, three types of interval estimation of the proposed indices are considered for both combined and uncombined data. Lower and upper confidence limits for the actual effect size indices are obtained and compared via bootstrapping. It is found that the length of the intervals based on the combined effect size estimator are almost half the length of the intervals based on the uncombined effect size estimators. Finally, we illustrate the proposed procedures for hypothesis testing and interval estimation using a real data set.