Fitting Categorical Models to Effect Sizes from a Series of Experiments

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Abstract
One method of combining the results of a series of two-group experiments involves the estimation of the effect size (population value of the standarized mean difference) for each experiment. When each experiment has the same effect size, a pooled estimate of effect size provides a summary of the results of the series of experiments. However, when effect sizes are not homogeneous, a pooled estimate can be misleading. A statistical test is provided for testing whether a series of experiments have the same effect size. A general strategy is provided for fitting models to the results of a series of experiments when the experiments do not share the same effect size and the collection of experiments is divided into a priori classes. The overall fit statistic H T is partitioned into a between-class fit statistic H B and a within-class fit statistic H w. The statistics H B and H w permit the assessment of differences between effect sizes for different classes and the assessment of the homogeneity of effect size within classes.