The metric comparability of meta-analytic effect-size estimators from factorial designs

The primary studies in a meta-analysis of standardized mean differences generally include a mixture of single-factor t tests and multifactor analysis of variance designs. Accordingly, there is a need for effect-size measures in multifactor designs that are metrically comparable with measures in single-factor t tests. Two models, the variance-preservation model and the variance-reduction model, provide a formal description of the 2 principal routes by which a single-factor design may evolve into a higher order factorial design. New metrically comparable effect-size measures and estimators are developed for designs that contain variance-preservation factors, variance-reduction factors, or a mixture of both types of factors. A statistical test for checking the validity of model assumptions is presented.