Generalized eta squared for multiple comparisons on between-groups designs

Psychological and educational researchers are experiencing many practical difficulties in following the guidelines of the American Psychological Association (APA) for their statistical analyses: one such difficulty is the reporting of an effect-size measure along with each test of statistical significance (APA, 2010). The problem is exacerbated when researchers focus on contrast analysis instead of omnibus tests and when the Type-I error rate per comparison has to be adjusted.

Several reasons for this problem are discussed, with emphasis on the facts that researchers may be presented with too many optional effect-size measures with varying degrees of adequacy in several designs, and common statistical packages fail to provide appropriate effect-size measures for contrast analysis.

This study proposes specific procedures (also implemented in spreadsheets) to compute generalized eta squared for various kinds of hypotheses, either general or specific, for one-factor and factorial between-group designs, and with manipulated and/or measured factors.

Finally, conclusions are drawn concerning the need to take into account the kind of design and the kind of hypothesis in order to calculate comparable effect-size indexes across different types of studies and to prevent an overestimation of effect size.