Group Overlap as a Basis for Effect Size

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Abstract
The research content of interest herein is that of comparison of means. It is generally recognized that statistical test p values do not adequately reflect mean comparison assessments. What is desirable is some effect-size assessment. The typical effect-size indexes used in mean comparisons are restricted to the variance homogeneity condition. What is proposed here is the use of the group-overlap concept. Group overlap may be assessed via prediction of group assignment, that is, using predictive discriminant analysis. The effect-size index proposed is that of improvement-over-chance classification ( I). The I index may be used in situations that are univariate, multivariate, homogeneous, heterogeneous, or any combination thereof. Some very tentative suggestions for cutoffs of I values to define index magnitude for some data situations are made.