The Efficacy of Two Improvement-Over-Chance Effect Sizes for Two-Group Univariate Comparisons Under Variance Heterogeneity and Nonnormality

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Abstract
The efficacy of two improvement-over-chance or I effect sizes, derived from predictive discriminant analysis (PDA) and logistic regression analysis (LRA), was investigated for two-group univariate mean comparisons. Data were generated under selected levels of population separation, variance pattern, sample size, and distribution shape. Based on the accuracy of sample estimates, both I indices are acceptable under optimal conditions except when both population separation and sample size are small. Under variance heterogeneity and normality, I derived from LRA is acceptable if n sizes are equal. When n sizes are unequal, I derived from LRA is acceptable only if variance heterogeneity is moderate and population separation is not small. Under nonnormality, I derived from LRA is acceptable regardless of the variance pattern provided n sizes are equal. Finally, for greater precision, I derived from LRA should be used under large sample sizes.