Contrasts and correlations in effect-size estimation

This article describes procedures for presenting standardized measures of e ffect size when contrasts are used to ask focused questions of data. The si mplest contrasts consist of comparisons of two samples (e.g., based on the independent t statistic). Useful effect-size indices in this situation are members of the g family (e.g., Hedges's g and Cohen's d) and the Pearson r. We review expressions for calculating these measures and for transforming them back and forth, and describe how to adjust formulas for obtaining g or d from t, or r from g, when the sample sizes are unequal. The real-life im plications of d or g calculated from t become problematic when there are mo re than two groups, but the correlational approach is adaptable and interpr etable, although more complex than in the case of two groups. We describe a family of four conceptually related correlation indices: the alerting corr elation, the contrast correlation, the effect-size con-elation, and the BES D (binomial effect-size display) correlation. These last three correlations are identical in the simple setting of only two groups, but differ when th ere are move than two groups.