Tail, Tusk, and Trunk: What Different Metrics Reveal About Racial Disproportionality in School Discipline

One possible reason for the continued neglect of statistical power analysis in research in the behavioral sciences is the inaccessibility of or difficulty with the standard material. A convenient, although not comprehensive, presentation of required sample sizes is provided here. Effect-size indexes and conventional values for these are given for operationally defined small, medium, and large effects. The sample sizes necessary for .80 power to detect effects at these levels are tabled for eight standard statistical tests: (a) the difference between independent means, (b) the significance of a product-moment correlation, (c) the difference between independent rs, (d) the sign test, (e) the difference between independent proportions, (f) chi-square tests for goodness of fit and contingency tables, (g) one-way analysis of variance, and (h) the significance of a multiple or multiple partial correlation.

The objective of this article is to offer guidelines regarding the selection, calculation, and interpretation of effect sizes (ESs). To accomplish this goal, ESs are first defined and their important contribution to research is emphasized. Then different types of ESs commonly used in group and correlational studies are discussed. Several useful resources are provided for distinguishing among different types of effects and what modifications might be required in their calculation depending on a study's purpose and methods. This article should assist producers and consumers of research in understanding the role, importance, and meaning of ESs in research reports.