Which Effect Size Measure is Appropriate for One-Way and Two-Way ANOVA Models?

A Monte Carlo Simulation Study

Abstract

It is very important to report some effect size measures that will show if the observed differences among the groups are also of practical significance along with statistical significance while reporting statistical analysis results. Performances of four commonly used effect size measures (Eta-Squared, Partial Eta Squared, Omega Squared and Epsilon Squared) were compared for one and two-way ANOVA models under 3000 different conditions. Results of simulation runs showed that the Epsilon and Omega-Squared estimates were quite unbiased when compared to Eta and Partial Eta-Squared which are directly reported by commonly used statistical packages while reporting ANOVA results. Thus, it could be concluded that reporting Epsilon or Omega-Squared is more appropriate to evaluate the practical significance of observed differences along with P-values.