Behavior Research Methods

, Volume 45, Issue 2, pp 536-546

First online:

Bias and precision of some classical ANOVA effect sizes when assumptions are violated

  • Susan Troncoso SkidmoreAffiliated withSam Houston State University
  • , Bruce ThompsonAffiliated withTexas A&M University Email author 


Previous simulation research has focused on evaluating the impact of analytic assumption violations on statistics related to the F test and associated p CALCULATED values. The present article evaluated the bias of classical estimates of practical significance (i.e., effect size sample estimators \( {\widehat{\eta}^2} \), \( {\widehat{\varepsilon}^2} \), and \( {\widehat{\omega}^2} \)) in a one-way between-subjects univariate ANOVA when assumptions are violated. The simulation conditions modeled were selected on the basis of prior empirical research. Estimated (1) sampling error bias and (2) precision computed for each of the three effect size estimates for the 5,000 samples drawn for each of the 270 (5 parameter Cohen's d values × 3 group size ratios × 3 population distribution shapes × 3 variance ratios × 2 total ns) conditions were modeled for each of the k = 2, 3, and 4 group analyses. Our results corroborate the limited previous related research and suggest that \( {\widehat{\eta}^2} \) should not be used as an ANOVA effect size estimator, even though \( {\widehat{\eta}^2} \) is the only available choice in the menus in most commonly available software.


Effect size Practical significance Analysis of variance Homogeneity of variance Type I error Power Eta squared Epsilon squared Omega squared