title: Negative estimate of variance-accounted-for effect size: How often it is obtained, and what happens if it is treated as zero.
abstract: Researchers recommend reporting of bias-corrected variance-accounted-for effect size estimates such as omega squared instead of uncorrected estimates, because the latter are known for their tendency toward overestimation, whereas the former mostly correct this bias. However, this argument may miss an important fact: A bias-corrected estimate can take a negative value, and of course, a negative variance ratio does not make sense. Therefore, it has been a common practice to report an obtained negative estimate as zero. This article presents an argument against this practice, based on a simulation study investigating how often negative estimates are obtained and what are the consequences of treating them as zero. The results indicate that negative estimates are obtained more often than researchers might have thought. In fact, they occur more than half the time under some reasonable conditions. Moreover, treating the obtained negative estimates as zero causes substantial overestimation of even bias-corrected estimators when the sample size and population effect are not large, which is often the case in psychology. Therefore, the recommendation is that researchers report obtained negative estimates as is, instead of reporting them as zero, to avoid the inflation of effect sizes in research syntheses, even though zero can be considered the most plausible value when interpreting such a result. R code to reproduce all of the described results is included as supplemental material.
authors.affiliation: Department of Psychology, Senshu University, 2-1-1 Higashimita, Tama-ku, Kawasaki, Kanagawa, Japan, 214-8580. ken@psy.senshu-u.ac.jp.
authors.forename: Kensuke
authors.identifier: 0000-0003-1663-5812
authors.initials: K
authors.lastname: Okada
mesh_terms: D015982:Bias; D006801:Humans; D018401:Sample Size
keywords: ANOVA; Effect size; Eta squared; Variance-accounted-for