eta2

Eta squared, denoted as η² and sometimes written as eta2, is a statistic used to measure effect size in the context of analysis of variance (ANOVA). It represents the proportion of total variance in the dependent variable that is associated with a particular factor or effect, providing a sense of how large an effect is in relation to the overall variability.

For a given effect in an ANOVA, η² is calculated as η² = SS_effect / SS_total, where SS_effect is the sum of squares for the effect and SS_total is the total sum of squares. In designs with multiple effects, the interpretation can depend on the model. A related measure is partial eta squared, defined as ηp² = SS_effect / (SS_effect + SS_error), which assesses the effect while accounting for error associated with the model.

Interpretation of η² values is context-dependent, but common rough guidelines are that values near 0 indicate a very small effect, around 0.01 a small effect, around 0.06 a medium effect, and around 0.14 or higher a large effect. However, these benchmarks vary by field and design, and η² should be interpreted in conjunction with sample size, design orthogonality, and other statistics.

Eta squared has limitations. It can overestimate population effect size in small samples or in non-orthogonal designs, and partial eta squared can inflate effects in factorial designs. Alternative measures, such as omega squared (ω²) and epsilon squared (ε²), tend to provide less biased estimates of population effect size. In regression contexts, η² relates to R² but is not identical to it.

Historically attributed to Karl Pearson, η² remains a widely reported measure of effect size in ANOVA results across psychology, education, and social sciences.