etasquared

Eta squared, often denoted η², is a statistic used in the analysis of variance (ANOVA) to express effect size. It represents the proportion of the total variance in the dependent variable that is attributable to a given factor or interaction. For a one-way ANOVA, η² is calculated as the sum of squares for the effect divided by the total sum of squares (η² = SS_effect / SS_total). Values range from 0 to 1, with larger values indicating a stronger effect.

Partial eta squared, denoted ηp², is a related measure used in designs with multiple effects. It is computed as SS_effect divided by the sum of SS_effect and SS_error (ηp² = SS_effect / (SS_effect + SS_error)). It reflects the proportion of variance attributed to the effect after accounting for other factors in the model. Unlike η², each ηp² is bounded between 0 and 1 for a given model, but the values can be difficult to compare across different models or designs.

Interpretation and cautions: There are no universal benchmarks for what constitutes a small, medium, or large η² or ηp²; conventions (e.g., small ≈ 0.01, medium ≈ 0.06, large ≈ 0.14) are approximate and context-dependent. Both η² and ηp² can overestimate the population effect, especially in small samples. Omega squared (ω²) is a related, less biased alternative often recommended for estimating population effect size.

Usage: These measures are commonly reported in psychology, education, and social sciences to supplement F statistics and p-values, aiding in understanding the practical importance of findings. When reporting, specify which measure is used and the model context.