Enter your between-groups sums of squares (SS_between) and total sums of squares (SS_total) to calculate Eta Squared (η²) — a measure of effect size for one-way ANOVA tests. You get the η² value plus an interpretation of whether the effect is small, medium, or large.
Eta Squared (η²)
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Effect Size Interpretation
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Within-Groups SS (SS_within)
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Variance Explained
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Eta Squared (η²) is an effect size statistic used with one-way ANOVA. It tells you what proportion of the total variance in the dependent variable is explained by the independent variable (group membership). Values range from 0 to 1, where higher values indicate a stronger effect.
Eta Squared is calculated by dividing the between-groups sums of squares (SS_between) by the total sums of squares (SS_total): η² = SS_between / SS_total. The result represents the proportion of variance accounted for by the grouping factor.
According to Salkind & Frey (2019), η² ≈ .01 indicates a small effect, η² ≈ .06 indicates a medium effect, and η² ≥ .14 indicates a large effect. These are conventional benchmarks — always interpret effect size in the context of your specific field and study design.
SS_between (between-groups sums of squares) measures the variability in scores that is due to differences between group means. SS_total is the overall variability across all scores regardless of group. SS_total = SS_between + SS_within (within-groups sums of squares).
They are conceptually similar — both express the proportion of variance explained — but are computed in different contexts. R-squared is used in regression analysis, while Eta Squared is the ANOVA equivalent. For one-way ANOVA, they produce the same numerical result when calculated from the same data.
Eta Squared divides SS_between by SS_total (all variance in the design). Partial Eta Squared divides SS_between by (SS_between + SS_error), ignoring variance from other factors. In a one-way ANOVA, they are identical; in factorial designs, they can differ substantially.
No. Because SS_between can never exceed SS_total, Eta Squared always falls between 0 and 1. If your SS_between value is larger than SS_total, there is an error in your data — double-check your sums of squares values.
You should report Eta Squared (or another effect size measure) alongside your ANOVA F-statistic and p-value. Statistical significance alone does not indicate practical importance — effect size provides the magnitude of the observed difference, which is critical for interpreting and replicating research findings.