Eta Squared Calculator

Eta squared

What this answers

Eta squared answers "what fraction of the total variation in my outcome is explained by which group an observation belongs to?" It ranges from 0 (group membership explains nothing) to 1 (group membership explains everything), giving a magnitude for an ANOVA result the way Cohen's d does for a t-test.

How it is calculated

Eta squared is simply the sum of squares between groups divided by the total sum of squares from your ANOVA. Both values come directly from the ANOVA table (this calculator does not recompute them from raw data; use the One-Way ANOVA Calculator first if you need those sums of squares computed from your raw data).

Worked example

For an ANOVA with SS between of 4 out of an SS total of 10: eta squared is 4 divided by 10, exactly .4, meaning 40% of the total variation in the outcome is associated with which group each observation belonged to.

Assumption audit

Calculated from your data: eta squared directly from the two sums of squares you supplied.

Evidence to review: eta squared tends to overstate the true population effect, especially with many groups or a small sample; compare it against omega squared, a less biased alternative estimate.

You must verify: that conventional labels for eta squared (small, medium, large) are descriptive benchmarks, not universal thresholds for whether an effect matters in your specific context.

What this result does not mean

A large eta squared describes how much of your sample's variation is associated with group membership; it does not by itself establish that group membership causes that variation, and conventional size labels (small, medium, large) are descriptive conventions, not universal practical-importance thresholds.

Common mistakes

A frequent mistake is reporting eta squared alone as if it were the final word on practical importance, when a "large" eta squared can still come from a study too small to trust its own estimate. Another is entering raw group data instead of the ANOVA table's sums of squares; this calculator takes the sums of squares directly, so raw data must first go through the One-Way ANOVA Calculator to produce them. A third is treating eta squared computed from a Welch ANOVA's adjusted sums of squares the same as one from a classic ANOVA; the two are not always directly comparable when variances differ substantially across groups.

Limitations

Eta squared is a sample statistic and tends to be a biased, optimistic estimate of the true population effect, particularly with more groups or fewer observations relative to the number of groups.