Eta squared (η²): what it means and how to read it
In the report: eta2 — The share of the total variance explained by the groups: 0 — none, 1 — all.
How to read it
How much the grouping explains. η² = 0.10 means that 10% of the differences between people go with the group they are in.
p says whether there is an effect, η² says how big it is: 0.01 small, 0.06 medium, 0.14 large.
Report it next to p: F(2, 147) = 4.12, p = .018, η² = .05 — close to a medium effect.
A common guide (Cohen): 0.01 small, 0.06 medium, 0.14 large. η² overstates the effect in small samples — ω² corrects it.
In plain words
A school tried three ways of studying, and a teacher wanted to know how much of the difference in marks between pupils goes with the way they studied. She counted eta squared and got 0.10: about 10 out of every 100 parts of the differences in marks go with the way of studying, and the other 90 parts go with something else. Now she can tell the school that the way of studying goes with one tenth of the differences between pupils, and that most of the differences, 90 parts out of 100, are left to other things that the three ways of studying do not show.
How it is computed
η² = ssb / (ssb + ssw)Example
The cell with eta2 is selected in each report; point at a label to see its note.
- — the sample data (50 rows) the examples use
- — classic one-way ANOVA
=STATS_ANOVA(Data!A1:T51, "x1,x2") - — new syntax, 3 reports
=STATS_ANALYZE(Data!A1:T51, "PAIRED('before,after', 0.99, 'greater') ANOVA('x1,x2,x') DESCRIPTIVE('mean,std,n', 'x1,x2')")
Where you see it
STATS_ANOVA— One-way ANOVA: each selected column is a group. Classic (Student) or Welch ANOVA, chosen by welch (auto by default), with homogeneity of variances and post-hoc comparisons.STATS_ANALYZE— Runs several analyses on one range and returns one report.
Related values
- Omega squared (ω²) — The share of variance explained by the groups, corrected for sample size: a less biased η², slightly smaller. Can be below 0 when there is no effect.
- McFadden pseudo R² — How much the model improves the log-likelihood over the model with the intercept only.
- Cox & Snell pseudo R² — A pseudo R² from the likelihood ratio; even a perfect model stays below 1.
- Nagelkerke pseudo R² — Cox & Snell R² rescaled so that a perfect model reaches 1.
- Classification accuracy — The share of rows classified correctly when a predicted probability of 0.5 or more is read as 1.
Get it in your sheet
One formula in a cell gives the whole report, Eta squared (η²) included. ALS Stats is a free add-on for Google Sheets™.
Install ALS Stats from Google Workspace Marketplace (opens in a new tab)