Omega squared (ω²): what it means and how to read it
In the report: omega2 — 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.
How to read it
The same share as η², corrected for the size of the sample, so a little more modest and more honest.
If ω² is close to 0 while η² is not, the effect is probably mostly noise. Many journals prefer ω² for this reason.
The same guide as η²: 0.01 small, 0.06 medium, 0.14 large.
In plain words
A teacher with only 12 pupils counted eta squared and found that about 10 parts out of 100 of the differences in marks go with the way pupils studied. But with so few pupils that number tends to come out a little too big. So she counted omega squared, the more careful version, and got 0.04: only about 4 parts out of 100. Now she can be more honest: the way of studying goes with a small part of the marks. If omega squared had come out close to zero while eta squared did not, she would say the link is probably mostly luck. Many science magazines prefer omega squared for this reason.
How it is computed
ω² = (ssb − (k − 1) · msw) / (ssb + ssw + msw)Example
The cell with omega2 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
- 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.
- Odds ratio — The odds ratio: how many times the odds of Y = 1 multiply for one unit more of the predictor. In the Intercept column it is the odds of Y = 1 when every predictor is 0, not a ratio. Empty when lambda is above 0.
Get it in your sheet
One formula in a cell gives the whole report, Omega squared (ω²) included. ALS Stats is a free add-on for Google Sheets™.
Install ALS Stats from Google Workspace Marketplace (opens in a new tab)