Omega Squared Calculator

Raw omega squared
Omega squared (displayed)

What this answers

Omega squared answers the same question as eta squared (what proportion of variation is explained by group membership), but with a correction that removes some of eta squared's tendency to overstate the true population effect, especially with a small sample or many groups.

How it is calculated

Omega squared subtracts an adjustment based on the degrees of freedom between groups and the within-group mean square error from the sum of squares between groups, then divides by the total sum of squares plus that same mean square error. This correction can produce a negative raw value when the true effect is very small relative to sampling noise; this calculator displays that raw value directly, but shows 0 as the reported omega squared in that case, since a negative proportion of variance explained has no meaningful interpretation.

Worked example

For a hand-computed ANOVA table with SS between of 54, SS total of 60, 2 degrees of freedom between, and a mean square error of 1: omega squared works out to a value close to but below the corresponding eta squared of .9, illustrating the correction's typical downward adjustment.

Assumption audit

Calculated from your data: the raw and displayed omega squared values from your four inputs, and whether the raw value came out negative.

Evidence to review: a warning appears below the result if the raw omega squared was negative, transparently disclosed rather than silently hidden.

You must verify: that conventional size labels for omega squared are descriptive benchmarks, not universal thresholds for practical importance in your specific context.

Common mistakes

A common mistake is treating a negative raw omega squared as a calculation error rather than an expected outcome; it simply means the observed between-group variation was no larger than would be expected from sampling noise alone given that many groups and that much within-group error, so displaying 0 is the honest interpretation, not a bug. Another is comparing an omega squared computed here against an eta squared computed elsewhere and treating a difference between them as a discrepancy; the two use different formulas by design and are expected to diverge, more so with fewer observations per group. A third is forgetting that mean square error, not the raw within-group sum of squares, is required for this specific formula.

Limitations

This calculator assumes a one-way, fixed-effects ANOVA design; the formula changes for more complex designs (repeated measures, multiple factors), which this calculator does not cover.