Omega Squared Calculator

Omega squared (ω²) is an effect size measure for ANOVA that estimates the proportion of variance in the dependent variable attributable to the independent variable in the population. It is preferred over eta squared (η²) because eta squared is positively biased — it tends to overestimate the true population effect size, especially with small samples. Omega squared corrects for this bias, providing a more accurate estimate.

You need five values from your ANOVA output: degrees of freedom for the model (dfm), degrees of freedom for error (dfe), mean square for the model (MSm), mean square for error (MSe), and the total sum of squares (SST). These are all standard values reported in any ANOVA summary table.

The formula is: ω² = (dfm × (MSm − MSe)) / (SST + MSe). The numerator represents the model's explained variance corrected for bias, and the denominator is the corrected total variance. This formula applies to one-way and multi-way ANOVA designs.

Cohen's (1988) conventional benchmarks are commonly used: ω² ≈ 0.01 is considered a small effect, ω² ≈ 0.06 is a medium effect, and ω² ≈ 0.14 or larger is a large effect. These are guidelines rather than strict cutoffs — always interpret effect size in the context of your research area.

Yes, omega squared can technically be negative when the F-statistic is less than 1 (i.e., MSm < MSe). A negative value simply means the effect is essentially zero — the model explains no variance beyond chance. In practice, negative values are reported as 0 or near 0.

Partial eta squared (η²p) expresses the proportion of variance explained by a factor after removing variance attributable to other factors, and it is computed per-factor in multi-way ANOVA. Omega squared is a global measure corrected for bias. Partial eta squared tends to overestimate effect sizes even more than eta squared, especially with multiple predictors.

Yes, the formula used here works for both one-way and multi-way ANOVA designs, provided you carefully select the correct error term (MSe and dfe) for the specific factor you are computing ω² for. For factorial designs, use the appropriate within-cell error term.

Cohen's f is another ANOVA effect size measure related to omega squared by the formula f = √(ω² / (1 − ω²)). Cohen's f is used in power analysis (e.g., G*Power), while omega squared is more directly interpretable as a proportion of variance explained. You can convert between the two using this relationship.