About the Eta-Squared
The Eta-Squared Calculator converts the between-groups and total sums of squares from an ANOVA into a single effect-size number showing how much of the total variance in an outcome is explained by group membership. It answers a question the ANOVA F-statistic alone cannot: not just whether groups differ, but how much that difference actually matters.
How It Works
You enter the sum of squares between groups and the total sum of squares, both values that come out of an ANOVA table. The calculator divides the first by the second to get eta-squared, expresses it as a percentage of variance explained, and labels the result negligible, small, medium, or large based on fixed cutoffs.
Formula & Methodology
Take the sum of squares between groups from your ANOVA output and divide it directly by the total sum of squares (which equals SS between plus SS within). The result is a proportion between 0 and 1; multiplying by 100 gives the percentage of the outcome's total variability attributable to which group a case belongs to, with the remainder attributable to within-group variation.
Examples
Three-group teaching method study
With SS between groups of 240 and SS total of 900, eta-squared works out to 0.2667, meaning about 26.7% of the variance in test scores is explained by teaching method, a large effect by the calculator's own bands.
Weak treatment effect
If SS between groups is only 18 out of an SS total of 900, eta-squared is 0.02, or 2% variance explained, which the calculator labels a small effect even if the ANOVA F-test happened to be statistically significant.
Advantages
- Turns raw ANOVA sums of squares into a standardized, easy-to-interpret proportion of variance explained
- Lets you compare effect sizes across different studies or outcome variables, since it is unitless and scaled from 0 to 1
- Automatically classifies the result using conventional small, medium, and large effect-size bands so you don't need a separate lookup table
Common Mistakes
- Treating a statistically significant ANOVA result as automatically meaningful without checking eta-squared, when a large sample can make even a negligible effect size significant
- Entering SS within by mistake instead of SS total, which inflates the ratio and produces an eta-squared value that is too large
- Comparing eta-squared values across studies with very different numbers of groups without accounting for how that structure affects the ceiling on possible values
Edge Cases to Watch For
- The calculator requires SS total to be positive and SS between to fall between 0 and SS total inclusive; values outside that range return an error since eta-squared cannot be negative or exceed 1.
- The strength labels use fixed thresholds: under 0.01 is negligible, under 0.06 is small, under 0.14 is medium, and 0.14 or above is large.
- Eta-squared tends to overestimate the true population effect size, especially with small samples or many groups, since it does not adjust for degrees of freedom the way omega-squared does.
Common Use Cases
- Researchers reporting ANOVA results who need an effect-size measure alongside the F-statistic and p-value for publication standards
- Students learning the relationship between sums of squares and proportion of variance explained in a one-way ANOVA
- Analysts comparing the practical impact of different categorical factors (e.g., treatment group, region, product line) on a measured outcome