Eta Squared (η²) Effect Size Calculator
One-way ANOVA effect sizes from raw groups — eta-squared, omega-squared and Cohen’s f, with the F statistic and p-value.
How it works
η² = SS_between ÷ SS_total; ω² = (SS_between − df_b·MS_within) ÷ (SS_total + MS_within); f = √[η² ÷ (1 − η²)]
Eta squared is the proportion of total variance attributable to group differences — R² for ANOVA. It overstates the population effect in small samples because it does not account for degrees of freedom; omega squared corrects that and is preferred for reporting. Cohen’s f is the form power calculators use (0.10 small, 0.25 medium, 0.40 large), and the benchmark bands for η² are 0.01, 0.06 and 0.14.
Worked example
Three groups of five: SS_between = 16.9, SS_total = 27.7 → η² = 0.61 (large), ω² = 0.55, F(2,12) = 9.4, p = 0.003.
Frequently asked questions
Partial eta squared?
In a one-way design partial η² equals η². In factorial designs partial η² divides by SS_effect + SS_error instead of SS_total.
Why is ω² smaller?
It subtracts the variance that chance alone would attribute to groups, giving an unbiased estimate that shrinks most for small n.
Related calculators
For education — check assumptions (sample size, distribution, independence) before using a test result in a real decision.