Eta Squared [η²]

Eta squared (η²) is a measure of effect size for a specific variable in an ANOVA model after accounting for the other variables. It describes the proportion of variance of an outcome variable that a specific predictor variable explains. In the context of ANOVA, eta squared measures how much of the total variability in the dependent variable is associated with each main effect or interaction effect being tested.

Eta squared is calculated by taking the sum of squares (SS) for the effect of interest and dividing it by the total sum of squares for the model. Mathematically, η² = SS_effect / SS_total. The value of eta squared ranges from 0 to 1, where higher values indicate that a larger portion of the variability is explained by that particular effect. It gives a sense of relative importance beyond just statistical significance.

For example, if a study comparing different diets finds that η² = 0.15 for diet type, it means that 15% of the variation in weight loss can be explained by differences between the diets, while the remaining 85% of the variation is due to other factors or random variability.