Other measures of effect size for ANOVA

Because of the relationship between ANOVA and multiple regression, we can use the correlation coefficient as a measure of effect size in ANOVA. The value of the correlation coefficient is given by Multiple R in the Regression data analysis tool. E.g., for Example 1 of ANOVA using Regression, r = .285 (see Figure 2 of ANOVA using Regression), which indicates a medium effect (since r ≈ .3).

The correlation coefficient metric (often called eta) is based on the data from the sample, but doesn’t always provide a good representation for the population as a whole. As a result, another measure of effect size, called omega, is more commonly used. Omega is given by the following formula:

Omega square

The first version uses the terminology of regression analysis, while second uses the terminology of ANOVA. We also have the following alternative form:

Omega squared

For the one factor ANOVA in Example 3 of Basic Concepts for ANOVAω2 = 0.14 (as can be seen in Figure 1 of Confidence Interval for ANOVA). For the two factor ANOVA in Example 2 of ANOVA using Regression we calculate omega square as follows:

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In general, omega is a more accurate measure of the effect, where ω2 = .01 is considered a small effect and ω2 = .06 and .14 are considered medium and large effects respectively.

Effect sizes for the omnibus ANOVA results, however, are not really that interesting. More useful are effect sizes for planned tests. As explained in Linear Regression for Comparing Means, a useful measure of effect size here is

Effect size contrast r

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