Section author: Danielle J. Navarro and David R. Foxcroft
Effect size¶
There’s a few different ways you could measure the effect size in an ANOVA, but the most commonly used measures are η² (eta squared) and partial η². For a one-way analysis of variance they’re identical to each other, so for the moment I’ll just explain η². The definition of η² is actually really simple
That’s all it is. So when I look at the ANOVA table in Fig. 132, I see that SSb = 3.45 and SStot = 3.45 + 1.39 = 4.84. Thus we get an η² value of
The interpretation of η² is equally straightforward. It refers to the
proportion of the variability in the outcome variable (mood.gain) that can
be explained in terms of the predictor (drug). A value of η² = 0 means that
there is no relationship at all between the two, whereas a value of η = 1 means
that the relationship is perfect. Better yet, the η² value is very closely
related to R², as discussed previously in subsection The *R*²
(R-squared) value, and has an equivalent
interpretation.
Although many statistics text books suggest η² as the default effect size measure in ANOVA, there’s an interesting blog post by Daniel Lakens suggesting that eta-squared is perhaps not the best measure of effect size in real world data analysis, because it can be a biased estimator. Usefully, there is also an option in jamovi to specify omega-squared (ω²), which is less biased, alongside eta-squared.