(adjusted)R-squared / eta-squared / omage-squared for ANOVA

#1
Dear all,

When obtaining ANOVA results with SPSS we also get a R-squared and an adjusted R-squared. For a multi-way ANOVA the eta-squared is given per factor or interaction.

The measures are criticized by - among others - Andy Field:
"However, this measure of effect size is slightly biased because it is based purely on sums of squares from the sample and no adjustment is made for the fact that we're trying to estimate the effect size in the population."

He proposes to use the omega-squared. Especially when running Multi-way ANOVA's it causes a lot of extra work to calculate the omega-squares for all factors and interactions. Because ... SPSS does not give you omega-squares, so you have to calculate them by hand. As far as I know, omega-squared is also not in R.

My question: how wrong is it to simply use the measures given by SPSS?
Other question: what's the difference between R-squared and the adjusted R-squared?

Best regards,

Wilbert
 

Miner

TS Contributor
#2
R-square and Eta-square are measuring two different things. R-square measures the contribution of the entire model in explaining the study variation. Eta-square and Omega-square measure the contribution of the individual model terms. So, they are similar, yet different.

Eta-square has a positive bias, so it overestimates the individual contributions. From a practical standpoint, this bias is small (e.g., 65.16% vs. 64.98%), so it depends on your situation.

R-square can be significantly inflated by adding non-significant terms to the model. R-square adjusted compensates for this by penalizing you for additional model terms. Use it instead. R-square predicted is even better because it protects against overfitting the model.