Variance Explained in ANOVA (1 of 2)
The simplest way to measure the proportion of variance explained in an analysis of variance is to divide the sum of squares between groups by the sum of squares total. This ratio represents the proportion of variance explained. It is called eta squared or η².
If there is no error variance, then the sum of squares between equals the sum of squares total and η² = 1. If all the groups means are equal, then sum of squares between equals zero and η² = 0. In the former case, 100% of the variance is explained by the treatment; in the latter case, 0% of the variance is explained.
Researchers in statistics have determined that η² has a positive bias. A alternative and unbiased statistic called omega squared (ω²) has been developed. Its formula is:
