A commonly used measure of effect size, despite it being positively biased, is eta squared, η2, which is simply r2. For Example 1 of Basic Concepts of ANCOVA,
Another commonly used measure of effect size is partial η2 = which for Example 1 of Basic Concepts of ANCOVA is
We can also use these measures of effect size for the covariate.
This shows that the covariate explains a larger part of the variance (either total or unattributed to other variables) than the method.
For the contrasts we can use the usual measure r = . For the comparison in Example 1 of Contrasts for ANCOVA, we have
which is a relatively large effect.
We can also compute the effect size of the covariate using the regression coefficient information in Figure 5 of Regression Approach to ANCOVA (cell U36), and see that it is a very large effect.