Summary

We can construct analysis-of-variance tables for all linear model analyses with any mixture of continuous and categorical variables. The tables partition the overall variability into signal(s) and noise, which can be compared using F-tests (variance ratio tests). For complex datasets where many pairwise comparisons can be performed, an initial F-test can provide a check of whether there’s evidence for any differences at all. It also reduces the risk of over-testing and generating false positives.