Chapter 11: Analysis of Variance

The $z$- and $t$-tests can be used to test the equality between two population means $\mu_{1}$ and $\mu_{2}$. When we have more than two groups, we would inflate the probability of making a type I error if we were to compare just two at a time and make a conclusion about all the groups together. To account for this P(Type I Error) inflation, we instead will do an analysis of variance (ANOVA) to test the equality between 3 or more population means $\mu_{1}, \mu_{2}, \mu_{3}, \ldots, \mu_{k}$.

The F-test (for ANOVA) is a statistical test for testing the equality of $k$ population means.