We previously learned how to compare two population means using either the pooled two-sample t-test or Welch's t-test. What happens if we want to compare more than two means? In this lesson, we'll learn how to do just that. More specifically, we'll learn how to use the analysis of variance method to compare the equality of the (unknown) means \(\mu_1 , \mu_2 , \dots, \mu_m\) of m normal distributions with an unknown but common variance \(\sigma^2\). Take specific note about that last part.... "an unknown but common variance \(\sigma^2\)." That is, the analysis of variance method assumes that the population variances are equal. In that regard, the analysis of variance method can be thought of as an extension of the pooled two-sample t-test.