So far we discussed how to compare one or two population means. In this section we discuss a method called Analysis of Variance (ANOVA), which allows us to compare several population means.

More specifically, we discuss the so-called one-way analysis of variance. This type of ANOVA compares the means of a variable that result from the classification by one other variable, called the factor. To illustrate the concept let us design a simple example. Say we compare the mean annual salary of German residents grouped by federal sates (by the way there are sixteen federal states, which are collectively referred to as “Bundeslaender”), then we get 16 means of annual salaries, one for each of federal state. Thus, in this example the state variable is that one particular classification variable, the so-called factor.

Please note that the one-way analysis of variance is the generalization to more than two populations of the pooled t-test.