In the last chapter, we learned how to test whether two independent samples were obtained from the same population. In this chapter, we confront the same problem, but work with more than two samples.

This chapter provides a review of a limited aspect of ANOVA: model I, oneway analysis of variance. Excluded are the more complex experimental designs such as two-way, nested, and multi-way ANOVAS, as well as the computation of the added variance component of model II designs. These more complex ANOVAS are frequently discussed in psychology and biology texts, since in these fields carefully planned laboratory experiments are possible (see Sokal and Rohlf, 1981). This chapter begins by introducing the reader to a model I, one-way ANOVA, emphasizing the null hypothesis tested. The next section introduces the nomenclature, and explains how ANOVA information is usually displayed in tables. An example and a practice problem then follow. Finally a discussion of post-ANOVA comparison of means is presented.

One-way ANOVA

In a one-way ANOVA we deal with a problem similar to an unpaired ttest, but use more than two samples. The null hypothesis is that the means we compare were obtained from the same population. In other words, the hypothesis states that the µ of the population from which the samples were obtained is the same. Thus HO: µ1 = µ2 = … = µa, where a is the number of samples being compared.