The analysis of variance or “ANOVA” (one-way, type I)

Abstract

If the means of several groups were compared pairwise using Student’s t (section 9.8), the number of comparisons would rapidly become larger than the number of groups (Figure 12.1.1). Besides breaking up and drawing out the analysis, this would also increase the probability of rejecting erroneously at least once the hypothesis that parametric means are equal. In fact, if ten statistical conclusions are drawn at significance level α, the probability α that the preliminary hypothesis is rejected at least once when it is true is multiplied by ten. If ten conclusions are drawn at level α= 0.05, there is thus a probability of 1/2 that the preliminary hypothesis is rejected erroneously at least once. Even though it is possible to compensate for such a risk (section 26.2), it is often desirable to carry out a single overall comparison of the means of several samples.