All the NHSTs in previous chapters compare two dependent variable means. When there are three or more group means, it is possible to use unpaired two-sample t-tests for each pair of group means, but there are two problems with this strategy. First, as the number of groups increases, the number of t-tests required increases faster. Second, the risk of Type I error increases with each additional t-test.
The analysis of variance (ANOVA) fixes both problems. Its null hypothesis is that all group means are equal. ANOVA follows the same eight steps as other NHST procedures. ANOVA produces an effect size, η2. The η2 effect size can be interpreted in two ways. First, η2 quantifies the percentage of dependent variable variance that is shared with the independent variable’s variance. Second, η2 measures how much better the group mean functions as a predicted score when compared to the grand mean.
ANOVA only says whether a difference exists – not which means differ from other means. To determine this, a post hoc test is frequently performed. The most common procedure is Tukey’s test. This helps researchers identify the location of the difference(s).
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