One-Way Within-Groups ANOVA
We use a one-way within-groups ANOVA (also called a repeated-measures ANOVA) when we have one nominal or ordinal variable with at least three levels and a scale dependent variable, and every participant experiences every level of the independent variable. We use the same six steps of hypothesis testing for one-way within-groups ANOVA as we do for one-way between-groups ANOVA, except that for the former, we calculate statistics for four sources instead of three. We still calculate statistics for the between-groups, within-groups, and total sources, but we also calculate statistics for a fourth source, “subjects.” Although we calculate two F statistics, one for the between-groups variability and one for the subjects variability, we compare the between-groups F statistic to a critical value and either reject or fail to reject the null hypothesis.
Beyond Hypothesis Testing for the One-Way Within-Groups ANOVA
As we do with the one-way between-groups ANOVA, we calculate a measure of effect size, usually R2, and we conduct a post hoc test, such as the Tukey HSD test, if we reject the null hypothesis. There is one exception to the requirement that the same participants experience every level of the independent variable if we want to use a paired-samples t test or within-groups ANOVA. If we match the participants in each group on all likely confounding variables, then we can treat the groups—in a statistical sense—as if they include the same participants.