 Solution

Use one-way analysis of variance to compare a quantitative response variable across levels of one categorical factor; for example, compare task accuracy across three independently assigned teaching methods. The ordinary independent-groups procedure tests the null hypothesis that all group population means are equal. Its F-test compares variation associated with the group factor against within-group error variation; a significant result indicates that not all population means are equal, without identifying which groups differ.^[ref]

The classical one-way normal linear model assumes independent observations and within-group errors approximately following a normal distribution with a common variance. Repeated observations on the same people require a different dependence structure; pronounced unequal variances may call for Welch's one-way analysis of variance. Planned contrasts or appropriately controlled follow-up comparisons identify scientifically relevant differences. Report the means, differences and confidence intervals, not just significance. Causal interpretation depends on the design of experiments, particularly randomization, rather than on the F-test alone.