In statistics this week we are learning about ANOVA and Tukey's HSD.
If ANOVA only tells you whether the differences in the means of the groups are significant, but Tukey's HSD gives you the difference, CI and p-value for each pair of means, what's the point of using ANOVA?
Are there any situations where ANOVA is more helpful? Or is learning about ANOVA purely useful for learning the theoretical basis for testing multiple groups?
In some situations, researchers know in advance (i.e., when they design their study) what groups they would like to compare with respect to the mean value of an outcome variable. In that case, they would not perform an omnibus ANOVA F-test but rather focus directly on performing the desired a priori group comparisons.
In other situations, researchers will not know in advance what groups to compare. In that case, they would perform an omnibus ANOVA F-test and only if the p-value for that test is statistically significant they would proceed to perform all possible pairwise comparisons of the groups to detect which groups differ in terms of the mean value of the outcome variable.
