Track 10 · Comparing Groups and Categorical Data · Lesson 5 of 11
Post-hoc comparisons
Explain why many unadjusted t-tests inflate the false-positive rate, and use Tukey's HSD (and Bonferroni/Holm adjustments) to find which group means differ after an ANOVA.
A field trial finds that fertilizer treatment matters for wheat yield. The agronomist's next question is the practical one: is nitrogen plus phosphorus better than nitrogen alone, or only better than no fertilizer? Answering it means several comparisons at once — and each extra comparison is another chance of a false alarm.
A significant one-way ANOVA says that not all group means are equal. It does not say which differ. With groups there are pairs: 3 pairs for 3 groups, 6 for 4, 15 for 6.
Included with a Formula Quest membership
It has 7 graded exercises with feedback, hints and worked solutions. After it you will be able to:
- Calculate how the family-wise error rate grows with the number of comparisons
- Compute and interpret Tukey's q, adjusted p-values and simultaneous confidence intervals
- Choose between Tukey, Tukey–Kramer, Dunnett, Bonferroni/Holm and Games–Howell
- Report non-significant pairs with intervals rather than as “equal”