POST HOC COMPARISONS What is the Purpose? How Do Post Hoc Methods Differ? How Does the Tukey’s HSD Work?

What is the Purpose? A significant F in ANOVA tells you only that there is a difference among the groups, not which groups are different. Post hoc tests can be done to make specific comparisons. Post hocs also control experimentwise alpha level.

How Do Post Hoc Methods Differ? Some post hocs are more conservative, meaning careful about avoiding Type I error. Post hocs methods also differ in what type of comparisons they allow Pairwise: one condition compared to another Nonpairwise: combinations of conditions

How Do Post Hoc Methods Differ? Commonly used post hoc methods: Fisher’s PLSD Scheffe Tukey’s HSD

Fisher’s PLSD Protected Least Significant Difference Less conservative F-test in ANOVA must be significant Pairwise comparisons only

Scheffe Very conservative Pairwise or nonpairwise comparisons High critical value in exchange for allowing any comparison

Tukey’s HSD Medium conservative Pairwise comparisons only Each group must have same n

How Does the Tukey’s HSD Work? Honestly Significant Difference is calculated. Any difference between means must be larger than the HSD to be significant. Larger differences are needed as more groups are being compared; this controls Type I error rate.