POST HOC COMPARISONS 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.

Fisher’s PLSD Protected Least Significant Difference F-test in ANOVA must be significant Pairwise comparisons only – pairwise - compares two groups Less conservative post hoc

Tukey’s HSD Honestly Significant Difference Each group must have same N Pairwise comparisons only Critical value increases with number of groups Medium conservative post hoc

Scheffe Pairwise or non-pairwise comparisons High critical value in exchange for allowing any comparison Very conservative post hoc

Examples of Non-Pairwise Comparisons: (Therapy A & Therapy B) vs. Placebo (No Noise & Low Noise) vs. High Noise

Computation of Tukey’s HSD Example: An ANOVA was done comparing spelling performance in three noise conditions. Determine which conditions were significantly different from each other. (Data and ANOVA table follow)

No noiseLow noiseHigh noise x=16x=15x=11 overall x = 14

SourceSSdfMSF p Between <.05 Within Total9611

Formula for HSD

STEP 1: Look up q. k = 3 groups df error = df Within = 9 q from table = 3.95

STEP 2: Compute HSD.

STEP 3: Compute mean differences. No noise vs. Low noise: 16-15=1 No noise vs. High noise: 16-11= 5 Low noise vs. High noise: = 4

STEP 4: Compare differences to HSD. If the difference is equal to or greater than the HSD, it is significant. No noise vs. Low noise: not sig. No noise vs. High noise: significant Low noise vs. High noise: not sig.

APA Format Post hoc comparisons were done using Tukey’s HSD. The difference between the no noise and high noise conditions was significant. The difference between the no noise and low noise condition was not significant, and the difference between the low noise and high noise conditions was not significant.