1. Post-hoc Tests for ANOVA Explaining significant differences in 1-way ANOVA

2. Multiple comparisons Post hoc procedures vs. a priori comparisons (we look at only post hoc) Comparisonwise error rate - alpha for each comparison Experimentwise error rate - the probability of making a Type I error for the set of all possible comparisons alpha e = 1 - (1-alpha) c

3. Multiple comparisons If you are comparing 3 groups (A, B, C), than you can do 3 total comparisons  A – B  A – C  B – C The experimentwise error rate without any adjustments would be: alpha e = 1 - (1-alpha) c = 1 – (1-.05) 3 = 1 -.95 3 = 1 -.86 =.14

4. Using SPSS, LSD post hoc comparison does not control experimentwise error rate (e.g. comparisonwise error rate = 0.05 per comparison). –This is considered a liberal post hoc analysis Tukey method for making comparisons maintains an experimentwise error rate –based on the distribution called the Q distribution –makes comparisons without inflating the experimentwise error rate

5. Post-hoc analysis on SPSS –Compare Means –Click “post-hoc” button –Select method of analysis

6. Results from tire data Tukey test

7. Results from Tire data Bridgestone Goodyear Uniroyal Firestone Michelin

8. In words Bridgestone is different than firestone, Michelin, and Uniroyal Goodyear is different than Michelin Uniroyal is different than Bridgestone Firestone is different than Bridgestone Michelin is different than Goodyear and Bridgestone