1. Business 205

2. Review 2 Factor ANOVAs Excel 2 Independent T-tests ANOVA 2-Factor ANOVAs

3. Preview Post-Hoc Tests Scheffé Tukey HSD (Honest Significant Difference)

4. Rationale behind Post Hoc Tests Omnibus F Compare pairwise treatments to see where the significance is coming from Must meet certain conditions after you run an ANOVA: 1.) You reject the null hypothesis (you accept your hypothesis; it is statistically significant). 2.) There are 3 or more treatments (k ≥ 3).

5. Post-hoc Test: Scheffé Identify all pairwise comparisons. Choose the largest mean difference between conditions. Compute the SS between,, MS between, and F-ratio for these two treatments. Use the k value from the ANOVA for df between. Use the MS within from the ANOVA Find the F critical value from the F-distribution table using the df within and df between values from the ANOVA. Compare the F-ratio you found with that of the F critical values. Repeat for ALL pairs. Repeat for all pairwise and other comparisons of interest.

6. Example of Scheffé Golf Club AGolf Club BGolf Club CGolf Club D n = 3 T = 3 T = 12T = 18 M = 1 M = 4M = 6 1.) Assume your ANOVA was significant 2.) MS within = 2 3.) df within = 8

7. Step 1: Find largest mean difference Golf Club AGolf Club BGolf Club CGolf Club D n = 3 T = 3 T = 12T = 18 M = 1 M = 4M = 6 What are the pairwise comparisons? Which has the largest mean difference between the pairwise comparisons?

8. Step 2: Calculate SS, MS, F A – D Calculation: F critical (3, 8) = 4.07

9. Step 3: Chose 2 nd largest mean difference Golf Club AGolf Club BGolf Club CGolf Club D n = 3 T = 3 T = 12T = 18 M = 1 M = 4M = 6 1.) Assume your ANOVA was significant 2.) MS within = 2 3.) df within = 8

10. Step 4: Calculate SS, MS, F B – D Calculation: F critical (3, 8) = 4.07

11. Step 5: Choose 3 rd largest mean difference Golf Club AGolf Club BGolf Club CGolf Club D n = 3 T = 3 T = 12T = 18 M = 1 M = 4M = 6

12. Step 6: Find SS, MS, F C – A Calculation : F critical (3, 8) = 4.07

13. Stop the cycle and report findings 3 rd largest mean difference is not significant Any smaller mean differences between pairs will not be significant Stop calculating and report findings

14. Reporting Results Table Form ---------------------------------------------------------------------------- Treatment Conditions Golf Club Golf Club Golf Club Golf Club ABCD ---------------------------------------------------------------------------- M 1.0 1.0 4.0 6.0* SD 1.73 1.00 1.00 1.73 ---------------------------------------------------------------------------- * Differs from Golf Club A and Golf Club B, p <.05

15. Reporting Results Written Form Post hoc analyses were performed using the Scheffé post-test to identify exactly where significant differences exist. The analysis revealed that condition 4 differed significantly from condition 1, F(3, 8) = 6.25, p <.05 and from condition 2, F (3, 8) = 6.25, p <.05. No other differences were found.

16. In-Class Example of Scheffé Golf Club AGolf Club BGolf Club CGolf Club D n = 3 T = 18T = 10T = 12 M = 8M = 2M = 5M = 1 1.) Assume your ANOVA was significant 2.) MS within = 2 3.) df within = 8