1. Repeated Measures meets Latin Squares
Crossover Design
Repeated Measures meets Latin Squares

2. Layout for Crossover design
Group I II
Subject 1 … 9 10 18
Time A B 2
Layout for Crossover design

3. First nine subjects at Time 1
Group
Time
Drug Y 1 A
41.9 2
35.1 3
38.6 4
36.1 5
34.6 6
39.7 7
37.8 8
38.8 9
39.1
First nine subjects at Time 1

4. Crossover model (split–plot univariate analysis)
Yijkl=µ+Gi+S(i)j Between Subjects
+Tk+Dl+εijkl Within Subjects
Crossover model (split–plot univariate analysis)

5. Enter all terms in the Model as Fixed to get all SS from JMP

6. This gives all Model and error SS

7. If we specify Subject as Random

8. Subject(Group) tests Group, Residual tests the Within terms

9. Usually hope Time is not significant, but at least we controlled for it

10. What would happen if we believed our Model and Tested Drug A at Time 1 and Drug B at time 2?
Hint is next slide…..

11. Consider the Drug effect

12. Plot Time*Drug

13. Look at A at time 1 and B at time 2, they are about equal.

14. Moral: Crossing is good
Main Effects would have been confounded
Moral: Crossing is good

15. Actually only four distinct Predicted values. Why?

16. Now check Normality