1. CROSSOVER DESIGN Repeated Measures meets Latin Squares 1

2. LAYOUT FOR CROSSOVER DESIGN  Group III Subject1…910…18 Time 1A…AB B 2B…BA A 2

3. FIRST NINE SUBJECTS AT TIME 1  SubjectGroupTimeDrugY 111A41.9 211A35.1 311A38.6 411A36.1 511A34.6 611A39.7 711A37.8 811A38.8 911A39.1 3

4. CROSSOVER MODEL (SPLIT–PLOT UNIVARIATE ANALYSIS)  Y ijkl =µ+G i +S (i)j Between Subjects  +T k +D l +ε ijkl Within Subjects 4

5. ENTER ALL TERMS IN THE MODEL AS FIXED TO GET ALL SS FROM JMP  5

6. THIS GIVES ALL MODEL AND ERROR SS  6

7. IF WE SPECIFY SUBJECT AS RANDOM  7

8. SUBJECT(GROUP) TESTS GROUP, RESIDUAL TESTS THE WITHIN TERMS  8

9. USUALLY HOPE TIME IS NOT SIGNIFICANT, BUT AT LEAST WE CONTROLLED FOR IT  9

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….. 10

11. CONSIDER THE DRUG EFFECT  11

12. PLOT TIME*DRUG  12

13. MORAL: CROSSING IS GOOD  Main Effects would have been confounded 13

14. ACTUALLY ONLY FOUR DISTINCT PREDICTED VALUES. WHY?  14

15. NOW CHECK NORMALITY 15