1. Matrix Approach to 1-Way ANOVA
Comparison of Sexual Side Effects in 4 Antidepressants
JG Modell, et al (1997). "Comparative Sexual Side Effects of Bupropion, Fluoxetine, Paroxetine, and Sertraline ", Clinical Pharmacology and Therapeutics, Vol.61(4),pp

2. Model

3. Matrix Approach with no constraints (g=3)

4. Applying Constraint 1 – Part 1

5. Applying Constraint 1 – Part 2

6. Applying Constraint 1 – Part 3

7. Applying Constraint 1 – Part 4

8. Applying Constraint 2 – Part 1

9. Applying Constraint 2 – Part 2

10. Applying Constraint 2 – Part 3

11. Applying Constraint 2 – Part 4

12. Applying Constraint 3 – Part 1

13. Applying Constraint 3 – Part 2

14. Applying Constraint 3 – Part 3

15. Applying Constraint 4

16. S U M A R Y

17. Estimable Functions
A linear function of the parameter vector b, h’b is said to be estimable if h’=t’X. That is, if h’ can be written as a linear function of the rows of X

18. Uniqueness of Estimates of Estimable Functions

19. Application: Comparison of g=4 Antidepressants
Response: Y = Change in libido scores for patients on antidepressants
Treatments: g=4 Brands of antidepressants
Prozac (n1 = 37)
Paxil (n2 = 21)
Zoloft (n3 = 27)
Wellbutrin (n4 = 22)
N=107, g=4, Prozac, Paxil, Zoloft are SSRI’s, Wellbutrin not
Will make generalizations of case g=3

20. Data and Analysis of Variance
H0 : Brand Means are all equal
Conclude brand means are not all equal Note: s2 = MSE = 0.96

21. Parameter Estimates – Constraint 1

22. Parameter Estimates – Constraint 2

23. Parameter Estimates – Constraint 3

24. Parameter Estimates – Constraint 4