1. One way ANALYSIS OF VARIANCE (ANOVA)
Farrokh Alemi, Ph.D.

2. Purpose of ANOVA
One-way
Two-way or Factorial

3. Why not do repeated t-tests?
Multiple comparison problem
5 groups, 10 comparison of means
Type one error is 0.29 not .05

4. Framework for Hypothesis Testing
Recall the framework for hypothesis testing. First we examine the assumptions, then state the hypothesis, calculate the statistic, look up the p value and then decide to reject or fail to reject the null hypothesis.

5. Framework for Hypothesis Testing
In this set of slides we apply this framework to analysis of variance for comparing 3 or more means. We will use One-way Analysis of Variance to test when the mean of a variable differs among three or more groups

6. Test Assumptions Independent samples
Independent observations within samples
Dependent variable normally distributed
Population variances are equal

7. State Hypotheses Always Two Sided Test Ho: 1 = 2 = 3 = 4
Ha: Not Ho
Any 1  2 or 2  3 or 1  3 will reject
Always Two Sided Test

8. Calculate Test Statistics
Test statistic for ANOVA is based on between & within groups SS

9. Logic Behind the Test Statistic
Partitioning of variance
A. Between Group Variability
B. Within Group Variability

10. Total Sum of Squares

11. Between Groups Sum of Squares

12. Within Groups Sum of Squares

13. Partitioning of Variance

14. Calculating Test Statistics
Mean difference between pairs of values

15. Lookup P-Value

16. Reject or Fail to Reject
α = .05
If Fc > Fα Reject H0
If Fc > Fα Can not Reject H0

17. Example Group 1: Patients in 4 West Group 2: Patients in 4 East
Group 3: Patients in 3 Floor

18. Example
Satisfaction Rating (0-10)
Treatment Conditions (3 Groups)

19. Observations

20. SS Within

21. SS Between

22. Sum of Squares Total

23. Components of Variance

24. Degrees of Freedom

25. Test Statistic

26. Lookup Critical Value

27. Conclusion

28. Take home lesson