1. 2-Way Mixed Analysis of Variance
Women’s PBA

2. Data Description
Women’s Professional Bowling Association – Qualifying rounds at Alan Park, Michigan (2009).
Factors:
A: Oil Pattern (Fixed) with a=4 levels:
1=Viper, 2=Chameleon, 3=Scorpion, 4=Shark
B: Bowler (Random) with b=15 levels:
1=Diandra Abaty, 2=Shalin Zulkiffi, 3=Liz Johnson, 4=Kelly Kulick, 5=Clara Guerrero, 6=Jennifer Petrick, 7=Wendy MacPherson, 8=Shannon Pluhowski, 9=Stephanie Nation, 10=Tammy Boomershine, 11=Amanda Fagan, 12=Aumi Guerra, 13=Michelle Feldman, 14=Shannon O'Keefe, 15=Jodie Woessner
Replicates: Each bowler rolled 2 sets of 7 games on each pattern (Y = Total Pins in a game, n=14)

3. Statistical Model

4. Covariance Structure / ANOVA (Unrestricted Model)

5. Expectations and Variances of Means - I

6. Expectations and Variances of Means - II

7. Expected Mean Squares - I

8. Expected Mean Squares - II

9. Expected Mean Squares III & F-Tests

10. Bowling Results (a=4, b=15, n=14)

11. Estimating Population Mean Score

12. Simple Effects – Comparing Oil Patterns Within Bowlers

13. Marginal Effects – Comparing Oil Patterns Across Bowlers

14. Pairwise Comparisons Among Oil Patterns

15. Estimating Variance Components

16. Output from SAS PROC MIXED