2-Way Mixed Analysis of Variance Women’s PBA

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)

Statistical Model

Covariance Structure / ANOVA (Unrestricted Model)

Expectations and Variances of Means - I

Expectations and Variances of Means - II

Expected Mean Squares - I

Expected Mean Squares - II

Expected Mean Squares III & F-Tests

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

Estimating Population Mean Score

Simple Effects – Comparing Oil Patterns Within Bowlers

Marginal Effects – Comparing Oil Patterns Across Bowlers

Pairwise Comparisons Among Oil Patterns

Estimating Variance Components

Output from SAS PROC MIXED