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Two-Way Mixed ANOVA of Women's PBA 2009 Data: Analyzing Oil Patterns and Bowlers’ Performance

This study investigates the performance of 15 professional women bowlers during qualifying rounds of the Women’s Professional Bowling Association at Alan Park, Michigan, in 2009. Utilizing a two-way mixed analysis of variance (ANOVA), the analysis examines how different oil patterns (Viper, Chameleon, Scorpion, Shark) affect bowler performance, measured by total pins across multiple games. The study includes statistical modeling of expected means, variances, mean squares, and pairwise comparisons to draw insights into variance components and oil pattern effects on scores.

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Two-Way Mixed ANOVA of Women's PBA 2009 Data: Analyzing Oil Patterns and Bowlers’ Performance

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  1. 2-Way Mixed Analysis of Variance Women’s PBA - 2009

  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=DiandraAbaty, 2=ShalinZulkiffi, 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

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