1. Univariate Split-Plot Analysis 2003 LPGA Data

2. Background Information 6 Golfers (Treated as only 6 of interest  Fixed) 8 Tournaments (Treated as random sample of all possible tournaments) 4 Rounds per tournament (fixed factor) Daniel KungOchoaPak Park Webb

3. Data Description and Model Tournaments act as blocks. They are each associated with a particular golf course, region and weather pattern (they may differ significantly in terms of difficulty) Tournaments are made up of Rounds (these tournaments are all 4 rounds). It is impossible to break up rounds within blocks, thus they are the whole plot factor (in an experiment, the treatments would be randomly assigned to whole plots) Golfers all play rounds on the same day (all play round 1, then 2, etc), thus they are the subplot factor (in an experiment, their positions would be assigned at random within whole plots)

4. Data Description and Model Let factor A be whole plot factor (round) with a=4 levels and subscript i be associated with it Let factor B be block factor (tournament) with b=8 levels and subscript j be associated with it Let factor C be subplot factor (golfer) with c=6 levels and subscript k be associated with it Interaction between round and tournament allows for climate effects to vary across courses (WP error term) Interaction between golfer and round allows golfer skill to vary across rounds (e.g. pressure effects) Model assumes no tournament by golfer interaction (can be tested) or 3-way interaction (SP error term)

5. Data Description and Model

6. Observed Means Means of Golfer/Courses and Golfer/Rounds and Courses/Rounds are on separate EXCEL spread sheet

7. Analysis of Variance There are significant differences among golfers, none among rounds, nor a golfer by round interaction

8. Post-hoc Comparisons Among Golfers

9. Post-Hoc Comparisons Daniel (70.44) Kung (72.09)Ochoa (71.34) Pak (69.50)Park (69.59) Webb (70.50)

10. Another Possibility - Mixed Model In reality, there are hundreds of golfers that are “certified” members of LPGA Re-analyze the data as a mixed model (rounds are still fixed) ANOVA hasn’t changed, but error terms have. The golfer effects are now random variables that we assume to be normal with variance  c 2

11. Expected Mean Squares (Fixed WP/Random SP)

12. Testing for WP (Round) Fixed Effects

13. Testing for SP Effects and WP/SP Interaction

14. SAS Program (Fixed Effects Model)