Univariate Split-Plot Analysis

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Univariate Split-Plot Analysis

• 2003 LPGA Data

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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
Park
Kung
Ochoa
Pak
Webb
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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)

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Data Description and Model

• Let factor A be whole plot factor (round) with
  a4 levels and subscript i be associated with it
• Let factor B be block factor (tournament) with
  b8 levels and subscript j be associated with it
• Let factor C be subplot factor (golfer) with c6
  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)

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Data Description and Model
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Observed Means
Means of Golfer/Courses and Golfer/Rounds and
Courses/Rounds are on separate EXCEL spread sheet
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Analysis of Variance
There are significant differences among golfers,
none among rounds, nor a golfer by round
interaction
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Post-hoc Comparisons Among Golfers
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Post-Hoc Comparisons
Daniel (70.44)
Pak (69.50)
Park (69.59)
Kung (72.09)
Ochoa (71.34)
Webb (70.50)
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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 hasnt changed, but error terms have.
• The golfer effects are now random variables that
  we assume to be normal with variance sc2

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Expected Mean Squares (Fixed WP/Random SP)
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Testing for WP (Round) Fixed Effects
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Testing for SP Effects and WP/SP Interaction
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SAS Program (Fixed Effects Model)