SplitPlot Designs

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Split-Plot Designs

• Is a method of dealing with restricted
  randomization within blocks
• Takes it name from agricultural roots
• Example Paper Tensile Strength (Table 13-14)
• A Preparation method (3 levels)
• B Temperature (4 levels)
• Three replicates, blocked as one replicate per
  day.
• Regular factorial approach would be randomly
  picking within the 12 tests per day
• Split-plot approach is
• make a batch using a random level of A, then
  test those at 4 temps

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Savings from Split-Plot

• By using the Split-plot approach for this expt,
  only 3 batches were made per day, rather than 12.
• Replicate (random) and prep method are considered
  whole plots, temperature is a split plot (both
  prep and temp are fixed vars)
• In the model, include all three factors, and the
  2-way interactions, but remember that the day
  (which is our replicate) is a block var, and
  should be analyzed as such

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3K Designs

• 3 Levels of k factors
• (low, medium, high) or
• (-1 , 0 , 1)
• (See figures 9-1, 9-2)
• From the designs where all factors are
  quantitative, we can create a regression model.
  For 2 factors, this would be

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3K Designs

• Note, however, if you have a quadratic design
  (one with curvature), it is more effective to use
  an RSM design.
• Also, centerpoints in a 2K design can show if
  curvature exists and is cheaper than running a 3K
  design.

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3K Designs

• Main effects have 2 dfs
• 2 factor interactions have 4 dfs (SSAB for LXL,
  LXQ, QXL and QXQ effects)
• 3 factor interactions have 8 dfs
• For n replicates, there n3K-1 total dfs
  3K(n-1) dfs for error