Split-Plot and 3Level - should be analyzed as such 3 K...

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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
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Unformatted text preview: should be analyzed as such 3 K 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 ε β + + + + + + = 2 2 22 2 1 11 2 1 12 2 2 1 1 ˆ x x x x x x y 3 K 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 2 K design can show if curvature exists and is cheaper than running a 3K design. 3 K Designs • Main effects have 2 df’s • 2 factor interactions have 4 df’s (SS AB for LXL, LXQ, QXL and QXQ effects) • 3 factor interactions have 8 df’s • For n replicates, there n*3 K-1 total df’s + 3 K (n-1) df’s for error...
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