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Lecture 4B - Introduction to Factorial Designs Centerpoints...

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Introduction to Factorial Designs Centerpoints © Diane Schaub, University of Florida Lecture4B.ppt
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Centerpoints When we are not certain of linearity in the factor effects, we may want to consider the addition of centerpoints to the design Our interaction terms do provide some degree of curvature induced by the Β ij x i x j terms in the model ∑∑ = < + + + = k j j i j i ij j j x x B x B B y 1 0 ε Eqn 6-26
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Model Inadequacy In some cases the response function won’t be adequately modeled by Eqn 6-26, so we must add a pure second-order term Β jj x j 2 We then create a second-order response surface model ∑∑ = < = + + + + = k j j i k j j jj j i ij j j x B x x B x B B y 1 1 2 0 ε Eqn 6-27
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Addition of Centerpoints If we replicate certain points in a 2k design, we: 1. have protection against curvature from second order effects, i.e., check for non-linearity 2. allow an independent estimate of error to be obtained 3.
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