Cubic Lack of Fit for Three-Level Second Order Response Surface Designs.
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WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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A recent paper by Box and Draper 1982 discussed the detection of cubic lack of fit in second order composite design experiments, and its possible removal by the use of power transformations in the predictor variables. The designs examined were five-level designs whose coded predictor variables could assume levels -alpha, -1, 0, 1, alpha for alpha not equal 1 and, typically, alpha equal 1. When alpha equal 1, only three levels exist in the design and certain singularities occur. Cubic interaction contrasts exist, but it becomes impossible to estimate the power transformations, as previously when alpha not equal 1. This note describes how this happens. Author
- Statistics and Probability