Isolation of Degrees of Freedom for Box-Behnken Designs

The Box-Behnken three-level designs have proved useful for fitting second-order response surfaces to experimental data. Here, we discuss an aspect of their value in the detection of lack of model fit. The degrees of freedom in excess of those needed to fit the model can be used advantageously for co...

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Bibliographic Details
Published in:Technometrics 1994-08, Vol.36 (3), p.283-291
Main Authors: Draper, Norman R., Davis, Timothy P., Pozueta, Lourdes, Grove, Daniel M.
Format: Article
Language:English
Subjects:
Coefficients
Degrees of freedom
Detection of model bias
Engines
Exact sciences and technology
Experiment design
Experimental design
Factorial design
Lack of fit
Mathematics
Parametric models
Polynomials
Probability and statistics
Sciences and techniques of general use
Second-order models
Statistics
Three-level designs
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Summary:The Box-Behnken three-level designs have proved useful for fitting second-order response surfaces to experimental data. Here, we discuss an aspect of their value in the detection of lack of model fit. The degrees of freedom in excess of those needed to fit the model can be used advantageously for contrasts which estimate certain higher-order departures from the model. These can be expressed in various forms. Some forms, in which these contrasts are orthogonal, permit the plotting of the contrasts in a normal plot for easy detection of model bias.
ISSN:0040-1706
1537-2723
DOI:10.1080/00401706.1994.10485805