Identifying significant effects in fractional factorial single and multiresponse experiments

Summary

A forward selection procedure for identifying active contrasts in unreplicated factorial multiresponse
experiments is presented. To test the multivariate effects, p values are calculated by Monte Carlo
sampling; the ordinary Hotelling’s T2 test is a special case. Collinear responses are effectively handled
by successive principal-component decompositions, as when, for instance, the number of response
variables exceeds the number of observations. In the univariate case, the test statistic pools the smallest
effects as error. Independent sources for error degrees of freedom can be incorporated. The method is
illustrated with examples from baguette and mayonnaise production.

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DOI : doi.org/10.1198/00401700152672...