Identifying Significant Effects in Fractional Factorial Multiresponse Experiments

Abstract

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.

KEY WORDS :

• Active factors
• Experimental design
• Monte carlo testing
• Multiple response
• Subset selection
• Unreplicated fractional factorials