Analyzing designed experiments with multiple responses
Journal : Journal of Applied Statistics , vol. 34 , p. 1275–1296 , 2007
International Standard Numbers
Printed : 0266-4763
Electronic : 1360-0532
Publication type : Academic article
Issue : 10
DOI : doi.org/10.1080/02664760701594...
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This paper is an overview of a unified framework for analyzing designed experiments with univariate or multivariate responses. Both categorical and continuous design variables are considered. To handle unbalanced data, we introduce the so-called Type II* sums of squares. This means that the results are independent of the scale chosen for continuous design variables. Furthermore, it does not matter whether two-level variables are coded as categorical or continuous. Overall testing of all responses is done by 50-50 MANOVA, which handles several highly correlated responses. Univariate p-values for each response are adjusted by using rotation testing. To illustrate multivariate effects, mean values and mean predictions are illustrated in a principal component score plot or directly as curves. For the unbalanced cases, we introduce a new variant of adjusted means, which are independent to the coding of two-level variables. The methodology is exemplified by case studies from cheese and fish pudding production.