Analyzing Designed Experiments with Multiple Responses

Øyvind Langsrud, Kjetil Jørgensen, Ragni Ofstad and Tormod Naes

Journal of Applied Statistics, 2007, vol. 34, issue 10, pages 1275-1296

Abstract: 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.

Keywords: 50-50 MANOVA; general linear model; least-squares means; multiple testing; principal component; rotation test; unbalanced factorial design (search for similar items in EconPapers)

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