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Langsrud, Ø., Jørgensen, K., Ragni Ofstad, R. and Næs, T. (2007), Analyzing Designed Experiments with Multiple Responses, Journal of Applied Statistics, 34, 1275-1296. [ PDF]

Author Posting. (c) Taylor & Francis, 2007. This is the author's version of the work. It is posted here by permission of Taylor & Francis for personal use, not for redistribution. The definitive version was published in Journal of Applied Statistics, Volume 34 Issue 10, December 2007. doi:10.1080/02664760701594246

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.

KEY WORDS: 50-50 MANOVA, General linear model, Least-squares means, Multiple testing, Principal component, Rotation test, Unbalanced factorial design.