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Analyzing Designed Experiments with Multiple Responses

Author

Listed:
  • Øyvind Langsrud
  • Kjetil Jørgensen
  • Ragni Ofstad
  • Tormod Næs

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.

Suggested Citation

  • Øyvind Langsrud & Kjetil Jørgensen & Ragni Ofstad & Tormod Næs, 2007. "Analyzing Designed Experiments with Multiple Responses," Journal of Applied Statistics, Taylor & Francis Journals, vol. 34(10), pages 1275-1296.
    • Handle: RePEc:taf:japsta:v:34:y:2007:i:10:p:1275-1296
    DOI: 10.1080/02664760701594246
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    References listed on IDEAS

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    1. Langsrud, Oyvind & Naes, Tormod, 1998. "A unified framework for significance testing in fractional factorials," Computational Statistics & Data Analysis, Elsevier, vol. 28(4), pages 413-431, October.
    2. J. A. Nelder, 2000. "Functional marginality and response-surface fitting," Journal of Applied Statistics, Taylor & Francis Journals, vol. 27(1), pages 109-112.
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    Cited by:

    1. Angelo Del Giudice & Andrea Acampora & Enrico Santangelo & Luigi Pari & Simone Bergonzoli & Ettore Guerriero & Francesco Petracchini & Marco Torre & Valerio Paolini & Francesco Gallucci, 2019. "Wood Chip Drying through the Using of a Mobile Rotary Dryer," Energies, MDPI, vol. 12(9), pages 1-16, April.

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