A note on the degrees of freedom in an experimental design model based on an orthonormal system

Yoshifumi Ukita, Toshiyasu Matsushima, Shigeichi Hirasawa

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Experiments usually aim to study how changes in various factors affect the response variable of interest. Since the response model used most often at present in experimental design is expressed through the effect of each factor, it is straightforward to ascertain how each factor affects the response variable. However, since the response model contains redundant parameters, we must calculate the degrees of freedom defined by the number of independent parameters in the analysis of variance. In this paper, we show that through a description of experimental design based on an orthonormal system, the response model can be expressed using only independent parameters. Hence, we do not have to calculate the degrees of freedom defined by the number of independent parameters.

Original languageEnglish
Title of host publication2011 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2011 - Conference Digest
Pages2181-2185
Number of pages5
DOIs
Publication statusPublished - 2011 Dec 23
Event2011 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2011 - Anchorage, AK, United States
Duration: 2011 Oct 92011 Oct 12

Publication series

NameConference Proceedings - IEEE International Conference on Systems, Man and Cybernetics
ISSN (Print)1062-922X

Other

Other2011 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2011
CountryUnited States
CityAnchorage, AK
Period11/10/911/10/12

Keywords

  • Fourier transform
  • analysis of variance
  • mean square
  • sum of squares

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Control and Systems Engineering
  • Human-Computer Interaction

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    Ukita, Y., Matsushima, T., & Hirasawa, S. (2011). A note on the degrees of freedom in an experimental design model based on an orthonormal system. In 2011 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2011 - Conference Digest (pp. 2181-2185). [6084000] (Conference Proceedings - IEEE International Conference on Systems, Man and Cybernetics). https://doi.org/10.1109/ICSMC.2011.6084000