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

Yoshifumi Ukita; Toshiyasu Matsushima; Shigeichi Hirasawa

doi:10.1109/ICSMC.2011.6084000

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

Yoshifumi Ukita^*, Toshiyasu Matsushima, Shigeichi Hirasawa

^*Corresponding author for this work

School of Fundamental Science and Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference 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 language	English
Title of host publication	2011 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2011 - Conference Digest
Pages	2181-2185
Number of pages	5
DOIs	https://doi.org/10.1109/ICSMC.2011.6084000
Publication status	Published - 2011 Dec 23
Event	2011 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2011 - Anchorage, AK, United States Duration: 2011 Oct 9 → 2011 Oct 12

Publication series

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

Other

Other	2011 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2011
Country/Territory	United States
City	Anchorage, AK
Period	11/10/9 → 11/10/12

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

Access to Document

10.1109/ICSMC.2011.6084000

Cite this

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). Article 6084000 (Conference Proceedings - IEEE International Conference on Systems, Man and Cybernetics). https://doi.org/10.1109/ICSMC.2011.6084000

A note on the degrees of freedom in an experimental design model based on an orthonormal system. / Ukita, Yoshifumi; Matsushima, Toshiyasu; Hirasawa, Shigeichi.
2011 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2011 - Conference Digest. 2011. p. 2181-2185 6084000 (Conference Proceedings - IEEE International Conference on Systems, Man and Cybernetics).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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., 6084000, Conference Proceedings - IEEE International Conference on Systems, Man and Cybernetics, pp. 2181-2185, 2011 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2011, Anchorage, AK, United States, 11/10/9. https://doi.org/10.1109/ICSMC.2011.6084000

Ukita Y, Matsushima T, Hirasawa S. 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. 2011. p. 2181-2185. 6084000. (Conference Proceedings - IEEE International Conference on Systems, Man and Cybernetics). doi: 10.1109/ICSMC.2011.6084000

Ukita, Yoshifumi ; Matsushima, Toshiyasu ; Hirasawa, Shigeichi. / A note on the degrees of freedom in an experimental design model based on an orthonormal system. 2011 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2011 - Conference Digest. 2011. pp. 2181-2185 (Conference Proceedings - IEEE International Conference on Systems, Man and Cybernetics).

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

Abstract

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Keywords

ASJC Scopus subject areas

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