A note on ANOVA 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

1 Citation (Scopus)

Abstract

Experiments usually aim to study how changes in various factors affect the response variable of interest. Since the model used most often at present in experimental design is expressed through the effect of each factor, it is easy to understand how each factor affects the response variable. However, since the model contains redundant parameters, a considerable amount of time is often necessary to implement the procedure for estimating the effects. On the other hand, it has recently been shown that the model in experimental design can also be expressed in terms of an orthonormal system. In this case, the model contains no redundant parameters. Moreover, the theorem with respect to the sum of squares for the 2-factor interaction, needed in the analysis of variance (ANOVA) has been obtained. However, 3-factor interaction is often to be considered in real cases, but the theorem with respect to the sum of squares for the 3-factor interaction has not been obtained up to now. In this paper, we present the theorem with respect to the sum of squares for the 3-factor interaction in a model based on an orthonormal system. Furthermore, we can also obtain the theorem for interactions with 4 or more factors by the similar proof. Hence, in any real case, we can execute ANOVA in the model based on an orthonormal system.

Original languageEnglish
Title of host publicationProceedings 2012 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2012
Pages1990-1995
Number of pages6
DOIs
Publication statusPublished - 2012 Dec 1
Event2012 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2012 - Seoul, Korea, Republic of
Duration: 2012 Oct 142012 Oct 17

Publication series

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

Other

Other2012 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2012
CountryKorea, Republic of
CitySeoul
Period12/10/1412/10/17

Keywords

  • Analysis of variance
  • Bandlimited function
  • Design for experiments
  • Estimation
  • Fourier transforms
  • Sampling theorem

ASJC Scopus subject areas

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

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  • Cite this

    Ukita, Y., Matsushima, T., & Hirasawa, S. (2012). A note on ANOVA in an experimental design model based on an orthonormal system. In Proceedings 2012 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2012 (pp. 1990-1995). [6378030] (Conference Proceedings - IEEE International Conference on Systems, Man and Cybernetics). https://doi.org/10.1109/ICSMC.2012.6378030