A note on ANOVA in an experimental design model based on an orthonormal system

Yoshifumi Ukita*, Toshiyasu Matsushima, Shigeichi Hirasawa

*この研究の対応する著者

研究成果: Conference contribution

1 被引用数 (Scopus)

抄録

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.

本文言語English
ホスト出版物のタイトルProceedings 2012 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2012
ページ1990-1995
ページ数6
DOI
出版ステータスPublished - 2012 12 1
イベント2012 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2012 - Seoul, Korea, Republic of
継続期間: 2012 10 142012 10 17

出版物シリーズ

名前Conference Proceedings - IEEE International Conference on Systems, Man and Cybernetics
ISSN(印刷版)1062-922X

Other

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

ASJC Scopus subject areas

  • 電子工学および電気工学
  • 制御およびシステム工学
  • 人間とコンピュータの相互作用

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