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 publicationConference Proceedings - IEEE International Conference on Systems, Man and Cybernetics
    Pages1990-1995
    Number of pages6
    DOIs
    Publication statusPublished - 2012
    Event2012 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2012 - Seoul
    Duration: 2012 Oct 142012 Oct 17

    Other

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

    Fingerprint

    Analysis of variance (ANOVA)
    Design of experiments
    Experiments

    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

    Cite this

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

    A note on ANOVA in an experimental design model based on an orthonormal system. / Ukita, Yoshifumi; Matsushima, Toshiyasu; Hirasawa, Shigeichi.

    Conference Proceedings - IEEE International Conference on Systems, Man and Cybernetics. 2012. p. 1990-1995 6378030.

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

    Ukita, Y, Matsushima, T & Hirasawa, S 2012, A note on ANOVA in an experimental design model based on an orthonormal system. in Conference Proceedings - IEEE International Conference on Systems, Man and Cybernetics., 6378030, pp. 1990-1995, 2012 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2012, Seoul, 12/10/14. https://doi.org/10.1109/ICSMC.2012.6378030
    Ukita Y, Matsushima T, Hirasawa S. A note on ANOVA in an experimental design model based on an orthonormal system. In Conference Proceedings - IEEE International Conference on Systems, Man and Cybernetics. 2012. p. 1990-1995. 6378030 https://doi.org/10.1109/ICSMC.2012.6378030
    Ukita, Yoshifumi ; Matsushima, Toshiyasu ; Hirasawa, Shigeichi. / A note on ANOVA in an experimental design model based on an orthonormal system. Conference Proceedings - IEEE International Conference on Systems, Man and Cybernetics. 2012. pp. 1990-1995
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