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 publicationConference Proceedings - IEEE International Conference on Systems, Man and Cybernetics
    Pages2181-2185
    Number of pages5
    DOIs
    Publication statusPublished - 2011
    Event2011 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2011 - Anchorage, AK
    Duration: 2011 Oct 92011 Oct 12

    Other

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

    Fingerprint

    Design of experiments
    Analysis of variance (ANOVA)
    Experiments

    Keywords

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

    ASJC Scopus subject areas

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

    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 Conference Proceedings - IEEE International Conference on Systems, Man and Cybernetics (pp. 2181-2185). [6084000] 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.

    Conference Proceedings - IEEE International Conference on Systems, Man and Cybernetics. 2011. p. 2181-2185 6084000.

    Research output: Chapter in Book/Report/Conference proceedingConference 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 Conference Proceedings - IEEE International Conference on Systems, Man and Cybernetics., 6084000, pp. 2181-2185, 2011 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2011, Anchorage, AK, 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 Conference Proceedings - IEEE International Conference on Systems, Man and Cybernetics. 2011. p. 2181-2185. 6084000 https://doi.org/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. Conference Proceedings - IEEE International Conference on Systems, Man and Cybernetics. 2011. pp. 2181-2185
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