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

Yoshifumi Ukita, Toshiyasu Matsushima, Shigeichi Hirasawa

    Research output: Contribution to journalArticle

    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, in the analysis of variance we must calculate the degrees of freedom defined by the number of independent parameters. In this letter, we propose the idea of calculating the degrees of freedom over the model based on an orthonormal system for the first time. In this way, we can easily obtain the number of independent parameters associated with any component, which reduces the risk of mistakes in the calculation of the number of independent parameters and facilitates the implementation of estimation procedures.

    Original languageEnglish
    Pages (from-to)658-662
    Number of pages5
    JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
    VolumeE96-A
    Issue number2
    DOIs
    Publication statusPublished - 2013 Feb

    Fingerprint

    Orthonormal System
    Experimental design
    Design of experiments
    Degree of freedom
    Model-based
    Analysis of variance (ANOVA)
    Analysis of variance
    Calculate
    Experiments
    Model
    Experiment

    Keywords

    • Analysis of variance
    • Fourier transform
    • Mean square
    • Sum of squares

    ASJC Scopus subject areas

    • Electrical and Electronic Engineering
    • Computer Graphics and Computer-Aided Design
    • Applied Mathematics
    • Signal Processing

    Cite this

    A study on the degrees of freedom in an experimental design model based on an orthonormal system. / Ukita, Yoshifumi; Matsushima, Toshiyasu; Hirasawa, Shigeichi.

    In: IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, Vol. E96-A, No. 2, 02.2013, p. 658-662.

    Research output: Contribution to journalArticle

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