A Study on the Degrees of Freedom in an Experimental Design Model Based on an Orthonormal System
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概要
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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.
著者
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UKITA Yoshifumi
Department of Management Information, Yokohama College of Commerce
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MATSUSHIMA Toshiyasu
Department of Applied Mathematics, Waseda University
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HIRASAWA Shigeichi
Research Institute for Science and Engineering, Waseda University, and Cyber University
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Ukita Yoshifumi
Department Of Management Information Yokohama College Of Commerce
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HIRASAWA Shigeichi
Research Institute for Science and Engineering, Waseda University
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- A Study on the Degrees of Freedom in an Experimental Design Model Based on an Orthonormal System