A Study on the Degrees of Freedom in an Experimental Design Model Based on an Orthonormal System

• UKITA Yoshifumi

  Department of Management Information, Yokohama College of Commerce

• MATSUSHIMA Toshiyasu

  Department of Applied Mathematics, Waseda University

• HIRASAWA Shigeichi

  Research Institute for Science and Engineering, Waseda University

抄録

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.

収録刊行物

• IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

  IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E96.A (2), 658-662, 2013

  一般社団法人 電子情報通信学会

キーワード

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

詳細情報

• CRID: 1390282681286445824
• NII論文ID: 10031167165
• NII論文ID: 130003370561
• NII書誌ID: AA10826239
• DOI: 10.1587/transfun.e96.a.658
• ISSN: 17451337
• ISSN: 09168508
• Web Site: https://www.jstage.jst.go.jp/article/transfun/E96.A/2/E96.A_658/_pdf
• 本文言語コード: en
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