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

Yoshifumi UKITA  Toshiyasu MATSUSHIMA  Shigeichi HIRASAWA  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E96-A   No.2   pp.658-662
Publication Date: 2013/02/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E96.A.658
Print ISSN: 0916-8508
Type of Manuscript: LETTER
Category: Digital Signal Processing
Keyword: 
analysis of variance,  Fourier transform,  mean square,  sum of squares,  

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Summary: 
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.