Title :
A note on the degrees of freedom in an experimental design model based on an orthonormal system
Author :
Ukita, Yoshifumi ; Matsushima, Toshiyasu ; Hirasawa, Shigeichi
Author_Institution :
Dept. of Manage. Inf., Yokohama Coll. of Commerce, Yokohama, Japan
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.
Keywords :
Fourier transforms; design of experiments; linear algebra; degree of freedom; experimental design model; independent parameters; orthonormal system; redundant parameters; response model; Analysis of variance; Analytical models; Business; Educational institutions; Estimation; Fast Fourier transforms; Fourier transform; analysis of variance; mean square; sum of squares;
Conference_Titel :
Systems, Man, and Cybernetics (SMC), 2011 IEEE International Conference on
Conference_Location :
Anchorage, AK
Print_ISBN :
978-1-4577-0652-3
DOI :
10.1109/ICSMC.2011.6084000