TY - GEN
T1 - A note on ANOVA in an experimental design model based on an orthonormal system
AU - Ukita, Yoshifumi
AU - Matsushima, Toshiyasu
AU - Hirasawa, Shigeichi
PY - 2012/12/1
Y1 - 2012/12/1
N2 - Experiments usually aim to study how changes in various factors affect the response variable of interest. Since the model used most often at present in experimental design is expressed through the effect of each factor, it is easy to understand how each factor affects the response variable. However, since the model contains redundant parameters, a considerable amount of time is often necessary to implement the procedure for estimating the effects. On the other hand, it has recently been shown that the model in experimental design can also be expressed in terms of an orthonormal system. In this case, the model contains no redundant parameters. Moreover, the theorem with respect to the sum of squares for the 2-factor interaction, needed in the analysis of variance (ANOVA) has been obtained. However, 3-factor interaction is often to be considered in real cases, but the theorem with respect to the sum of squares for the 3-factor interaction has not been obtained up to now. In this paper, we present the theorem with respect to the sum of squares for the 3-factor interaction in a model based on an orthonormal system. Furthermore, we can also obtain the theorem for interactions with 4 or more factors by the similar proof. Hence, in any real case, we can execute ANOVA in the model based on an orthonormal system.
AB - Experiments usually aim to study how changes in various factors affect the response variable of interest. Since the model used most often at present in experimental design is expressed through the effect of each factor, it is easy to understand how each factor affects the response variable. However, since the model contains redundant parameters, a considerable amount of time is often necessary to implement the procedure for estimating the effects. On the other hand, it has recently been shown that the model in experimental design can also be expressed in terms of an orthonormal system. In this case, the model contains no redundant parameters. Moreover, the theorem with respect to the sum of squares for the 2-factor interaction, needed in the analysis of variance (ANOVA) has been obtained. However, 3-factor interaction is often to be considered in real cases, but the theorem with respect to the sum of squares for the 3-factor interaction has not been obtained up to now. In this paper, we present the theorem with respect to the sum of squares for the 3-factor interaction in a model based on an orthonormal system. Furthermore, we can also obtain the theorem for interactions with 4 or more factors by the similar proof. Hence, in any real case, we can execute ANOVA in the model based on an orthonormal system.
KW - Analysis of variance
KW - Bandlimited function
KW - Design for experiments
KW - Estimation
KW - Fourier transforms
KW - Sampling theorem
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U2 - 10.1109/ICSMC.2012.6378030
DO - 10.1109/ICSMC.2012.6378030
M3 - Conference contribution
AN - SCOPUS:84872425981
SN - 9781467317146
T3 - Conference Proceedings - IEEE International Conference on Systems, Man and Cybernetics
SP - 1990
EP - 1995
BT - Proceedings 2012 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2012
T2 - 2012 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2012
Y2 - 14 October 2012 through 17 October 2012
ER -