| タイトル | A Note on ANOVA in an Experimental Design Model Based on an Orthonormal System |
|---|---|
| 著者 | 浮田善文 、松嶋敏泰 、平澤茂一 |
| 年度 | 2012 |
| 形式 | 国際学会 |
| 分野 | 知識情報処理 |
| 掲載雑誌名 | 2012 IEEE International Conference on Systems, Man, and Cybernetics (SMC 2012) |
| 掲載号・ページ | pp.1990-1995, Seoul, Korea |
| 掲載年 | 2012 |
| 掲載月 | 10 |
| アブスト （日本語） |
2012 IEEE International Conference on Systems, Man, and Cybernetics (SMC 2012) 2012年10月14日～17日 Seoul, Korea |
| アブスト （英語） |
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. |
| 備考 （日本語） |
1 |
| 備考 （英語） |
1 |
| 論文原稿 | |
| 発表資料 |
