分散分析における1公式について

Abstract

The formula for the analysis of variance in the case of two variables of ciassification with repeated measurements in each cell is not unique. According to the probability-model, some formulas are right but some are wrong. Namely, when the interaction exists, even in the orthogonal case, the formula for the variance-ratio (F-ratio) may be written in two ways ; one has the interaction mean-square as its denominator while the other has tbe within-groups mean-square as its denominator. In this study I have discussed which method would be more reasonable in ordinary experiments. The conclusion is as follows :
Only in the model I (systematic set-up) the former is usable, but in the model II (random-set-up) the latter should be used.