多變數離散觀念的起源和發展

統計是一種研究的科學方法，其目的之一，是期望能從實際觀察的資料裏，歸納出能描述全部資料的少數概念。變異數(Variance)是統計分析上一個很重要的概念。Fisher(1973)曾以變異數的概念定義統計。

In order to solve the difficulty of interpreting variance of correlated variables， generalized variance and total variance approaches have been used to summarize covariance matrix into a single number as univariate variance generalization. the purpose of this paper is to trace the origin and development of the two methods. Discussion also focuses on the generalization of η2 to multivariate analysis as explained variance concept， and Wilks two maximum likelihood indices U and Λ. Three numerical examples were utilized to demonstrate the similarities and discrepences resulted from the two models. It was known that there is a relationship between generalized variance and total variance in their application in statistical analysis. The paper also briefly reviewed Miller’s complete model as possible compensation of total variance approach. *The entire paper is available in English version from the author.