摘要
多變項變異數分析在教育，心理，行為，或社會科學方面的研究上，極為廣汎地被研究者採用來做計量效果差異分析的依據，然而，在所有介紹多變項變異數分析法的國外教科書中，大多僅就總括性的考驗（Omnibus test）做介紹，僅有少數提及在總括性考驗測得顯著差異後，進行事後追蹤比較的方法。又在這些介紹多變項事後追蹤比較方法的書籍中，幾乎千篇一律地集中在多重比較考驗的統計值本身，專注在控制第一類型錯誤的情境下，是否能夠正確地拒絕多重比較的虛無假設。至於在拒絕虛無假設後，到底吾人應該怎樣解釋平均數間的差異狀況呢？在回答這樣的問題時，時下通行的事後追蹤方法多為使用單變項變異數分析（ANOVA）針對各別依變項加以檢驗，即或使用Roy-Bose（1953）所提出的多變項同時推論（simultaneous inference）手續來計算多重比較之統計考驗值，下結論時仍是就各依變項逐一解釋，完全喪失多變項變異數分析要將組間之差異情形在多維依變項空間中做一個系統化解釋的原意。本篇論文先就時下盛行的後續追蹤方式加以批判，而後提出一套能夠將組間差異狀況在真正多變項分析（truely multivariate）的架構下具體化地解釋出來的方法，使用本篇論文所介紹的方法將可具體化地回答下列三個問題：（1）組間差異狀況是否可用一個或數個潛在特質（underlying construct）來加以解釋？如果可以，那麼這樣的潛在特質所代表的意義又是什麼？（2）個別依變項在全體其他依變項存在的狀況下，它們的相對重要性如何？（3）吾人是否可將多變項多重比較的效果，就前兩個問題加以解釋？以上的問題，都不是時下所採用的後續追蹤法所能顯示的。最後，本篇論文以一實際研究之資料情境，說明如何在多變項變異數分析的架構下進行資料分析與詮釋。
關鍵字
無資料並列摘要
This paper presents the multivariate statistical procedure, MANOVA, in a non-traditional way unfamiliar to most educational researchers. Whereas traditional way of using MANOVA has been viewed only as a preliminary test for safeguarding the experimentwise type I error rate for conducting the individual univariate tests, the non-traditional way as presented in this paper seeks to explain the grouping variable effect in a truely ”multivariate” framework. A challenge was made to the logic of traditional use of MANOVA with respect to both experimentwise type I error rate and statistical power.It was argued that all traditional MANOVA follow-up procedures fail to interpret the MANOVA effect in a multivariate context. For remedying the traditional procedures, some extensions were proposed through the use of discriminant analysis statistical procedure. These extensions were made in three perspectives: searching for underlying dimensions, determining relative variable importance, and conducting multivariate group contrasts.Finally, the techniques discussed in the paper were used to illustrate a real life research scenario. The example study attempts to investigate the differences of opinion as expressed by community residents, teachers, and school principals in a recent mail survey in Hualien area. Our analyses indicated that two underlying attitudes were present which could be accountable for the differences of opinion among these three categories of people: an apathetic attitude toward school-community relationship and the attitude toward schools providing extra-curriculum services for the community residents. None of our findings could have been reached with the traditional MANOVA follow-up procedures.