平均數事前比較的重要性及其統計方法

The Importance and Statistical Procedures of Priori Comparisons among Means

變異數分析(analysis of variance, ANOVA)統計方法，目前已被廣泛的應用於各種學術領域。過去國內一些研究者在使用這種統計方法時，習慣採用綜合的F考驗，如果發現F考驗達統計的顯著(Statistical significance)則繼續進行事後比較(Post hoc Comparison)，若無顯著，則告一段落。不可否認的，這種作法對於探究性的研究極為有用M，但有些研究應該使用計畫性的比較(Planned comparison)或稱事前的比較(Priori comparison)較具科學價值。
本文旨在敘述事前比較的意義、重要性、統計方法以及與統計方法有密切關係的錯誤率的問題，其中包括下列三種統計方法：(1)多重t考驗(Multiple t tests)，(2)正交比較(Orthogonal contrasts)，(3)杜納考驗(Dunn's tests)

The analysis of variance (ANOVA) currently enjoys the status of being probably the most uSed (some would say abused) statistical technique in every field of research. In the past， when this procedure was used， from the very begining researchers usually ran an overall F-test. If a significant F value was obtained， what they would have shown was simply that the overall null hypothesis was false and continue to run post hoc comparisons to investigate hypothesis involving means of individual groups or sets of groups. On the other hand， If the overall F value was not significant， then the procedure was brought to an end. While post hoc comparisons are important in actual research， especially for exploring one's data and for getting leads for future research， the method of priori comparisons is perhaps more powerful and of greater scientific value.bThe purposes of this article are : (1) to describe the meanning and importance of priori comparisons and related error rate and (2) to introduce the priori comparison procedures of multiple t test， orthognoal contrasts， and Dunn's test.