協和配對樣本在McNemar檢定中的角色扮演探討

Abstract

如果我們想要就一組相依樣本前後兩次調查所得到的比例是否有所差異進行探討，最常用的方法莫過於 McNemar 的檢定方法。然而 McNemar 檢定統計量基本上是一個非協和配對樣本的函數，與協和配對樣本完全無關。這個與直覺有些不符的想法，常常造成實際應用的困擾。在此計畫中，我們藉由絕對多數和相對多數的思考模式來重新詮釋此一問題。此外我們也推導出一個新的統計量，並利用模擬實驗與 McNemar 檢定來作比較。

When data arise as matched binary pairs, it is often of interest to compare the two correlated binomial proportions. McNemar`s test is perhaps the best known for this matter. McNemar`s test statistic itself, however, has nothing to do with the concordant pairs. It is somewhat counter-intuitive, and often frustrating for practitioners to learn that only the discordant pairs are necessary, given the effort to collect all the data. In this study, we clearify the ambiguity through the concept of the majority preference. We also derive a new test statistic and compare its small-sample behavior with McNemar`s test through simulation.