組內相關係數之費雪轉換區間估計與樣本數計算

Abstract

組內相關係數(ICC)s在許多社會科學研究上是不可或缺的一部分，為衡量組間變異和組內變異的相關程度，本研究從組內相關係數的數種近似公式中選取了兩種較方便計算的估計式來加以討論，主要是因為對文獻中所計算出來樣本數的數據有所疑惑，而其作者也並未利用各種方式來加以佐證。所以本研究使用所選取的兩種估計法來計算最佳樣本數，並利用各種情境下的模擬結果輔以單尾信賴區間和雙尾信賴區間覆蓋率，來探討最佳樣本數的取得和兩種方法的使用時機，希望能對往後使用組內相關係數(ICC)s為研究方法的研究者做為使用上的參考。

ICCs is an indispensable part of social science research, it has to use the F-distribution through the computing process, it seems pretty hard to find the optimal sample size in some specific situations, so the domestic and foreign researchers have debated on the ICCs estimator for many years. Mostly, researchers choose to use the normal distribution because the normal distribution is relatively easy to use to find the confidence interval and optimal sample size. This article is based on the theory which proposed by Bonett (2002) , he used the formula to compute the sample size, however, he didn't show the confidence interval as a proof, so this research use two method to compute the optimal sample size and further compare to the original method. I also use the simulation to develop the confidence interval coverage to help me discuss the optimal sample size and the timing of using these two methods. I hope that I can provide more information for those researchers who use the ICCs as the research meth-od.