共變異數分析之效率與樣本數計算

Abstract

ANCOVA是一種經常使用於教育和心理學研究的統計方法，目前已廣為各領域學者所使用，但仍是一種容易被誤用的統計方法。部分研究學者誤以為共變量的變異部分從組內的誤差變異扣除後，就能減少處理均差的標準誤及縮短估計區間寬度，這樣的誤會可能使得研究上的抽樣不足，導致ANCOVA的抽樣結果不一定比ANOVA的抽樣結果更正確。因此Liu利用效率指標計算出樣本數，計算多少樣本數足以確保使用共變量可以減少組內變異及增加研究的正確性，也就是說ANCOVA相對於ANOVA較有效率。而本文研究是計算各種參數組合下的樣本數，並計算實際保證機率來驗證其樣本數是否能達到目標保證機率。

ANCOVA is a statistical method which is often used in educational and psychological research. Today, it has been widely used in various fields of academics, but it is still easily misused. Some scholars mistakenly think that adding a covariate can reduce unexplained error variance, but the standard error of covariate-adjusted mean difference is not always smaller than that of the unadjusted mean difference. Actually, ANCOVA does not uniformly yield a smaller standard error or a shorter confidence interval for the treatment means comparison than does ANOVA. Such a misunderstanding may result in insufficient sample size, making the results of ANCOVA less accurate than the results of ANOVA. Therefore, Liu uses efficiency indicators to calculate sample size in order to ensure that using covariate can reduce variability and increase the accuracy of the research. In other words, Liu uses efficiency indicators to assure that ANCOVA is more efficient than ANOVA. In this study, all possible combinations of parameters are to calculate the sample size, and also examine the sample size formula whether it can achieve the desired guaranteed probability by the actual guaranteed probability.