單因子隨機效果模型下樣本數與檢定力計算

Abstract

在傳統變異數分析的研究上，容易忽略組內相關系數ICC 的存在，可能會使得組內 誤差變異數放大，故增加隨機效果後的變異數分析模型，將更精確測量組內資料相似性 或不獨立性的問題。在研究中樣本數的決定是重要的一環，如何決定最適化樣本數以提 供有用的資訊推論母體，為本文章主要貢獻。本文中樣本數的計算，是透過假設檢定法 使用正式F 分佈並固定其顯著水準及檢定力求得，當樣本數被計算出來並搭配成本函數 即可計算出最適化樣本數，而在文獻中以近似公式計算所需樣本數，我們對此部分進行 比對驗證，本篇研究使用統計軟體SAS 以IML 程式進行運算。

Concerning the field of study in the traditional analysis of variance, the intraclass correlation coefficient (ICC) is easily ignored, and this may amplify the group error variance. As a consequence, using the random effects ANOVA model, will measure the group similarity independence more accurately. The sample size is an essential key to infer the population, which I lay emphasis on. Via testing hypothesis method, I tend to use formal F distribution to calculate the sample size by fixing the level of significance and power. When the sample size is calculated with the cost function; thereupon the optimal sample size can be calculated. We confirm the accuracy of the previous reviews when exploring this part of this study by the statistical software SAS iteration operation to calculate the result.