共變異數分析之共變量係數檢定力與樣本數計算

Abstract

抽樣之樣本數大小是許多領域在研究時所關注的議題，若能掌握最適樣本數便能替研究省下人力、物力之成本，而共變異數分析因能降低膨脹均方誤差，使研究結果更為精準，成為廣泛應用的統計模型，故本論文以共變異數分析模型中的共變量係數為主體，進行檢定力分析及最適樣本數的推估。以SAS/IML建構出檢定力函數，並求得不同條件組合下之最適樣本數後，於兩隨機常態母體中隨機抽出該樣本數之樣本進行模擬，觀察理論的最適樣本數是否達成目標檢定力，並判斷理論公式及模擬情況是否正確，結果顯示出本論文之樣本數公式達成正確性，樣本數也較為精確。

Sample size is one of concerned issue in many fields of research. If researchers can master the technique of the optimum sample size for their study, they will save a lot of cost of human resources and time. However, analysis of covariance is a statistical model in wide use because it can reduce the inflated mean squared error and make the outcome more accurate. Based on this, we use the power analysis of coefficient of covariate to infer the optimum sample size. In the dissertation, the SAS/IML software is used to construct power function to find the optimal sample size, and selecting the sample size from the two randomly normal populations to observe whether theoretical sample size formula and simulations are correct. The results shows the correctness of the formula and the accuracy of sample size.