多變量群組標準化效用檢定之樣本數計算

在許多領域的研究上，抽樣之樣本數大小一直是被關注的議題，如果能掌握最適樣本數即能替研究節省人力以及物力的成本。而「效果量」為客觀表現出差異大小及相關程度的一項衡量方式，相較於顯著水準有實質上的解釋及運用，若於研究報告中加註效果量的使用，會更容易理解研究的重要性。而效果量的計算將會依照研究方法的不同、統計方法的使用而有所差異，為能更真實應用在現實生活的情境條件，本文採用多變量變異數分析為模型，採隨機模擬的方式，藉由假設檢定法，給定虛無假設之效果量，對於應該接受虛無假設或因證據不足拒絕虛無假設，探討在固定信心水準以及可接受的檢定力下，檢視在不同參數條件下群組內的最適樣本數以及最適總樣本數。

關鍵字

多變量變異數分析；效果量；非中心 F 分配；假設檢定；最適樣本數；檢定力

並列摘要

Sample size, an issue, which is concerned in many fields of research. We can save a lot of cost of human resources and time if researchers can master the technique of optimum sample size of their research. The term, called effect size, which is a quantitative measure of the strength association and the difference between populations. There are more practical meanings and applications with attaching the effect size in research. If we could attach the effect size with our study, we could easily understand the importance of studies. The form of effect size will be different in the method of statistic and the fields. In order to reflect the condition in real world, we use MANOVA model and Monte Carlo simulation. According to null-hypothesis significance testing we discuss the optimal sample size in groups given the significance level and the power we accepted.