變異數不確定時之樣本數方法論---檢定力考量

Abstract

在實際應用研究中，決定適當樣本數已符合預定檢定力是一項重要課題。對一般雙群 組和多群組檢定而言，可能以指定的平均數並配合相關研究之樣本變異數來進行檢定力 分析。鑑於樣本變異數估計式的基本隨機性質，本文提出兩種方式來改良傳統作法，藉 以反應估計值的不確定性。方法一以期望檢定力來決定樣本數，而方法二則控制檢定力 達成指定程度的機會來選擇樣本數。這兩種改良法的用處和優點將藉由數值分析來說明 和顯現。本文的貢獻在於強調現存方法的限制，並增進樣本數方法論的拓展。

The priori determination of a properly large sample size necessary to achieve some specified power is a prominent problem encountered frequently in practical studies. To establish the needed sample size for two- and multi-sample tests, researchers may conduct the power analysis by specifying scientifically important values as the underlying population means while using a variance estimate obtained from related research or pilot study. In order to take account of the variability of sample variance, this article presents two approaches to sample size determinations. One provides the necessary sample size such that the expected power attains the designated power level. The other gives the sample size required to guarantee with a given assurance probability that the actual power exceeds the planned power. Numerical results are presented to illustrate the usefulness and advantage of the proposed methods that accommodates the stochastic nature of the sample variance. The exposition helps to clarify the deficiency of existing demonstration and to extend the development of sample size methodology.