標準化線性組合信賴區間之樣本數計算-使用平均變異數

Abstract

在研究的設計上，樣本數多寡的決定是非常重要的一環。需要多少的樣本數才能夠提供我們有意義的資訊?在本文中，樣本數公式為使用平均變異數線性組合模式，並分為兩部份進行探討，首先我們使用同質變異數的假設進行討論，其次則使用異質變異數之假設，兩部份之研究皆由兩群體(k = 2)發展至多群體(k = 4)，透過微調參數的方式進行驗證，研究者將使用期望區間寬度法和區間容忍率法來評估此樣本數公式的模擬結果是否符合我們的預設值。本篇研究使用統計軟體SAS來建構模型，並在各種情境下進行一萬次的模擬。

Sample size determination is one of the most important aspects in the design of a study. How many sample size will be large enough to yield meaningful information? In this article, sample size formulas used average variance in linear contrasts is divided into two part discussion, one is used equal population variances assumption another is used heteroscedasticity assumption, both part will be examined from two population (k = 2)to multi-population (k = 4),through a fine-tuning parameters and researcher will use the expected interval width method and expected interval coverage probability method to assess this sample size formulas whether consistent with our original set. In this dissertation, the SAS software is used to construct model and simulation from10,000 Monte Carlo replications for each condition.