相關係數區間估計之最適樣本數

Abstract

由於兩變數之間的相關程度是許多社會科學中所關心的議題，因此利用樣本相關係數推論母體相關係數是一種常見的方法，然而最適樣本數的決定將會為整個研究省下許多時間與成本。傳統的樣本數決定除了假設檢定法之外，本研究將會介紹期望區間長度法與期望區間涵蓋率法，期望區間涵蓋率法是以區間估計為基礎，但可根據所設定的涵蓋率不同來調整樣本數的寬鬆。 在此研究裡我們採用SAS軟體來建置模型，在求出最適樣本數之後，並在設計的兩母體中隨機抽出該樣本數，並觀察該樣本所組成的區間寬度與區間涵蓋率是否符合我們的原始設定，其結果顯示：期望區間長度法唯有在樣本數夠大時才會有較佳的模擬效果；而期望區間涵蓋率法在母體參數接近於0時會有涵蓋率不穩定的情形。

As the degree of correlation between two variables is one of concern to many social science issues, thus using the sample correlation coefficient to infer population correlation coefficient is a common method. However, the decision of the optimum sample size for the entire study will save a lot of time and cost. Traditionally, the sample size determination in addition to hypothesis testing method, this research will introduce the expected interval length method and the expected interval coverage probability method. Expected interval coverage probability method is based on interval estimation, but it can adjust sample size strict and loose according to the different set coverage probability. In this dissertation, the SAS software is used to construct model, after finding the optimal sample size, we will select the sample size randomly from the two designed population, and observe the interval width and interval coverage probability composed of sample size whether consistent with our original set. The results shows: the expected interval length method will have a better simulation results only when the samples are large enough, and the expected interval coverage probability method will shows unstable when the population parameters very close to 0.