複相關分析之運算與應用

Abstract

迴歸分析已廣泛運用於管理、心理、組織、及策略等各領域研究中。然而，其中複相關係數分佈的結構十分複雜，許多研究者對直接相關的統計推論，如檢定力計算、區間估計、與所需求之樣本數等議題的不熟悉，故衍生許多經驗法則，但許多文獻証明由經驗法則所得之數據並不精確，故本研究主要針對研究者經常遇到的統計分析：假設檢定、檢定力計算、區間估計、以及樣本數等四大議題，利用Excel介面的親和性與普及性，配合電腦的迅速運算能力，提供便利與即時的統計分析軟體，以克服研究者因運算複雜而束手無策的窘境，並同時破除經驗法則的迷失，提供研究者一個精確的依據，以作為研究規劃與分析之用。

Regression analysis is widely used in many areas of science, and the literature is very extensive. Classical inferences on correlation coefficients are conducted mainly under the assumption that all variables have a joint multivariate normal distribution. Although the underlying normality assumption provides a convenient and useful setup, the resulting probability density function of the multiple correlation coefficients is notoriously complicated in form. Consequently, considerable attention has been devoted to the construction of useful approximations and rules of thumb for the inferential procedures of squared multiple correlation coefficient. In general, the rules of thumb fail to incorporate effect size and have often provided inaccurate results. In view of the ultimate aim of presenting exact procedures for correlation analysis and the extensive accessibility of Microsoft Excel software, the associated computer routines for hypothesis testing, interval estimation, power calculation, and sample size determination are developed. The statistical methods and available programs of multiple correlation analysis described in this article purport to enhance pedagogical presentation in academic curriculum and practical application in research.