複相關分析之運算與應用

The Computation and Application of Multiple Correlation Analysis

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，如檢定力計算與所需求之樣本數等議題不熟悉，故衍生許多經驗法則，但許多文獻證明由經驗法則所得之數據並不精確。Shieh與Kung(2007)在Behavior Research Methods中發展一精確可靠且完整之複相關係數相關功能的軟體。故本研究除了介紹該統計分析軟體之外，也針對研究者經常遇到的統計分析：假設檢定、檢定力計算，以及樣本數等三大議題，利用該軟體之Excel介面的親和性與普及性，提供一全面性且實務性的介紹，以做為研究規劃與分析之用。另外，本研究針對研究者經常遇到的問題，利用該軟體運算出大量的資料，彙整圖表，期望研究者能藉由此圖表對於複相關分析有進一步深入的體認。最後，並配合個案詳細的說明如何運用此軟體於規劃研究決策或教學展示上。

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, 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. Summary tables, figures and related discussions are provided to demonstrate the impact of each of the factors and how they work as whole in multiple correlation analysis. Moreover, a numerical illustration with real data is described to exemplify the usage of the versatile package for management research.