“共變數分析”模式之介紹與圖解

雖然共變數分析模式在1927年便由R.A. Fisher提出，且發展已非常成熟，但國內護理研究或臨床工作者對共變數分析之使用仍不普遍，或不甚瞭解。本文嘗試採用簡單易懂方式來介紹共變數分析，並處擬多組情況，透過圖解來幫助讀者對共變數分析模式有一更具體及清晰的瞭解。另一方面，因爲共變數分析牽涉到交互作用之觀念，本文亦希望藉此說明統計上交互作用之意羲。所謂共變數分析就是合併變異數分析及線性迴歸的一種統計分析方法。假如研究的主要目的爲比較Z因子（類別變項）內不同層次之Y有沒有差異，共變數分析假設X（連續變項）與Y（連續變項）存在一直線關係，又此X與Y之直線相關係不會隨Z值改變（即X與Z沒有交互作用(interaction)，考慮或調整X與Y之直相關係後，Y之測量誤差得以降低，再比較Z因子內不同層次Y之差具，便會較具效益。經由虛擬多種情況，分別使用共變數分析及雙樣本t檢定，建議先劃X、Y、Z的散佈圖瞭解關係後，再透過t檢定、partial F-test測驗X與Z之交互作用是否達統計意羲，及以殘差分析檢查X與Y是否有一直線關係，來幫助判決共變數分析之使用是否合適，以作出正確推論。

關鍵字

共變數分析；交互作用

並列摘要

Although analysis of covariance (ANCOVA) was first proposed by R. A. Fisher in 1927, and has been well-established since then, this statistical technique is not popular or not well-understood among nursing researchers in Taiwan. This article attempts to use simple and easily-understood language to introduce ANCOVA. Several simulated data sets with graphical displays are shown to help users learn ANCOVA. Statistical interaction is also explained. ANCOVA is a combination of analysis of variance (ANOVA) and linear regression. The main purpose of ANCOVA is to study the difference in Y (continuous dependent variable) among Z (categorical variable, named factor in ANCOVA), assuming that there is a linear relationship between X (continuous independent variable, named covariate in ANCOVA) and Y, and that this X-Y linear relationship does not change with different values of Z (no statistical interaction between X and Z). Through the decomposition of covariance, error can be reduced and provide precise estimates and accurate significant test on Z effect. In order to use ANCOVA properly, we suggest users draw a scatter plot for X, Y, Z, and then use either t-test, partial F-test to check the interaction assumption of ANCOVA. Residual analysis should also be used to test linearity assumption between X and Y.

並列關鍵字

analysis of covariance ； interaction

國際替代計量

“共變數分析”模式之介紹與圖解

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