共變數分析功能、假設及使用之限制

作者:范德鑫(國立臺灣師範大學教育心理與輔導系)

摘要：

本文共分為六部分，第一部分敘述共變數分析的理論模式第二部分說名共變數分析的兩個主要功能──消除系統的偏差和增加實驗的精確性；第三部分陳述共變數分析所依據之假設和違反假設所造成的影響，同時也提出部分因應之策略。共變數分析所依據之主要假設包括：（1）隨機分派（2）共變量不受處理影響（3）共變量為固定且測量無誤差（4）共變量與依變數呈直線關係（5）回歸斜率相等（6）有關實驗誤差之假設（包括獨立性，變異同質性及常態性）；第四部份討論使用原樣團體（intact group）時應該注意的事項；第五部分指出使用共變數分析鷹留意的其他問題，最末部分指出研究者使用共變數分析鷹持之態度。共變數分析自創用至今已超過半世紀之久，由於它具有統計控制和增進研究之精確性的功能，因而為研究者所樂用。由於現有統計書籍大都強調如何計算而忽略討論此方法使用的限制，以致造成研究者經常誤用、濫用之情事。
本文主要目的在於提醒研究者，共變數分析是一個相當「脆弱」的工具，使用時應小心為要。也只有對此法之功能與限制透徹了解，研究結果才有意義。

《詳全文》

The Functions, Assumptions, and Limitations for Analysis of Covariance

Author: Der-Hsin Fan(Department of Educational Psychology and Counseling, National Taiwan Normal University )

Abstract：

The analsyis of covariance (ANCOVA) is one of the statistical techniques fre-quently used by educational researchers because it has the functions of statistical control and reduction of within group or error variance. However, it is a very deli-cate and commonly misunderstood procedure. So that users can accurately use AN-COVA, the author discusses it in terms of the following six parts.
The first part describes its rationale and model. The second part depicts AN-COVA's two major functions-elimination of systematic bias and reduction of within group or error variance. The assumptions of the model, effects of voilation, and corresponding strategies to be used are illustrated in the third part. The assump-tions examind are: (1) that cases are randomly assigned to treatment conditions, (2) that the covariate is independent of the treatment effect, (3) that the covariate is fixed and measured without error, (4) that the covariate is linearly related to the dependent variable, (5) that regression of the dependent variable on the covariate is the same for each group, and (6) that the assumptions regarding experimental error (including independence, homogeneity of variance, and nomality) have not been vio-lated. The use of ANCOVA with intact groups is discussed in the fourth part. Some miscellaneous considerations are raised in the fifth part. The final part sum-marizes the pratical steps involved in utilizing ANCOVA.