共變數分析功能、假設及使用之限制
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Date
1992-06-??
Authors
范德鑫
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Publisher
國立臺灣師範大學研究發展處
Office of Research and Development
Office of Research and Development
Abstract
本文共分為六部分，第一部分敘述共變數分析的理論模式；第二部分說明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）共變量與依變量呈直線關係（5）迴歸斜率相等（6）有關實驗誤差之假設（包括獨立性，變異同質性及常態性）；第四部分討論使用原樣團體（intact group）時應該注意的事項；第五部分指出使用共變數分析應留意的其他問題，最末部分指出研究者使用共變數分析應持之態度。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。 1932年Fisher創用共變數分析方法至今，整整近一甲子的歷史，雖然此法目前已廣為國內外研究者所使用，但是目前它仍是一種易為研究者誤解和誤用的統計方法（Porter & Raudenbush, 1987），難怪Elashoff（1967）說它是一種脆弱的工具（delicate instrument）。目前國內統計書雖然都有談及這種方法。可惜的是，作者大都把此方法視為變異數分析之延伸，強調如何計算，但對其功用與假設不是未交代清楚，就是根本未提。研究者在一知半解的情況下使用此種方法進行資料分析，研究的結果令人懷疑，更遑論有多少價值了。本文主要目的在討論共變數分析之理論依據、功能、所需之假設及其他一些使用此統計方法時應注意之事項。希望它有助於研究者對此方法的正確了解與應用。至於計算方法，讀者可以參閱林清山（民81）心理與教育統計學；朱經明（民78）教育統計學，或謝廣全（民73）最新實用心理與教育統計學。
The analsyis of covariance (ANCOVA) is one of the statistical techniques frequently 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 delicate and commonly misunderstood procedure. So that users can accurately use ANCOVA, the author discusses it in terms of the following six parts. The first part describes its rationale and model. The second part depicts ANCOVA'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 assumptions 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 violated. 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 summarizes the pratical steps involved in utilizing ANCOVA.
The analsyis of covariance (ANCOVA) is one of the statistical techniques frequently 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 delicate and commonly misunderstood procedure. So that users can accurately use ANCOVA, the author discusses it in terms of the following six parts. The first part describes its rationale and model. The second part depicts ANCOVA'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 assumptions 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 violated. 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 summarizes the pratical steps involved in utilizing ANCOVA.