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.

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