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Parametric ANCOVA and the Rank Transform ANCOVA When the Data are Conditionally Non-Normal and Heteroscedastic

University of Florida

Parametric analysis of covariance was compared to analysis of covariance with data transformed using ranks. Using a computer simulation approach, the two strategies were compared in terms of the proportion of Type I errors made and statistical power when the conditional distribution of errors was normal and homoscedastic, normal and heteroscedastic, non-normal and homoscedastic, and non-normal and heteroscedastic. The results indicated that parametric ANCOVA was robust to violations of either normality or homoscedasticity. However, when both assumptions were violated, the observed levels underestimated the nominal level when sample sizes were small and = .05. Rank ANCOVA led to a slightly liberal test of the hypothesis when the covariate was non-normal, the sample size was small, and the errors were heteroscedastic. Practical significant power differences favoring the rank ANCOVA procedures were observed with moderate sample sizes and a variety of conditional distributions.

Key Words: Analysis of covariance • nonparametric ANCOVA • rank transformations • Type I error • power

Journal of Educational and Behavioral Statistics, Vol. 9, No. 2, 129-149 (1984)
DOI: 10.3102/10769986009002129


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