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

Stephen F. Olejnik and James Algina

Journal of Educational and Behavioral Statistics, 1984, vol. 9, issue 2, 129-149

Abstract: 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 α levels underestimated the nominal α level when sample sizes were small and α = .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.

Keywords: Analysis of covariance; nonparametric ANCOVA; rank transformations; Type I error; power (search for similar items in EconPapers)
Date: 1984
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Persistent link: https://EconPapers.repec.org/RePEc:sae:jedbes:v:9:y:1984:i:2:p:129-149

DOI: 10.3102/10769986009002129

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