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

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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.