A Monte Carlo Test of the Robustness of Parametric and Nonparametric Analysis of Covariance Against Unequal Regression Slopes

TLDR: The power of parametric ANCOVA was compared with the power of three nonparametric techniques both when the parametric assumption of equal slopes was violated and when all parametric assumptions were met as discussed by the authors.

Abstract: The power of parametric ANCOVA was compared with the power of three nonparametric ANCOVA techniques both when the parametric assumption of equal slopes was violated and when all parametric assumptions were met. The data situations involved two groups with one covariate and one criterion, normal distributions, equal group sizes, and varying slope combinations. Parametric ANCOVA maintained larger empirical power for nearly all of the data situations. Both parametric and nonparametric techniques appeared not to be robust when violation of the parametric assumption of equal slopes was coupled with unequal group sizes and distributions were normal.