The Effects of Type I Error Rate and Power of the ANCOVA <i>F</i> Test and Selected Alternatives Under Nonnormality and Variance Heterogeneity

Abstract

Abstract The authors sought to identify through Monte Carlo simulations those conditions for which analysis of covariance (ANCOVA) does not maintain adequate Type I error rates and power. The conditions that were manipulated included assumptions of normality and variance homogeneity, sample size, number of treatment groups, and strength of the covariate-dependent variable relationship. Alternative tests studied were Quade's procedure, Puri and Sen's solution, Burnett and Barr's rank difference scores, Conover and Iman's rank transformation test, Hettmansperger's procedure, and the Puri-Sen-Harwell-Serlin test. For balanced designs, the ANCOVA F test was robust and was often the most powerful test through all sample-size designs and distributional configurations. With unbalanced designs, with variance heterogeneity, and when the largest treatment-group variance was matched with the largest group sample size, the nonparametric alternatives generally outperformed the ANCOVA test. When sample size and variance ratio were inversely coupled, all tests became very liberal; no test maintained adequate control over Type I error. Key Words: ANCOVAMonte Carlo simulationsnonparametricsrobustness