Assumptions and Design Considerations

Statistical assumptions refer to the properties under which a model is mathematically derived; they are not the same thing as properties of the design but they are often related. Additional distinctions between assumptions and design considerations are discussed subsequently. The statistical assumptions for the “normal error” ANCOVA model are relatively straightforward because it is simply another linear model. Violations of this assumption are not important with most applications of ANCOVA, but there are some cases in which serious interpretation errors are likely. The reliability of the covariate is critical in nonrandomized observational studies, but not in most biased assignment and randomized-group experiments. The effect of moderate nonlinearity is a slight conservative bias in the ANCOVA F-test. When nonlinearity is suspected, an alternative method such as nonlinear ANCOVA should be considered. Robust linear model ANCOVA is recommended when either or both of these assumptions are obviously violated in randomized experiments. Controlled Vocabulary Terms analysis of covariance; statistical probability