Modelling and Simulation

The type I error control and power of a number of analysis of covariance (ANCOVA) and randomized block (RB) designs with curvilinear data were studied for tests of the additive treatment effect and interaction. For tests of additive effects, the analysis was also conducted using systematic assignment to treatments and using random assignment with a higher order covariate. Each of the analyses was conducted using the normal measure of random variability, score variation from parallel lines, and score variation from unique lines. A FORTRAN program was written to simulate data that could be analyzed with each alternative. The most interesting finding is the monumental inflation of the Type I error rate for the standard ANCOVA with random assignment of subjects when used to detect differences in slope. The source of this inflated error rate lies in the assumptions of ANCOVA. Because of this inflated error rate, it is recommended that systematic assignment be used when an individual difference variable is built into an experimental design. There may be situations in which use of a higher order covariate or RB designs will serve the experimenter better, but ANCOVA with systematic assignment and errors about unique regression lines appears to be the current best practice. (Contains 3 tables, 1 figure, and 13 references.) (SLD) Reproductions supplied by EDRS are the best that can be made from the original document