Summarizing Monte Carlo results in methodological research: The single-factor, fixed-effects ANCOVA case

Results from exact statistical theory and Monte Carlo studies have provided evidence that the test size and power of the F test in analysis of covariance are sensitive to violations of certain assumptions. However, a comprehensive summary of the effect of assumption violations has not been available. In this article, metaanalytic methods are used to summarize the results of Monte Carlo studies of the test size and power of the F test in the single-factor, fixed-effects analysis of covariance model, updating and extending narrative reviews of this literature. Monte Carlo results for the nonparametric rank-transform test in the analysis of covariance model are also analyzed. Guidelines for using these tests when assumptions are violated are presented to promote more judicious use of these procedures.