One-way ANOVA versus best-fit polynomials in the analysis of small-sample quantitative biomedical data

Monte Carlo simulations were used to compare one-way ANOVA related tests of significance ( F , Dunnett’s and t , the latter with no correction for multiple comparisons) with best-fit polynomial (BFP) selection according to standard criteria. BFP statistical significance was assessed with bootstrapped F and t tests. Both Type I and Type III Errors were considered, with the null hypothesis (NH) of no treatment effect assumed a priori false in the latter case. BFPs and Dunnett’s test performed well with regard to Type I/III Error rates, while the ANOVA F was a little liberal. As expected, t tests with no correction for multiple comparisons performed poorly. Various response functions were used to assess power. BFPs were often more powerful than ANOVA (Dunnett’s test), but results were mixed, and overall there was not much to choose between the two approaches. As expected, two-sided tests based on Type III Errors were more powerful than conventional two-sided tests.