The appropriateness of analysis of variance to the statistical analyses of dental clinical trials

Abstract

The extreme skewness and kurtosis of dental caries increments raise a question concerning the validity of analysis of variance for the statistical analysis of dental clinical trials. While it is acknowledged that moderate departures from normality do not strain the validity of parametric methods, the extent to which such departures from normality may be tolerated is not well known. In order to test the appropriateness of analysis of variance procedures in the statistical analysis of dental caries clinical trials, the increments in caries from clinical trials were simulated by computer for groups of varying size and number by random sampling from populations showing highly skewed distributions of new caries counts. Populations with both zero and nonzero true differences in the caries increments were sampled. Analysis of results of 320,000 simulated trials involving over 57 × 10 6 observations indicates that in spite of the extreme skewness and kurtosis of distributions of new caries counts, conclusions drawn from analysis of variance methods may be accepted with probabilities of Type I and II errors no greater than those predicted from normal distribution statistical theory. The evidence of the simulations suggests that analysis of variance and Dunnett's t-test, using the tabled critical values of F or t, may provide slightly conservative tests of significance. These results are in the same direction as predicted from the application of theoretical procedures and supply a justification for the extension of these theoretical procedures to distributions possessing the extreme skewness and kurtosis of caries count distributions, when the sample sizes and number of treatment groups are similar to those actually encountered in dental clinical trials.