Specific non-parametric approaches to analyzing caries clinical trials.

The usual parametric procedures are valid for the analysis of most caries clinical trials. If the sample sizes are small, non-parametric procedures should probably be used, such as the Wilcoxon two-sample test or the Kruskal-Wallis test. The Wilcoxon test can be expressed in terms of the difference between one of the rank sums and its expected value. This difference is evaluated in terms of its standard deviation. The Wilcoxon test is extended to produce an overall test, which takes the stratification into account. The procedure accumulates the differences between the rank sum of one of the two treatments and its expected value, and the corresponding variances. The Kruskal-Wallis test can be expressed in an analysis-of-variance-like form. The test can also be expressed in terms of the differences between the observed and expected rank sums. To extend the test to two or more strata, we need the variance-covariance matrices of I - 1 of the rank sums. There is presently no test available for interaction. The expected values of the rank sums depend on the sample sizes, and these differ from stratum to stratum. The use of weights, to produce a common expected value for each stratum, may provide a test of interaction. This needs further exploration.