Two important examples of this iterated procedure are given. The first one describes the test of the equality of the means ofmindependent normal distributions having common, but unknown, variance. This test is based on a sequence of Studenttstatistics: the firstttests the equality of the first two means, the secondttests the equality of the first three means (given that the first two means are equal), and so on. Since, under the null hypothesis, these statistics are mutually stochastically independent, it is easy to find the significance level of this procedure. Moreover, a rejection by this iterated scheme provides some reason why allmmeans are not equal. In the second example, the test of the equality ofmindependent distributions is based on a sequence of independent two-sample distribution-free statistics, such as the statistics proposed by Smirnov and Wilcoxon.