Six FORTRAN IV programs for conducting simple randomization tests

Abstract

Bradley (1968) has shown that, for data that deviate substantially from the assumption of normally distributed error variance required by parametric tests, randomization tests can be more powerful than their parametric counterparts. In addition, randomization tests offer a more finely stepped distribution of the test statistic than do conventional nonparametric tests. This is of particular advantage in cases where group sizes are small, producing very coarse-grained distributions of the more commonly used nonparametric test statistics. Description. This suite of six programs uses several of the combinatorial algorithms from Nijenhuis and Wilf (1975) to carry out two types of test: exhaustive randomization tests and Monte Carlo randomization tests. The exhaustive randomization test calculates values of the test statistic that are obtained by rearranging the given data in all the possible ways consistent with the null hypothesis concerned. From this information, a cumulative probability distribution of the test statistic is derived, against which the observed value can be compared, using either a one-tailed or a two-tailed test. The Monte Carlo randomization test, on the other hand, takes a random sample (with replacement) of the total number of permissible data arrangements in order to derive the distribution of values for the test statistic concerned. The latter method is particularly useful in cases where the total number of permissible arrangements is prohibitively large in terms of the computing time required to perform an exhaustive test. A fuller account of the Monte Carlo procedure is given by Edgington (1969). The first pair of programs, EMATCH and RMATCH, are the exhaustive and Monte Carlo versions, respectively, of a randomization procedure to test the significance of the difference between the means of two matched samples, XI' X2, · .. , Xn and Y I , Y2, ... , YnFor this test, the null hypothesis is that each matched pair of scores (Xi, Vi) is drawn from the same