A procedure suggested by Barnard in 1963, for testing whether a set of data is consistent with a null hypothesis. It is appropriate for a situation where the theoretical distribution of the test statistic is unknown, although the distribution of the individual observations is known. The test procedure is to use Monte Carlo methods to generate 99 (say) further data sets of the same size as the true data, under the conditions defined by the null hypothesis. The value for the test statistic is calculated for each data set and the distribution of these values is examined. If the value of the test statistic for the actual data is similar to the values obtained from the artificial data sets, then the null hypothesis is accepted, whereas if it is extreme the hypothesis is rejected.
Subjects: Probability and Statistics.