Tests for Differences between Several Small Proportions

SUMMARY Motivated by the practical problem of analysing data from in vitro chromosome aberration assays this paper considers tests for differences between several proportions. Various test statistics are described, and the small sample behaviour of tests which refer these statistics to approximating continuous distributions is investigated. The inaccuracies of these approximate tests can be avoided by using the exact conditional distribution of the test statistic. The calculation of the exact significance probability is described and the computation costs are shown to be negligible compared with the costs of data acquisition. Finally the use of the mid‐ p value is advocated for discretely distributed test statistics.