Use of the beta-binomial distribution in dominant-lethal testing for "weak mutagenic activity".

When the results of biological experiments are tested statistically for a possible difference between a treatment and its control, the statistical inferences are valid only if the statistical procedure is derived from a model that fits the experimental results satisfactorily. In this paper it is shown that a beta-binomial distribution provided a better fit than a binomial distribution when the data used were based on a large number of counts of dead and total implants on dominant-lethal tests on mice. This suggests that the probability P that an implant will die is not constant over the experimental units. Tests derived from the beta-biomial distribution have been used and their results compared with those of the tests based on the binomial or constant P assumption. The tests based on the binomial model are erroneously too severe when P is not constant in a group. The problem of knowing whether the males or the females should be considered as the experimental units is considered. In this paper, calculations are carried out for the two situations. This problem will be further studied by computer simulation and the result will be presented in a next paper.It is also shown that a negative binomial distribution could be fitted to the dead implant counts. No test based on this model was used because it ignores the total implants. No familiar distribution could be fitted to the total implant counts.