AbstractWhile estimators of the relative frequency of responding cells in limiting dilution assays (LDAs) have been critically evaluated, other statistical issues concerning this quantal assay have not received similar attention. This study investigates LDA validity tests designed to detect deviations from the single‐hit Poisson model. The method employed by Armitage (1959) to detect host variability, or a variable number of false negatives, is extended to other violations of the single‐hit Poisson model. In general, this methodology, based on the general theory of Neyman (1955), is shown to produce asymptotically most powerful and locally most efficient tests for many alternative hypotheses. In addition to composite hypotheses, this method can be extended to produce tests for separate families of hypotheses. These methods are compared with existing LDA validity tests including the weighted regression method of Gart and Weiss (1967), the double‐hit model of Cox (1962), and the general chi‐square goodness‐of‐fit statistic. Monte Carlo simulations show that these score tests have good power and acceptable rejection levels at 0.05 and 0.01. In particular, the score test designed to detect deviations from the Weibull model is shown to produce good power for many alternative models. The chi‐square goodness‐of‐fit statistic, the most widely used LDA validity test, is shown to lack power in detecting many alter