Cochran''s Q test is designed for testing the hypothesis that a number of correlated proportions are equal. In his presentation of the Q test, Cochran assumed that the allocation of treatments (e.g. media for the growth of diphtheria bacilli) to the different experimental units (e.g. throat specimens from suspected cases) is independent and random. In this note a model is proposed for dichotomous responses elicited in experiments within which randomisation is not necessarily incoporated, but under which the Q test remains appropriate for testing the null hypothesis.