It is shown that certain simply defined probabilities, which involve the joint classification of two random cells by tissue and postinactivation clone, play a key role in the analysis of X-chromosome inactivation data and can be used to define tissue-specific and composite indices of 'incoherence', or lack of association, between clones and tissues. The experimental estimation of these probabilities is developed, with numerical illustration, for a general model of assay errors that embraces a spectrum of different assay techniques. Three estimation techniques are considered: the first, unconstrained by the requirements of any specific model for clone--tissue association; the second, constrained by a condition of dominated off-diagonal equality (DODE) that delineates a general class of models of the type used by Nesbitt (1971, Developmental Biology 26, 252-263); the third, additionally constrained by a condition of on- and off-diagonal equality (OODE) that holds for an 'equisampling' specialization of the Nesbitt model. The effects of natural relaxations of the assumptions implicit in the latter type of model are analysed within the framework constructed here.