There is growing interest in devising non-statistical classification algorithms for multivariate populations. Statistical algorithms are avoided either because they are too costly, or because an adequate statistical model for the population does not exist (e.g. use of trainable linear machines in pattern recognition). Such algorithms may be sensitive (unstable) to errors in their data. The particular case of populations of objects characterised by binary attributes susceptible to independent and equiprobable errors is examined. The determination of stability requires the prior computation of the expectation of a statistical function of the object-pair similarities. The order and convergence of a numerical approximation for determining these expectations with prescribed accuracy is examined in the sub-asymptotic case in which normality does not occur. A number of results are given.