Three tests for randomness of attack of social groups during an epidemic

It is suggested that investigation of the attack of social units can be more illuminating of an epidemic process than the usual study of secondary attack rates of individuals. Three tests for detecting non-random differences in the occurrence of a disease between two groups of social units are presented. In each method the number of units attacked (X) in one of two groups of units is considered, rather than the number of individuals attacked. The tests are: (a) to use the Monte Carlo method, computer simulation of the epidemic process, to obtain an empirical distribution to which the observed value of X is compared; (b) to obtain the exact distribution of X; (c) to standardize X and compare it to the standard normal distribution. The three approaches are compared using data obtained from an epidemic of variola minor in two schools and the differences between the results are trivial. However, for large samples the only feasible approach is the Monte Carlo method.