A statistical test has been developed to ascertain whether a given number of presumptive synapomorphies between one pair of taxa is significantly greater than the number between another pair of taxa. This is shown to be a form of testing the significance of a difference between two proportions. It is necessary first to adjust for common patterns of synapomorphy that raise or lower both numbers. The method has been checked by simulation, and is illustrated by data on the relationships of tetrapods. It proves that Hennigian cladistics has statistical constraints.