The use of a linear function for discriminating with dichotomous variables is discussed and evaluated. Four such functions are considered: Fisher's linear discriminant function, two functions based upon a logistic model, and a function based upon the assumption of mutual independence of the variables. The evaluation of these functions as well as of a completely general multinomial procedure is carried out within the context of a 1st order interaction model by means of computer experiments. The product moment correlation of the optimal function with the linear function under evaluation plays a central role as a criterion for judging the relative merits of the procedures considered.