This paper discusses the extension of discriminatory analysis to the case where the primary data are qualitative. The general principle in the use of the discriminant function in the case of two classes is to determine a set of adjustable coefficients so chosen as to maximize the ratio of the difference between sample means to the standard deviation within the two classes. When only a single chosen component is to be maximized relative to a set of other components, the equations are linear. In the case discussed here we have a two-way table of non-numerical observational data where the solution of equations of higher degree is required. Appropriate values are to be determined in order that the observations may be made as additive as possible. Application is made to the problem of scoring letter grades in school subjects so as to maximize individual differences.