A Note on Classifying Ordinal-Scale Data

Abstract

In their paper on classifying interval-scale and ordinalscale univariate data, Bryson and Phillips (1974) show that the use of a simple rule, known to be approximately optimal for interval-scale data, is also nearly optimal for ordinal-scale data. Here optimality is defined in terms of the amount of information lost by the classification rule. The primary purpose of this note is to point out that an even simpler rule is optimal for classifying ordinal-scale data. A secondary purpose is to show that the measure of information lost for ordinal-scale data has the undesirable feature that it ignores order. This defect becomes clear when we inspect the optimal rule. I shall suggest possible remedies for this situation.