Index for Proportional Reduction in Error in Two-way Contingency Tables with Ordinal Categories

摘要

For two-way contingency tables with nominal categories in which the explanatory and response variables are not defined clearly, Goodman and Kruskal (1954) considered a proportional reduction in error (PRE) measure, which describes the relative decrease in the probability of making an error in predicting the value of one variable when the value of the other is known, as opposed to when it is not known. The present paper proposes a new PRE measure for two-way contingency tables with ordered categories in which the explanatory and response variables are not defined clearly. The proposed measure lies between 0 and 1. The proposed measure is useful for comparing the degree of PRE in several tables with ordered categories. Examples are given.