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In a two-way contingency table analysis with explanatory and responsevariables, the analyst is interested in the independence of the two variables.However, if the test of independence does not show independence or clearlyshows a relationship, the analyst is interested in the degree of theirassociation. Various measures have been proposed to calculate the degree oftheir association, one of which is the proportional reduction in variation(PRV) measure which describes the PRV from the marginal distribution to theconditional distribution of the response. The conventional PRV measures canassess the association of the entire contingency table, but they can notaccurately assess the association for each explanatory variable. In this paper,we propose a geometric mean type of PRV (geoPRV) measure that aims tosensitively capture the association of each explanatory variable to theresponse variable by using a geometric mean, and it enables analysis withoutunderestimation when there is partial bias in cells of the contingency table.Furthermore, the geoPRV measure is constructed by using any functions thatsatisfy specific conditions, which has application advantages and makes itpossible to express conventional PRV measures as geometric mean types inspecial cases.

Geometric Mean Type of Proportional Reduction in Variation Measure for Two-Way Contingency Tables