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

TL;DR

This paper introduces a geometric mean-based proportional reduction in variation (geoPRV) measure for two-way contingency tables, improving the assessment of variable associations especially with partial biases.

Contribution

It proposes a novel geoPRV measure that captures variable-specific associations more accurately and can generalize conventional PRV measures using geometric means.

Findings

geoPRV effectively detects associations with partial bias

It generalizes existing PRV measures as special cases

Provides a more sensitive analysis of variable relationships

Abstract

In a two-way contingency table analysis with explanatory and response variables, the analyst is interested in the independence of the two variables. However, if the test of independence does not show independence or clearly shows a relationship, the analyst is interested in the degree of their association. Various measures have been proposed to calculate the degree of their association, one of which is the proportional reduction in variation (PRV) measure which describes the PRV from the marginal distribution to the conditional distribution of the response. The conventional PRV measures can assess the association of the entire contingency table, but they can not accurately assess the association for each explanatory variable. In this paper, we propose a geometric mean type of PRV (geoPRV) measure that aims to sensitively capture the association of each explanatory variable to the response variable by using a geometric mean, and it enables analysis without underestimation when there is partial bias in cells of the contingency table. Furthermore, the geoPRV measure is constructed by using any functions that satisfy specific conditions, which has application advantages and makes it possible to express conventional PRV measures as geometric mean types in special cases.