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.

翻译：在含有解释变量与响应变量的二维列联表分析中，研究者关注两个变量间的独立性。然而，若独立性检验未显示独立性或明确显示存在关联，研究者则需关注其关联程度。已有多种度量被提出用于计算关联程度，其中变异比例缩减（PRV）度量描述了从响应变量的边缘分布到条件分布的变异缩减。传统PRV度量可评估整个列联表的关联性，但无法准确评估每个解释变量的关联程度。本文提出一种几何均值型PRV（geoPRV）度量，通过几何均值方法灵敏地捕捉各解释变量与响应变量间的关联，从而在列联表格存在局部偏倚时避免低估问题，实现更精准的分析。此外，geoPRV度量可通过满足特定条件的任意函数构建，这一特性赋予其应用优势，并使传统PRV度量在特殊情况下得以表达为几何均值类型。