  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.
