Exact conditional tests for a reciprocal interpretation of hierarchical classifications built on a two-way contingency table

Given a two-way contingency table and two hierarchical classifications on both rows and columns, indexes are proposed to identify suitable cut-points and mutual influences between nodes of either hierarchy and both nodes and group of the other. The indexes distribution is found and exact conditional tests are given, to check for significance of the found values. An application to Nobel Awards is given as an example.