  Testing hypothesis of independence between two random elements on a joint
alphabet is a fundamental exercise in statistics. Pearson's chi-squared test is
an effective test for such a situation when the contingency table is relatively
small. General statistical tools are lacking when the contingency data tables
are large or sparse. A test based on generalized mutual information is derived
and proposed in this article. The new test has two desired theoretical
properties. First, the test statistic is asymptotically normal under the
hypothesis of independence; consequently it does not require the knowledge of
the row and column sizes of the contingency table. Second, the test is
consistent and therefore it would detect any form of dependence structure in
the general alternative space given a sufficiently large sample. In addition,
simulation studies show that the proposed test converges faster than Pearson's
chi-squared test when the contingency table is large or sparse.
