Abstract: A new approximation to the distribution of Pearson's chi-square statistic for testing independence in two-way contingency tables is described. Using the exact first three moments of the test statistic under the conditional permutation distribution, the distribution is approximated by that of (aW)k, where W has a chi-square distribution. In an extensive comparison of the new generalized chi-square procedure and several other tests of independence with the ``exact'' conditional test, the new method consistently yields estimated p-values which agree closely with the exact results.
Key words and phrases: Generalized gamma approximation, Pearson's chi-square statistic, test of independence, two-way contingency table.