An adjusted test for cross-classified cluster sample data

A first-order corrected test statistic for analyzing frequency data when the data are obtained from a two-stage sampling scheme is presented in this paper. The data are summarized in a cross-classified table in such a way that the cell values are not necessarily a count. Comparisons are made with the Wald statistic, Pearson statistic, other modified Pearson statistics, and a proposed first-order corrected test for comparing vectors of proportion. The proposed test shows that a convenient approximation to the Wald test statistic is to construct a modification of the Pearson type statistic based on the pre-adjusted table cell values. Simulated data are used to examine the behavior of the first-order statistic under the two-stage sampling scheme.