The score test for independence in R x C contingency tables with missing data

In this paper, the score test statistic for testing independence in R x C contingency tables with missing data is proposed. Under the null hypothesis of independence, the statistic has an approximate chi-squared distribution with (R - 1)(C - 1) degrees of freedom. The proposed test statistic is quite similar to the Pearson chi-squared statistic with complete data and, unlike the likelihood ratio statistic for testing independence, its computation is simple and noniterative. In addition, a score test statistic is proposed for testing independence when the rows and columns of the R x C table are ordinal. Finally, extensions of the score statistics to test for conditional independence in a set of (R x C) contingency tables with missing data are described. This yields score test statistics that are natural extensions of the Mantel-Haenszel statistic. An example, using a subset of data from the Six Cities Study, is presented to illustrate the methods.