An empirical investigation of some effects of sparseness in contingency tables
A simulation study investigates some effects of having 'sparse' categorical data, for which the ratio of the sample size to the number of cells is relatively small. In this study, the true cell proportions satisfy the uniform association model for ordinal variables. Conclusions include the following: (1) For direct testing of the model, the distribution of the Pearson goodness-of-fit statistic is closer to the asymptotic chi-squared distribution than is the distribution of the likelihood-ratio statistic. (2) For comparing two unsaturated loglinear models (such as in testing independence under the assumption that a particular model holds), it is usually preferable to compare likelihood- ratio statistics rather than Pearson statistics. (3) A beneficial aspect of sparseness is that the power of certain single-degree-of-freedom test statistics tends to increase as the table becomes more sparse, for a fixed sample size. (4) The common practice of adding constants to empty cells can cause havoc with the distribution of the Pearson statistic.
single-degree-of-freedom test statistics
scientific article; zbMATH DE number 3978170
scientific article