Constructing two-sided simultaneous confidence intervals for multinomial proportions for small counts in a large number of cells

Confidence intervals for multinomial proportions are often constructed using large-sample methods that rely on expected cell counts of 5 or greater. In situations that give rise to a large number of categories, the cell counts may not be of adequate size to ensure the appropriate overall coverage probability and alternative methods of construction have been proposed. Sison and Glaz (1995) developed a method of constructing two-sided confidence intervals for multinomial proportions that is based on the doubly truncated Poisson distribution and their method performs well when the cell counts are fairly equally dispersed over a large number of categories. In fact, the Sison and Glaz (1995) intervals appear to outperform other methods of simultaneous construction in terms of coverage probabilities and interval length in these situations. To make the method available to researchers, we have developed a SAS macro to construct the intervals proposed by Sison and Glaz (1995).