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442 – Contributed Oral Poster Presentations: Government Statistics Section
Approximate Test for Comparing Parameters of Several Inverse Hypergeometric Distributions
Lei Zhang
Mississippi State Department of Health
Hongmei Han
Pennington Biomedical Research Center
Dachuan Zhang
Louisiana State University
William Johnson
Pennington Biomedical Research Center
Consider the case of two-stage sampling where (first stage) m bins are selected from a large population of M bins each containing N items, (second stage) inverse subsampling is performed without replacement from each of the m bins, and a binary observation is made on each subsample item (inverse hypergeometric distribution). Denote the two types of items Red and Blue. Assuming the N is known but the number of each type is not, we consider the hypothesis that the number of Red items is the same in all M bins. We employ an unbiased parameter estimator and use the Delta Method to approximate the estimator's variance. We then propose a large sample statistic for testing the hypothesis. We selected various parameter values for the inverse hypergeometric distribution to empirically investigate performance of the test in terms of exact calculations of the ability of the test to maintain significance at the nominal 0.05 level under the null hypothesis and inform power of the test for specified parameter values when the null hypothesis is false. The empirical findings provide pragmatic validation of the merits of the test.