Approximate Test for Comparing Parameters of Several Inverse Hypergeometric Distributions

• Activity Number: 421
• Type: Topic Contributed
• Date/Time: Tuesday, August 6, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Survey Research Methods Section
• Author(s): Lei Zhang*+ and Hongmei Han and William Johnson
• Companies: Mississippi State Department of Health and Pennington Biomedical Research Center and Pennington Biomedical Research Center
• Keywords: Empirical power ; Inverse sampling ; Large sample theory ; Negative hypergeometric distribution

Abstract

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.