Interval Estimation for Small-Area Proportions with Small True Proportions from Surveys with Stratified Random Sampling Designs

• Activity Number: 582
• Type: Contributed
• Date/Time: Wednesday, August 1, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Section on Survey Research Methods
• Author(s): Carolina Franco*+ and Partha Lahiri
• Companies: University of Maryland and University of Maryland
• Keywords: Confidence Intervals ; Proportions ; Complex Surveys ; Confidence Levels ; Stratified Random Sampling ; Coverage

Abstract

We consider interval estimation for small area proportions from stratified random sampling surveys. We focus on the case where the stratum sample sizes and the true proportions are small for all strata, and for simplicity we assume equal stratum sample sizes. The objective is to construct a confidence interval for each of the true stratum proportions, Pi. A commonly used small area empirical Bayes model for a single stratum's true proportion Pi assumes that both the distributions of the sampled stratum proportions and the prior distribution of the true stratum proportions are normal. The well-documented problems of the normal approximation to the binomial, particularly when the sample size is small and the probability of success is close to 0 or 1, raise questions about the adequacy of such a model when the Pi and the stratum sample sizes are small. We argue that a more reasonable model in this setting is to assume that the sampled stratum counts have binomial distributions and that the prior distribution of the true stratum proportions follows a beta distribution. We propose a new empirical Bayes confidence interval based on this model, and examine related simulation results.