Bayesian Methods for Estimating Sample Size in Surveys with Multiple Levels of Screening, Eligibility, and Nonresponse

• Activity Number: 321
• Type: Contributed
• Date/Time: Tuesday, August 9, 2005 : 2:00 PM to 3:50 PM
• Sponsor: Section on Survey Research Methods
• Author(s): Kristen Olson*+ and Trivellore Raghunathan
• Companies: University of Michigan and University of Michigan
• Keywords: Bayesian methods ; sample size ; nonresponse ; eligibility ; multi-stage survey

Abstract

In many scientific investigations, the needed sample size (n) is determined through power calculations. Obtaining the sample size may require a survey process with many screening stages to determine ultimate eligibility. At each screening stage, there will be nonresponse. Thus, the objective is to estimate the number of sample lines to be released (N) in order to achieve the ultimate sample size, accounting for uncertainties in screening, eligibility, and nonresponse. We formulate the problem of estimating N using a Bayesian framework. We assume a negative binomial model for the desired sample size at each stage of the eligibility and cooperation process with unknown probability of success. We simulate the posterior distribution of N; this simulation is used to determine the range of N that ensures the desired ultimate sample size will be achieved with high probability. This approach is in contrast to the naïve approach of determining N in which n is inflated by an estimated yield rate. Using a pilot study, both approaches are applied to estimate N for a stratified random sample survey. We find the naïve approach severely underestimates the number of sample lines needed.