Three-Stage Optimal Sampling Plans for Group Testing Data

• Activity Number: 520
• Type: Contributed
• Date/Time: Wednesday, August 6, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Survey Research Methods Section
• Author(s): Osval Antonio Montesinos Lopez*+ and Kent M. Eskridge
• Companies: University of Nebraska and University of Nebraska-Lincoln
• Keywords: three-stage ; group testing ; optimal sample size ; relative efficiency

Abstract

In surveys, sample size planning is important in achieving precise estimates at a low cost. However, this issue is not adequately addressed for group testing data obtained from a three-stage sampling process. In this study, we obtained the optimal allocation of localities, fields, pools per field and pool size in a three-stage group testing survey. Analytical expressions were derived for optimal values of localities, fields and pools per field for a given pool size. However, only computational solutions were possible when we also calculated the optimal values of pool size. These optimal values were obtained under the assumption of equal locality and field sizes. To handle the unequal sample size case, we derived the relative efficiency (RE) of unequal versus equal locality and field sizes to estimate the proportion. By multiplying the sample of localities and fields obtained assuming equal cluster size by the inverse of the corresponding REs, we adjusted the sample size required in the context of unequal localities and field sizes.