Two-Stage Cluster Samples with Judgment Post-Stratification
*Please be sure to mute upon entry
Omer Ozturk, The Ohio State University, Department of Statistics
This talk has two parts. In the first part, I will briefly talk about RA Fisher’s last three years at the University of Adelaide.
In the second part, we consider estimation of the population mean or total in a clustered population using a two-stage sampling design. Each stage of the sample is constructed either using judgment post-stratified (JPS) or simple random sampling (SRS) design. The SRS sampling is performed without replacement, while the JPS designs can be implemented with or without replacement. We present design-unbiased estimators, their variance estimates, and approximate confidence intervals for the population mean and total. The efficiency of the two-stage JPS designs relative to the SRS design is investigated. The proposed estimators have smaller variances under a JPS than the two-stage SRS design. The gain in efficiency depends on the intra-cluster correlation coefficient and the sampling design choices at each stage. To achieve a fixed cost, the optimal sample sizes are derived for each stage by maximizing the information content of the sample. The proposed sampling designs and estimators are illustrated in vineyard management in agricultural field sampling.
Key Words: Intra-cluster correlation coefficient, adjusted R-squared, cluster sample, finite population correction, without replacement, ranked set sample