Using Ranked Set Sampling with Hierarchical Linear Models

• Activity Number: 560
• Type: Topic Contributed
• Date/Time: Wednesday, August 3, 2011 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Xinlei "Sherry" Wang*+ and Lynne Stokes and Holly Stovall
• Companies: Southern Methodist University and Southern Methodist University and Southern Methodist University
• Keywords: hierarchical linear models ; judgement post-stratification ; order statistics ; power analysis ; ranking

Abstract

Ranked set sampling (RSS) is a well established method of data collection, which is useful in situations where the variable of interest is expensive to measure, but sampling units can be easily recruited and ranked by some means not requiring quantification. It utilizes the assigned ranks to provide auxiliary information about the measured units. It has been proved to provide improved estimators of the mean, variance and distribution functions over simple random sampling (SRS) of the same size. In this work, we will consider ranked set sampling for use with hierarchical linear models (HLM) that have a wide range of applications in education sciences, to achieve potential improvement in the parameter estimation as well as the statistical power . We will consider ranking based on covariates at the school level and ranking based on covariates at the student level. In addition, we consider judgement post-stratification, a variant of RSS that has an underlying SRS if ignoring the rank information, for use with HLMs. Numerical results from simulation and empirical studies will be provided to examine the performance of our proposed approach.