Ranked Set Sampling and Its Applications in Educational Statistics

• Activity Number: 280
• Type: Topic Contributed
• Date/Time: Tuesday, July 31, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Holly Stovall*+ and Lynn Stokes and Sherry Wang
• Companies: and Southern Methodist University and Southern Methodist University

Abstract

During the past decade, educational research has been galvanized by new legislation such as the No Child Left Behind Act. Increasing emphasis is being placed on accurately quantifying the success of treatment programs through student achievement scores, so precise estimation is vital for establishing the efficacy of new methodology. Ranked set sampling is a sampling design that uses the rankings of an inexpensive covariate in an attempt to select a more representative sample that provides better estimation of population parameters. The use of ranked set sampling for hierarchical linear models is developed for applications in educational data since a multitude of possible ranking information exists at both the student and school level. The performance of the maximum likelihood estimator of the treatment effect as well as a nonparametric estimator is explored, and results indicate that the precision of these estimators may be improved by ranked set sampling. Thus, a true difference in performance between the treatment group and control group may be more detectable when ranked set sampling is employed.