Partially Sequential Median Ranked Set Sample Test Procedure

• Activity Number: 497
• Type: Contributed
• Date/Time: Wednesday, August 12, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Michael Matthews* and Elizabeth Stasny and Douglas Wolfe
• Companies: The Ohio State University and The Ohio State University and The Ohio State University
• Keywords: distribution-free ; order statistics ; ranking ; sample size reduction ; two-sample location test

Abstract

A major portion of the expense in most statistical analyses is the cost of collecting the sample data. Ranked set sampling (RSS) is one approach to data collection that uses auxiliary ranking information from individual units in order to obtain a more representative sample from a population. Partial sequential (PS) methods is another approach to data collection designed to reduce the sample size in a treatment versus control two-sample setting. The PS approach uses a negative binomial sampling framework to minimize the number of treatment observations necessary for reaching satisfactory statistical conclusions regarding the treatment's efficacy. In this paper, we combine the RSS and PS methodologies to develop a partially sequential ranked set sample (PSRSS) two-sample test procedure to test for equality of the medians of two populations. This procedure is especially useful in the setting where measuring individual units is expensive, but ranking units according to the attribute of interest is relatively easy. We demonstrate via a simulation study that our PSRSS test procedure offers improvements in both power and sample size, as compared to the original PS test of Wolfe (1977).