Ranked Set Sampling under Randomization Framework
by
Praveen Krishna
IASRI
Coauthors: Anil Rai (IASRI)

Ranked Set Sampling under Randomization Framework

Praveen Krishna and Anil Rai (Indian Agricultural Statistics Research Institute) Library Avenue, New Delhi-110012

Abstract

In this article RSS procedure has been examined in randomization frame of work of survey sampling. It has been observed that this procedure falls in the category of equal probability sampling method, i.e. the probability of including every unit of the population in the sample is same. The ranked set sampling (RSS) provides efficient estimation of population mean as compared to simple random sampling (SRS). The procedure of RSS creates artificial stratification of the population; as a consequence of this it provides better representation as compared to SRS. Most of the articles available in literature are either based on infinite population theory or super population framework. In this article the estimator for estimating population mean has been proved to be unbiased and an expression of its variance has been derived in terms of variability of individual ranks. The expressions of finding inclusion probabilities of the individual sampling units and joint probabilities of including any pair of sampling units are also derived. The statistical properties of this estimator have been studied using simulation for two different cases, i.e. (i) usual case when N=mn2 and (ii) two phase sampling when N is the size of target population, N > mn2. Here, m denotes number of cycles and n is the sample size per cycle. Therefore, sample size of the RSS is mn. For both the cases it was found that the proposed RSS estimator is always better than SRS estimator. Gain of 20 to 40 percent is achieved in RSS of equivalent sample size as compared to SRS.

Date received: November 17, 2002

Copyright © 2002 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cakd-26.