Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, cilt.9, sa.4, ss.1469-1481, 2020 (Hakemli Üniversite Dergisi)
Ranked set sampling is a sampling technique that uses ranking
information when measuring units is difficult or expensive. In this study,
ratio estimation of the population mean is considered in the case of units
ranking by both auxiliary variable and the variable of interest in ranked set
sampling under bivariate normal distribution. We obtained some theoretical
inferences about the mean square error of the ratio estimation in this
situation in a simple form depending on coefficient of variation. Besides, we
made a theoretical comparison of mean square errors by ranking based on
auxiliary variable and interested variable. Using this comparison, one can choose which
ranking strategy should be utilized by using correlation coefficient and
coefficients of variation of interested variable and auxiliary variable in a
problem easily. When the coefficients of
variation are close to each other and the correlation coefficient is close to
one, ranking can be conducted according to any variable. However, when the
coefficient of variation of the interested variable is greater than the coefficient
of variation of the auxiliary variable and the correlation coefficient between
them is small, ranking should be preferred by using the interested variable. The performance of the ratio estimators was compared
by a simulation study. The simulation results indicated that the ranked set
sampling estimators were more efficient than the simple random sampling
estimators for the same sample size and correlation coefficient. A real data
example was also given to demonstrate for calculating relative efficiencies.