International Journal of Scientific and Research Publications, Volume 2, Issue 12, December 2012 1 ISSN 2250-3153 www.ijsrp.org A Note on Ratio Estimators in two Stage Sampling Sitanshu Shekhar Mishra Lecturer in Statistics, Trident Academy of Creative Technology (TACT), Bhubaneswar, Odisha, India. Abstract- In this paper a number of ratio estimators in two stage sampling are considered and their efficiencies are compared with an estimator without use auxiliary information. Numerical illustration is provided to compare the efficiencies. I. INTRODUCTION n large scale sample surveys it is usual practice to adopt multi stage sampling to estimate the population mean or total of the study variable y. The main purpose of using multi stage sampling in place of unrestricted unistage sampling is to reduce the cost of survey operations even if estimates derived from multi stage sampling are likely to be less efficient then those of the unrestricted uni-stage sampling. Sometimes, all auxiliary variable x compared with y may be available either at primary stage or of secondary stage or at both the stages to in case the efficiency of estimate of the finite population parametric functions such as population means or total. Thus, in the following we consider different ratio estimators of population mean of the study variable y in two –stage sampling using knowledge on a single auxiliary variable x. II. NOTATIONS Now, consider a finite population U partitioned into N first stage units (fsu) denoted by U 1 , U 2 , ……U N . Let M i be the number of second stage units in i U (i 1, 2, ...., N)  . Define N i i1 M M    and N i i1 1 M M N    . Let ij y and ij x denote values of the study variable y and the auxiliary variable x respectively for the jth ssu of U i = (j = 1, 2, …, M i, i= 1, 2, ….,N) . Define, i M i ij j1 i 1 Y y M    and i M i ij j1 i 1 X x M    (i = 1, 2, ….., N) The population mean of y, N i i i1 1 Y uY N    and the population mean of x, N i i i1 1 X uX N    , where i i M u M  . Further, define Y R X  and i i i Y R X  (i = 1, 2, ….., N)   N 2 2 by i i i1 1 S uY Y N 1         N 2 2 bx i i i1 1 S uX X N 1           N bxy i i i i i1 1 S uY Y uX X N 1          i M 2 2 iy ij i j1 i 1 S y Y , i 1, 2,..., N. M 1         i M 2 2 ix ij i j1 i 1 S x X , i 1, 2,..., N. M 1       I