OPTIMUM STRATIFICATION FOR STRATIFIED RANDOM SAMPLING

This paper considers the problem of optimum stratification for auxiliary variable x when the form of the regression of estimation variable y on the concomitant variable x and the form of variance function V((y) over bar /x) is known. Serfling (1968) has proposed the cum root f rule for stratification on the auxiliary variable x when the regression of y on x is linear with uncorrelated homoscedastic errors and nearly perfect correlation. Cum 3 root P(X) rule of Singh (1971) does not reduce to the rule recommended for optimum stratification on y when V((y) over bar /x) = 0 and C(x) = constant for all x in the range (a,b) of x with (b-a) < infinity. An alternative method for determining approximate optimum strata boundaries (AOSB) on the auxiliary variable x for optimum allocation has been proposed. The method reduces to Serfling (1968) method under certain regularity conditions. The numerical illustration for working rule of the proposed method has also been undertaken for different values of correlation coefficient rho(2) by taking various probability density functions viz. uniform, rectangular and exponential. It has been observed that the efficiency of the proposed rule increases with increase in the value of rho(2) and decreases with increase in the number of strata.