A Simplified Approach for Two-Dimensional Optimal Controlled Sampling Designs

Controlled sampling is a unique method of sample selection that minimizes the probability of selecting nondesirable combinations of units. Extending the concept of linear programming with an effective distance measure, we propose a simple method for two-dimensional optimal controlled selection that ensures zero probability to nondesired samples. Alternative estimators for population total and its variance have also been suggested. Some numerical examples have been considered to demonstrate the utility of the proposed procedure in comparison to the existing procedures. 1. Introduction Goodman and Kish [1] introduced controlled sampling as a method of sample selection that increases the probability of desired samples. Controlled sampling may be described as a technique of sampling from finite universe, which allows multiple stratifications beyond what is possible by stratified random sampling. There often arises a situation where some combinations of units may be less beneficial or even undesirable to be included in the sample due to considerations such as distance, similarity of units, and cost. The samples having undesirable combinations of units are known as nonpreferred or undesirable samples. Using the technique of controlled selection, one can exclude the possibility of including undesirable combinations of units in the sample or assign them minimum probability of selection. This results in an increase in the selection probability of preferred samples. The controlled sampling technique can be effectively used in two or more dimensions. Generally, researchers face multidimensional sampling problems in social research where various variables are involved in the population, requiring stratification in more than one dimension. The need of multidimensional stratification in various real life situations was discussed by Bryant [2], Hess and Srikantan [3], Moore et al. [4], and Jessen [5]. Jessen [5] considered with 12 geographical areas and 12 income classes, resulting in a total of 144 strata cells, out of which only 24 cells were to be selected. In such situations, the researcher requires stratification techniques which could permit fewer cells to be selected than the total number of strata cells permitted under stratified sampling, without sacrificing the requirements of probability sampling. This is known as controls beyond stratification. Goodman and Kish [1] were the first to address this problem under the name of two-dimensional controlled selection but did not provide any general method to solve such problems. Hess and Srikantan [3] and Groves and