Modified Systematic Sampling with Multiple Random Starts

Abstract

Systematic sampling has been facing two problems since its beginning; situational complications, e.g., population size N not being a multiple of the sample size n, and unavailability of unbiased estimators of population variance for all possible combinations of N and n. These problems demand a sampling design that may solve the said problems in a practicable way. In this paper, therefore, a new sampling design is introduced and named as, “Modified Systematic Sampling with Multiple Random Starts”. Linear systematic sampling and simple random sampling are the two extreme cases of the proposed design. The proposed design is analyzed in detail and various expressions have been derived. It is found that the expressions for linear systematic sampling and simple random sampling may be extracted from these expressions. Finally, a detailed efficiency comparison is also carried out in this paper.