Contribution to systematic sampling

Abstract

Systematic sampling has got a nice feature of selecting the whole sample with one random start. There are some disadvantages of systematic sampling viz, no valid estimate of sampling error can be obtained from sample itself. In the present investigation an alternative systematic sampling is suggested. The alternative method of systematic is superior to the usual systematic sampling method in the sense that a it besides providing unbiased estimate of population mean, suggests procedures for calculating unbiased estimate of the sampling variance from the sample itself. The method has however got some limitations. For a given population size n there is some restriction on the sample size. The limitation will not effect very much this sampling procedure from a large population but method may not be useful if a small fraction to be sampled from a population of small size. Modified systematic sampling is extended to multi-stage designs. Use of auxiliary variates is also made to improve the estimate in case of modified systematic sampling. Relative efficiency of modified systematic sampling is discussed for the populations with linear correlogram and it is observed that modified systematic sampling is always more efficient than simple random sampling and sometimes it may prove better than usual systematic sampling. For the populations with exponential correlogram modified systematic sampling is however noted to be less efficient than the usual systematic sampling but generally more efficient than simple random sampling. In the end some numerical examples are taken to illustrate the efficiency of modified systematic sampling.