A sampling procedure with inclusion probabilities proportional to size - ARCHIVED

A new unequal probability sampling scheme for selecting n(> 2) units without replacement from a finite population is proposed. This scheme ensures that the inclusion probabilities are proportional to sizes. It has the advantage of simplicity in selection and estimation and also provides a non-negative variance estimator. The variance of the Horvitz-Thompson (H-T) estimator under the proposed scheme is shown to be smaller than that of the customary estimator in probability proportional to size sampling with replacement. The proposed scheme also compares favourably with the without replacement scheme suggested by Sampford (1967) in an empirical study on a few natural populations.