Dawodu, O. O.Adewara, A. A.2023-06-222023-06-222016https://uilspace.unilorin.edu.ng/handle/20.500.12484/11234The importance of probability proportional to size sampling cannot be over emphasized. In recent times, Statisticians often work on complex survey data which involve weighting, as a result of the unequal probability nature of units. There is need to work on design weights, which is defined as the inverse of the probability of inclusion of single unit in the sample. Two simulated data sets are generated using ܴin order to obtain the probability of inclusion of single unit and also the joint probability of inclusion of units in the sample. Auxiliary variables and variables of interest were generated in such a way that there exists reasonable correlation between both. A procedure for selecting samples with probability proportional to size nature without replacement was proposed. This procedure could be used with Horvitz and Thompson estimator of variance. The variance estimates are obtained using the modified sample selection procedure and an existing procedure, and results obtained. For the two data sets, it is observed that the modified procedure is more efficient than the existing one.enInclusion probability, probability sampling, sampling scheme, unequal probability sampling, sampling without replacement.Article