Comparison of Efficiency of Balanced and PPS Sampling Under the Same Conditions and the Effect of Sample Size on The

In this article, the efficiency of balanced sampling is compared with that of PPS sampling under the same conditions, where in both methods, only one auxiliary variable is used. For this purpose, by performing a simulation study with different sampling fractions, the efficiency has been computed. The findings show that under the same conditions in terms of using auxiliary information, regardless of the size of sampling fraction, the use of balanced sampling leads to more gain than that of the PPS sampling and by increasing the sampling fraction, the gain is increased.