Determination of Probability of Selection for Two Measures of Sizes Using Unequal Probability Sampling in Agricultural Sample Surveys

Abdul Qayyum

doi:10.9734/ajea/2011/168

Abstract

In this paper an effort has been made to design a methodology for the determination of probability of selection for the cases where more than one measure of sizes are involved, especially in the case of agricultural sample surveys. So far no effort has been made for the cases of this sort in the literature of unequal probability sampling / probability proportional to size sampling. In this paper, a method has been developed to merge two measures of sizes in to one, which has combined proportional affect of both measures of sizes. The method is also valid for two measures of sizes having different units of measurements. It is also an unprecedented effort. A comparative study, using Horvitz - Thompson estimator and taking examples from agricultural surveys have been carried out to assess the performance of the new methodology.

Highlights

In case of unequal probability sampling design, a sample with varying probabilities of selection for each unit is selected
The probability of selection Pi of ith unit is proportional to its relevant measure of size Z i, and importantly, they are directly allied
There are many practical situations when it is required to select a sample using the technique of Probability Proportional to Size Sampling with consideration of more than one measure of sizes, i.e. there are two or more variables that are highly correlated with the main variable of interest

Summary

Introduction

In case of unequal probability sampling design, a sample with varying probabilities of selection for each unit is selected. The probability of selection Pi of ith unit is proportional to its relevant measure of size Z i , and importantly, they are directly allied. There are many practical situations when it is required to select a sample using the technique of Probability Proportional to Size Sampling with consideration of more than one measure of sizes, i.e. there are two or more variables that are highly correlated with the main variable of interest. In such cases, there is a need of selection of a sample having proportional effect of both measures of sizes

Methods

Results

Conclusion