INTRODUCTION

In this chapter, we discuss four basic sampling designs, namely, simple random sampling (SRS), stratified sampling, systematic sampling and cluster sampling. In the process of sample selection, it is possible to select elements directly, if a suitable sampling frame for their selection is available. Often, sampling frame is available only for a group of individual elements, instead of each element. These groups of individual elements, generally some areal units, are commonly referred to as clusters. If the sampling frame for each cluster in a population is available, the sample can be selected either in one stage or at multiple stages. In one stage, in a selected cluster, all the elements comprising it will be automatically included in a sample. Selection in two or more stages, discussed in Chapters 3 and 4, involves selection of elements from selected clusters.

Of the four designs, mentioned above, SRS and systematic sampling are the two basic methods for selection of sampling units (either units or clusters). Both provide equal chance to each sampling unit for inclusion in a sample. Another variant, known as PPS sampling wherein sampling units are selected with varying probability, is also elaborated here. Further, we discuss stratified sampling which is a technique of grouping sampling units in a population before selection where grouping is done to put restrictions on selection of a combination of sampling units to benefit the procedure of selection. The cluster sampling in which all the elements in a selected cluster are included in a sample is generally avoided. However, it facilitates understanding multistage designs. In each of the next four sections, we outline the essential steps in a design. They are as follows:

1. • Methods of selection of sampling units,

2. • Estimation of a parameter, and

3. • Providing estimate of the error such as sampling variance of an estimate.

SIMPLE RANDOM SAMPLING

2.2.1 Description

In this design, each and every sampling unit in a population receives equal chance of being included in a sample. The method is discussed assuming individual units as the sampling units, but remains true even if group of units, instead of individual units, is considered. Let there be N units in a population from which n are to be selected for inclusion in a sample.