Introduction to Sampling Lecture 23

 Introduction to Sampling

Lecture 23

Population

The aggregate of all individuals or objects having some characteristics of interest is called the population. The units or members of a population are represented by X1, X2,..., XN. The numerical value assigned to the units of interest is treated as a value of a random variable X, and the distribution of X is called population distribution.

A population can be classified into two:

1. Sampled Population

2. Target Population

Sampled population & Target population

A sampled population is that population from which a sample is selected. Whereas a population about which we wish to draw inferences is called the target population. The following example illustrates the difference between a sampled & a target population.

Suppose we desire to know the opinion of college students in the province of the KP with regard to the present examination system. Then our population will consist of the total number of students in all the colleges in the province. Suppose, on account of a shortage of resources & time, we are able to conduct such a survey only on six colleges scattered throughout the province. In such a case, the target population consists of the students of all the colleges in the province, while on the other hand, the sampled population consists of the students of six colleges, from which the sample of students will be selected. 


Sample

A small representative part is selected from the population for analysis.

Sampling Frame

A sampling frame is a complete list or a map that contains all the N sampling units in a population from which a sample is drawn.

e.g. A complete list of the name of all students in the college at particular point of time, a list of households in a city, a map of a village showing all fields, etc.

Sampling Plan

The sets of steps in selecting the sample from the population.

The following steps are involved in

developing a sampling plan:

        i.            Define the target population.

      ii.            Identify the sample population

    iii.            Develop a sampling frame.

    iv.            Define the sampling method.

      v.            Selection of sample size.

 

ERRORS IN SAMPLING

The following two main types of errors

involved in sampling.

1. Sampling Error

2: Non-Sampling Error.

Sampling Error

Sampling error is associated with sample selection from the population. The difference between an estimate and their corresponding parameter is called sampling error.

Let θ ^ be the estimate of  θ

The sampling error can be reduced by increasing the sample size.

Non-Sampling Errors

The errors that occur at the stage of gathering or processing the data are called non-sampling errors. All kinds of human errors, faulty sampling frames, etc. are included in non-sampling errors.

There are two main types of non-sampling errors.

i. Error in Response

ii. Non-response error

Bias

The difference between the expected value of the estimator and the true value of the parameter.

Let θ ^ be the estimate of  θ, then

If  θ^ is an unbiased estimator of θ , then E(θ ^) = θ

Bias(θ^) = 0


Sampling

Sampling is a statistical technique that is used in order to select a small part of a population.

There are two basic purposes of sampling:

i. It provides information about the population without examining all units of the population.

ii. The reliability of the estimates derived from the sample.

 

Types of Sampling

Sampling may be divided into two main branches:

1.      Probability Sampling

2.      Non - Probability Sampling

Probability Sampling

When each unit in a population has a known non-zero probability of being included in the sample. A probability sampling is also called random sampling.

The major types of probability sampling are:

        i.            Simple random sampling

      ii.            Stratified random sampling

    iii.            Systematic random sampling

    iv.            Cluster random sampling

Non-probability sampling

A process in which the personal judgment determines which units of the population are selected for a sample. A non-probability sampling is also called non-random sampling.

The common methods of noon probability sampling techniques are:

i. Purposive sampling.

ii. quota sampling.

iii.Snowball sampling


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