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
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
If
Bias(
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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