Sampling Techniques

1. Subject: Statistical Inference by Dr. Fahd Amjad
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Assignment: Sampling Techniques
Subject: Inferential Statistics
Submitted to: Dr. Fahd Amjad
Submitted by: Danish Alam
Roll No. FA-15 RMS-002
Program: MS (MS)
Department: Management Sciences

2. Subject: Statistical Inference by Dr. Fahd Amjad
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Sampling Techniques
Sample:
Definition: “It is the subset of population.” Or
“It is the collection of data or elements from population by a defined procedure.”
 Each element of sample is known as sample points.
For Example:
A sample of heights of 10 students collected from a population of 30 students in a class.
Sampling:
Definition: “the act of taking a portion or sample from population is called sampling.” Or
“It is concerned with the selection of a subset of individuals from within a statistical population
to estimate characteristics of whole population.”
Sampling Techniques:
There are two types of sampling;
 Probability Sampling
 Non-Probability Sampling
1) Probability Sampling (Definition):
Probability or random sampling gives all the members of population a known chance of being
selected for inclusion in the sample and this does not depend upon previous events in the
selection process. In other words, the selection of individuals does not affect the chance of
anyone else in the population being selected. Or

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Probability sampling is a sampling technique wherein the samples are gathered in a process
that gives all the individuals in the population equal chances of being selected.
 There are four types of Probability Sampling;
i) Simple Random Sampling
ii) Systematic Sampling
iii) Stratified Sampling
iv) Cluster or Multi-Stage Sampling
Diagram:
Diagram Showing types of Probability Sampling.
i) Simple Random Sampling:
This is the ideal choice as it is a perfect random method. Using this method, individuals are
randomly selected from a list of the population and every single individual has an equal
chance of selection. Or
In statistics, a simple random sample is a subset of individuals (a sample) chosen from a
larger set (a population). Each individual is chosen randomly and entirely by chance, such that
Simple
Random
Sampling
Systematic
Sampling
Stratified
Sampling
Cluster or
Multi-
Stage
Sampling

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each individual has the same probability of being chosen at any stage during the sampling
process
ii) Systematic Random Sampling:
It is defined as “the statistical method involve in the selection of elements from an ordered
sampling frame.” Or
Systematic sampling is a frequently used variant of simple random sampling. When
performing systematic sampling, every Kth element from the list is selected (this is referred to
as the sample interval) from a randomly selected starting point. Or
A random sampling with a system is called Systematic Random Sampling. From the sampling
frame, a starting point is chosen at random, and choices thereafter are at regular intervals.
Advantage: The sample usually will be easier to identify than it would be if simple random
sampling were used.
 For Example: Selecting every 100th listing in a telephone book after the first randomly
selected listing.
 For Example, if we have a listed population of 6000 members and wish to draw a
sample of 2000, we would select every 30th (6000 divided by 200) person from the list.
In practice, we would randomly select a number between 1 and 30 to act as our
starting point.
 The one potential problem with this method of sampling concerns the arrangement of
elements in the list? If the list is arranged in any kind of order e.g. if every 30th house is
smaller than the others from which the sample is being recruited, there is a possibility
that the sample produced could be seriously biased.
iii) Stratified Sampling:
Stratified sampling is a variant on simple random and systematic methods and is used when
there are a number of distinct subgroups, within each of which it is required that there is full
representation. A stratified sample is constructed by classifying the population in sub-
populations (or strata), base on some well-known characteristics of the population, such as
age, gender or socio-economic status. The selection of elements is then made separately from
within each stratum, usually by random or systematic sampling methods. Or

5. Subject: Statistical Inference by Dr. Fahd Amjad
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Stratified sampling refers to a type of sampling method. With stratified sampling, the
researcher divides the population into separate groups, called strata. Then, a
probability sample (often a simple random sample) is drawn from each group.
Advantage: If strata are homogeneous, this method is as “precise” as simple random sampling
but with a smaller total sample size.
For Example: The basis for forming the strata might be department, location, age, industry
type, etc.
 Stratified sampling methods is further divided into two types;
 In Proportionate Sampling, the strata sample sizes are made proportional to the strata
population sizes. For Example, if the first strata are made up of males, then as there
are around 50% of males in the UK population, the male strata will need to represent
around 50% of the total sample.
 In Disproportionate Methods, the strata are not sampled according to the population
sizes, but higher proportions are selected from some groups and not others. This
technique is typically used in a number of distinct situations:
 The costs of collecting data may differ from subgroup to subgroup.
 We might require more cases in some groups if estimations of populations’ values are
likely to be harder to make i.e. the Market Research World.
 Larger the sample size (up to certain limits), the more accurate any estimations are
likely to be.
iv) Cluster or Multi-Stage Sampling:
Benefits and Usage:
Cluster sampling is a frequently-used, and usually more practical, random sampling method. It
is particularly useful in situations for which no list of the elements within a population is
available and therefore cannot be selected directly. As this form of sampling is conducted by
randomly selecting subgroups of the population, possibly in several stages, it should produce
results equivalent to a simple random sample. It is often used in marketing research.
The sample is generally done by first sampling at the higher level(s) e.g. randomly sampled
countries, then sampling from subsequent levels in turn e.g. within the selected countries
sample counties, then within these postcodes, then within these households, until the final
stage is reached, at which point the sampling is done in a simple random manner e.g.
sampling people within the selected households. Or

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“It is often used in marketing research. In this technique, the total population is divided into
these groups (or clusters) and a simple random sample of the groups is selected.”
Advantage: The close proximity of elements can be cost effective (I.e. many sample
observations can be obtained in a short time).
Disadvantage: This method generally requires a larger total sample size than simple or
stratified random sampling.
For Example: A primary application is area sampling, where clusters are city blocks or other
well-defined areas.
Cluster Sampling is generally used if;
 Cluster sampling is a sampling technique used when "natural" but relatively
homogeneous groupings are evident in a statistical population.
 No list of the population exists.
 Well-defined clusters, which will often be geographic areas, exist.
 A reasonable estimate of the number of elements in each level of clustering can be
made.
 Often the total sample size must be fairly large to enable cluster sampling to be used
effectively.
2) Non-Probability Sampling (Definition):
“Non-Probability sampling is any sampling method where some elements of population have
no chance of selection (these are sometimes referred to as ‘out of coverage or under
covered’), or where the probability of selection can’t be accurately determined.” Or
“A core characteristic of non-probability sampling techniques is that samples are selected
based on the subjective judgment of the researcher, rather than random selection
(i.e., probabilistic methods), which is the cornerstone of probability sampling techniques.”
 There are five main types of Non-Probability Sampling;
i. Convenience Sampling
ii. Judgment Sampling
iii. Snowball Sampling
iv. Ad hoc quotas sampling

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v. Case Study Sampling
Diagram showing types of Non-Probability Sampling
i) Convenience Sampling:
 A statistical method of drawing representative data by selecting people because of
the ease of their volunteering or selecting units because of their availability or
easy access. Or
 It is a non-probability sampling technique. Items are included in the sample without
known probabilities of being selected.
 The sample is identified primarily by convenience.
 Advantage: Sample selection and data collection are relatively easy. The data in this
type of sampling is easily available and can gather data quickly.
 Disadvantage: It is impossible to determine how representative of the population the
sample is. The another disadvantages are the risk that the sample might
not represent the population as a whole, and it might be biased by volunteers.
 For Example: A professor conducting research might use student volunteers to
constitute a sample.
Convenience
Sampling
Judgement
Sampling
Snowball
Sampling
Ad Hoc Quota
Sampling
Case Study
Sampling

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ii) Judgment Sampling:
 Judgment sample is a type of non-random sample that is selected based on the
opinion of an expert. Results obtained from a judgment sample are subject to some
degree of bias, due to the frame and population not being identical. Or
 The person most knowledgeable on the subject of the study selects elements of the
population that he or she feels are most representative of the population.
 It is a non-probability sampling technique.
 Advantage: It is a relatively easy way of selecting a sample.
 Disadvantage: The quality of the sample results depends on the judgment of the
person selecting the sample.
 For Example: A reporter might sample three or four senators, judging them as
reflecting the general opinion of the senate.
iii) Snowball Sampling:
 A snowball sample is a non-probability sampling technique that is appropriate to use in
research when the members of a population are difficult to locate.
 A snowball sample is one in which the researcher collects data on the few members of
the target population he or she can locate, then asks those individuals to provide
information needed to locate other members of that population whom they know.
 Snowball sampling is hardly likely to lead a representative sample, but there are times
when it may be the best or only method available.
 For instance, if you are studying the homeless, you are not likely to find a list of all the
homeless people in your city. However, if you identify one or two homeless individuals
that are willing to participate in your study, it is likely that they know other homeless
individuals in their area and can help you locate them. The same goes for underground
subcultures, or any population that might want to keep their identity hidden, such as
undocumented immigrants or ex-convicts.
 Because snowball sampling is hardly representative of the larger study population, it is
primarily used for exploratory purposes.
iv) Ad Hoc Quota Sampling:
Quota sampling is a type of non-probability sampling that involves a two-step process:
 1. Specify a list of relevant control categories or quotas such as age, gender, income, or
education. A quota is some specific requirement or predefined category. The target
population is first segmented into mutually exclusive sub-groups, which means that
one individual can be a member of only one category or sub-group. The researcher

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takes special care to obtain a sample that is similar to the target population on some
specified control category.
 2. Collect a sample that has the same properties as the target population. To do this,
the researcher must know the distribution of these properties across that population.
 For example, let's look at a target population of college students at a local college.
Because the researcher can access this data, he knows that in this given population,
43% of the students are male and 57% are female. For a sample size of 1,000, the
researcher knows that 430 males and 570 females will need to be interviewed from
that population.
References:
www.google.com
www.wikipedia.org.com.