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Page 1: Assignment sampling techniques

Subject: Statistical Inference by Dr. Fahd Amjad

Page 1 of 9

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

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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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Subject: Statistical Inference by Dr. Fahd Amjad

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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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Subject: Statistical Inference by Dr. Fahd Amjad

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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

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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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Subject: Statistical Inference by Dr. Fahd Amjad

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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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Subject: Statistical Inference by Dr. Fahd Amjad

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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.