TERMINOLOGIES
Population or Universe: It refers to the group of people, items or units
under investigation and includes every individual. The entire aggregation of
items from which samples can be drawn is known as population. “N”
represents the size of the population.
Sample: A collection consisting of a part or subset of the objects or
individuals of population which is selected for the purpose, representing the
population
Sampling: It is the process of selecting a sample from the population. For
this population is divided into a number of parts called Sampling Units.
Large sample: The sample size n is greater than 30 (n≥30) it is known
as large sample.
Small Sample: The sample size n is smaller than 30 (n<30) it is known as
small sample.
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Need of Sampling
Large population can be conveniently covered.
Time, money and energy is saved.
Helpful when units of area are homogenous.
Used when percent accuracy is not acquired.
Used when the data is unlimited.
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Advantages of Sampling
Economical: Reduce the cost compare to entire population.
Increased speed: Collection of data, analysis and Interpretation of data
etc. take less time than the population.
Accuracy: Due to limited area of coverage, completeness and accuracy
is possible.
Rapport: Better rapport is established with the respondents, which
helps in validity and reliability of the results.
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Disadvantages of Sampling
Biasedness: Chances of biased selection leading to incorrect
conclusion.
Selection of true representative sample: Sometimes it is difficult to
select the right representative sample
Need for specialized knowledge: The researcher needs knowledge,
training and experience in sampling technique, statistical analysis and
calculation of probable error
Impossibility of sampling: Sometimes population is too small or too
heterogeneous to select a representative sample.
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Characteristics of Good sample
A true representative of the population.
Free from error due to bias.
Adequate in size for being reliable.
Units of sample should be independent and relevant.
Units of sample should be complete precise and up to date.
Free from random sampling error.
Avoiding substituting the original sample for convenience.
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Sampling and Sampling methods
Sampling definition: It is the process of selecting a sample from the
population. For this population is divided into a number of parts
called Sampling Units.
For example, if a drug manufacturer would like to research the
adverse side effects of a drug on the country’s population, it is almost
impossible to conduct a research study that involves everyone. In this
case, the researcher decides a sample of people from
each demographic(group) and then researches them, giving him/her
indicative feedback on the drug’s behavior.
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Probability Sampling
Probability sampling is a sampling technique in which researchers
choose samples from a larger population using a method based on the
theory of probability. This sampling method considers every member of
the population and forms samples based on a fixed process.
For example, in a population of 1000 members, every member will
have a 1/1000 chance of being selected to be a part of a sample.
Probability sampling eliminates bias in the population and gives all
members a fair chance to be included in the sample.
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1.Simple Random Sampling
Definition: Simple random sampling is defined as a sampling technique where
every item in the population has an even chance and likelihood of being selected in
the sample. Here the selection of items entirely depends on luck or probability, and
therefore this sampling technique is also sometimes known as a method of chances.
The main attribute of this sampling method is that every sample has the same
probability of being chosen.
The sample size in this sampling method should ideally be more than a few hundred
so that simple random sampling can be applied appropriately. They say that this
method is theoretically simple to understand but difficult to implement practically.
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Researchers follow these methods to select a simple random sample:
They prepare a list of all the population members initially, and then each member is
marked with a specific number ( for example, there are nth members, then they will
be numbered from 1 to N).
From this population, researchers choose random samples using two ways: Method
of lottery, Random number tables.
• Method of lottery: Using the lottery method is one of the oldest ways and is a
mechanical example of random sampling. In this method, the researcher gives each
member of the population a number. Researchers draw numbers from the box
randomly to choose samples.
•Use of random numbers: The use of random numbers is an alternative method that
also involves numbering the population. Researcher also uses random number
generator software. Researchers prefer a random number generator software, as no
human interference is necessary to generate samples.
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Steps to conduct simple random sampling
Follow these steps to extract a simple random sample of 100 employees out of
500.
1. Make a list of all the employees working in the organization. (as mentioned
there are 500 employees in the organization, the record must contain 500
names).
2. Assign a sequential number to each employee (1,2,3…n). This is your
sampling frame (the list from which you draw your simple random sample).
3. Figure out what your sample size is going to be. (In this case, the samples size is 100).
4. Use a random number generator For example, if your sample size is 100
and your population is 500, generate 100 random numbers between 1 and
500.
Advantages of simple random sampling
It is a fair method of sampling, and if applied appropriately, it helps to
reduce any bias involved compared to any other sampling method involved.
The person conducting the research doesn’t need to have prior knowledge of
the data he/ she is collecting. One can ask a question to gather the researcher
need not be a subject expert.
Don’t need any technical knowledge. You only require essential listening
and recording skills.
Since the population size is vast in this type of sampling method, there is no
restriction on the sample size that the researcher needs to create. From a
larger population, you can get a small sample quite quickly.
The data collected through this sampling method is well informed; more the
samples better is the quality of the data.
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2.Cluster Sampling
Cluster sampling is defined as a sampling method where the researcher
creates multiple clusters of people from a population where they are
indicative of homogeneous characteristics and have an equal chance of
being a part of the sample.
Example: Consider a scenario where an organization is looking to
survey the performance of smartphones across Germany. They can
divide the entire country’s population into cities (clusters) and select
further towns with the highest population and also filter those using
mobile devices.
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Types of cluster sampling
1. Single-stage cluster sampling: As the name suggests, sampling is done just once. An
example of single-stage cluster sampling – An NGO wants to create a sample of girls
across five neighboring towns to provide education. Using single-stage sampling, the
NGO randomly selects towns (clusters) to form a sample and extend help to the girls
deprived of education in those towns.
2. Two-stage cluster sampling: Here, instead of selecting all the elements of a cluster, only
a handful of members are chosen from each group by implementing systematic or simple
random sampling. An example of two-stage cluster sampling – A business owner wants to
explore the performance of his/her plants that are spread across various parts of the U.S.
The owner creates clusters of the plants. He/she then selects random samples from these
clusters to conduct research.
3. Multiple stage cluster sampling: Multiple-stage cluster sampling takes a step or a few
steps further than two-stage sampling. For conducting effective research across multiple
geographies, one needs to form complicated clusters that can be achieved only using the
multiple-stage sampling technique. An example of Multiple stage sampling by clusters –
An organization intends to survey to analyze the performance of smartphones across
India. They can divide the entire country’s population into states (clusters) and select
cities with the highest population, then select village with highest population among cities
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and also filter those using mobile devices.
Steps to conduct cluster sampling
1. Sample: Decide the target audience and also the sample size.
2. Determine groups: Determine the number of groups by including
the same average members in each group. Make sure each of these
groups are distinct from one another.
3. Select clusters: Choose clusters by applying a random selection.
4. Create sub-types: It is bifurcated into two-stage and multi-stage
subtypes based on the number of steps followed by researchers to
form clusters.
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Advantages of Cluster sampling
Consumes less time and cost
Convenient access: Researchers can choose large samples with this
sampling technique, and that’ll increase accessibility to various
clusters.
Data accuracy: Since there can be large samples in each cluster, loss
of accuracy in information per individual can be compensated.
Ease of implementation: Cluster sampling facilitates information
from various areas and groups. Researchers can quickly implement it
in practical situations compared to other probability sampling
methods.
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3.Systematic Sampling
Systematic sampling is defined as a probability sampling method
where the researcher chooses elements from a target population by
selecting a random starting point and selects sample members after a
fixed ‘sampling interval.’
Example: For a sample of 50 students from the population of 400
students, the sampling is 400/50 = 8 i.e. select one student out of every
eight students in the population. The starting points for the selection is
chosen at random.
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Steps to conduct Systematic sampling
1. Develop a defined structural audience to start working on the sampling aspect.
2. As a researcher, figure out the ideal size of the sample, i.e., how many people from the
entire population to choose to be a part of the sample.
3. Once you decide the sample size, assign a number to every member of the sample.
4. Define the interval of this sample. This will be the standard distance between the
elements.
5. For example, the sample interval should be 10, which is the result of the division of 5000
(N=size of the population) and 500 (n=size of the sample).
Systematic Sampling Formula for interval (i) = N/n = 5000/500 = 10
6. Select the members who fit the criteria which in this case will be 1 in 10 individuals.
7. Randomly choose the starting member (r) of the sample and add the interval to the
random number to keep adding members in the sample. r, r+i, r+2i, etc. will be the
elements of the sample.
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Advantages of Systematic sampling
It’s extremely simple and convenient for the researchers to create, conduct, analyze
samples.
As there’s no need to number each member of a sample, it is better for representing
a population in a faster and simpler manner.
The samples created are based on precision in member selection and free from
favoritism.
In the other methods of probability sampling methods such as cluster sampling
and stratified sampling or non-probability methods such as convenience sampling,
there are chances of the clusters created to be highly biased which is avoided in
systematic sampling as the members are at a fixed distance from one another.
The factor of risk involved in this sampling method is extremely minimal.
In case there are diverse members of a population, this sampling technique can be
beneficial because of the even distribution of members to form a sample.
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4.Stratified random Sampling
Stratified random sampling is a type of probability sampling using which
a research organization can branch off the entire population into multiple non-
overlapping, homogeneous groups (strata) and randomly choose final members
from the various strata for research which reduces cost and improves efficiency.
Members in each of these groups should be distinct so that every member of all
groups get equal opportunity to be selected using simple probability. This sampling
method is also called “random quota sampling”.
Age, socioeconomic divisions, nationality, religion, educational achievements and
other such classifications fall under stratified random sampling.
Let’s consider a situation where a research team is seeking opinions about religion
amongst various age groups. Instead of collecting feedback from 326,044,985 U.S
citizens, random samples of around 10000 can be selected for research. These
10000 citizens can be divided into strata according to age, i.e, groups of 18-29, 30-
39, 40-49, 50-59, and 60 and above. Each stratum will have distinct members and
number of members.
Types of Stratified Random sampling
1. Proportionate Stratified Random Sampling: In this approach, each stratum sample size is
directly proportional to the population size of the entire population of strata. That means each
strata sample has the same sampling fraction.
If you have 4 strata with 500, 1000, 1500, 2000 respective sizes and the research organization selects
½ as sampling fraction. A researcher has to then select 250, 500, 750, 1000 members from the
respective stratum. Irrespective of the sample size of the population, the sampling fraction will
remain uniform across all the strata.
Stratum A B C D
Population Size 500 1000 1500 2000
Sampling Fraction 1/2 1/2 1/2 1/2
Final Sampling
250 500 750 1000
Size Results
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2. Disproportionate Stratified Random Sampling:
Sampling fraction is the primary differentiating factor between the proportionate
and disproportionate stratified random sampling. In disproportionate sampling, each
stratum will have a different sampling fraction.
The success of this sampling method depends on the researcher’s precision at
fraction allocation. If the allotted fractions aren’t accurate, the results may be biased
due to the overrepresented or underrepresented strata.
Stratum A B C D
Population Size 500 1000 1500 2000
Sampling Fraction 1/2 1/3 1/4 1/5
Final Sampling
250 333 375 400
Size Results
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Steps to conduct Stratified Random sampling
1. Define the target audience.
2. Figure out the number of strata to be used.
3. Considering the entire population, each stratum should be unique and should cover each
and every member of the population. Within the stratum, the differences should be
minimum whereas each stratum should be extremely different from one another. Each
element of the population should belong to just one stratum.
4. Assign a random, unique number to each element.
5. Figure out the size of each stratum according to your requirement. The numerical
distribution amongst all the elements in all the strata will determine the type of
sampling to be implemented. It can either be proportional or disproportional stratified
sampling.
6. The researcher can then select random elements from each stratum to form the sample.
Minimum one element must be chosen from each stratum so that there’s representation
from every stratum.
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Advantages of Stratified Random sampling
Better accuracy in results in comparison to other probability sampling methods such
as cluster sampling, simple random sampling, and systematic sampling or non-
probability methods such as convenience sampling. This accuracy will be
dependent on the distinction of various strata, i.e., results will be highly accurate if
all the strata are extremely different.
Due to statistical accuracy of this method, smaller sample sizes can also retrieve
highly useful results for a researcher.
This sampling technique covers maximum population as the researchers have
complete charge over the strata division.
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Non-Probability sampling
Unequal chance of being included in the sample (non-random).
Non random or non – probability sampling refers to the sampling process in
which, the samples are selected for a specific purpose with a predetermined basis of
selection.
The sample is not a proportion of the population and there is no system in selecting
the sample. The selection depends upon the situation.
No assurance is given that each item has a chance of being included as a sample.
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1.Convenience sampling
Convenience sampling is defined as a method adopted by researchers where they collect market
research data from a conveniently available pool of respondents.
Researchers use convenience sampling in situations where additional inputs are not necessary for the
principal research. There are no criteria required to be a part of this sample. Thus, it becomes
incredibly simplified to include elements in this sample. All components of the population are
eligible and dependent on the researcher’s proximity to get involved in the sample.
The researcher chooses members merely based on proximity and doesn’t consider whether they
represent the entire population or not. Using this technique, they can observe habits, opinions, and
viewpoints in the easiest possible manner.
For example, a university student working on a project and wants to understand the average
consumption of soda on campus on a Friday night will most possibly call his/her classmates and
friends and ask how many cans of soda they consume. Or may go to a party nearby and conduct an
easy survey. There is always a chance that the randomly selected population may not accurately
represent the population of interest, thus increasing the chances of bias.
Another example of the 10,000 university students, if we were only interested in achieving a sample
size of say 100 students. we may simply stand at one of the main entrances to campus, where it
would be easy to invite the many students that pass by to take part in the research. So, it is very easy
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2.Quota Sampling
In this method, the sample size is determined first and then quota is fixed for various
categories of population, which is followed while selecting the sample.
In this method the quota has to be determined in advance and intimated to the investigator.
The quota for each segment of the population may be fixed at random or with a specific
basis. Normally such a sampling method does not ensure representativeness of the
population.
For example, a cigarette company wants to find out what age group prefers what brand of
cigarettes in a particular city. He/she applies quotas on the age groups of 21-30, 31-40, 41-
50, and 51+. From this information, the researcher gauges the smoking trend among the
population of the city.
TYPES OF QUOTA SAMPLING:
1.Controlled quota sampling: Controlled quota sampling imposes restrictions on the
researcher’s choice of samples. Here, the researcher is limited to the selection of samples.
2.Uncontrolled quota sampling: Uncontrolled quota sampling does not impose any
restrictions on the researcher’s choice of samples. Here, the researcher chooses sample
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members at will.
3. Purposive (Judgmental) Sampling
In this method, the sample selection is purely based on the judgment of the
investigator or the researcher. This is because, the researcher may lack information
regarding the population from which he has to collect the sample. Population
characteristics or qualities may not be known, but sample has to be selected.
In this method of sampling the choice of sample items depends primarily on the
judgment of the researcher. In other words, the researcher determines and includes
those items in the sample which he thinks are most typical of the universe with
regard to the characteristics of research project.
For example, suppose 100 boys are to be selected from a college with 1000 boys. If
nothing is known about the students in this college, then the investigator may visit
the college and choose the first 100 boys he meets. Or he may select 100 boys all
belonging to III Year. Or he might select 25 boys from Commerce course, 25 from
Science courses, 25 boys from Arts courses and 25 from Fine arts courses. Hence,
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4.Snowball Sampling
Selecting participants by finding one or two participants and then asking them to
refer you to others.
This sampling method that researchers apply when the subjects are difficult to
trace.
For example, it will be extremely challenging to survey shelterless people or illegal
immigrants. In such cases, using the snowball theory, researchers can track a few
categories to interview and derive results.
Researchers also implement this sampling method in situations where the topic is
highly sensitive and not openly discussed—for example, surveys to gather
information about HIV Aids. Not many victims will readily respond to the questions. Still, researchers can contact people they might know or volunteersa ssociated with the cause to get in touch with the victims and collect information.