01.sampling Fundamentals-Probability Sampling

Module-III
Sampling and Sampling

Distributions
Dr.Srilakshminarayana.G
Drawing a random sample using Standard
Sampling Procedures
Sample vs. Census
Conditions Favoring the Use of
Type of Study Sample Census
1. Budget Small Large
2. Time available Short Long
3. Population size Large Small
4. Variance in the characteristic Small Large
5. Cost of sampling errors Low High
6. Cost of nonsampling errors High Low
7. Nature of measurement Destructive Nondestructive
8. Attention to individual cases Yes No

The Sampling Design Process
Define the Population
Determine the Sampling Frame
Select Sampling Technique(s)
Determine the Sample Size
Execute the Sampling Process

Define the Target Population
The target population is the collection of elements or objects that possess the
information sought by the researcher and about which inferences are to be made.
The target population should be defined in terms of elements, sampling units,
extent, and time.
• An element is the object about which or from which the information is

desired, e.g., the respondent.
• A sampling unit is an element, or a unit containing the element, that is
available for selection at some stage of the sampling process.
• Extent refers to the geographical boundaries.
• Time is the time period under consideration.
Define the Target Population
Important qualitative factors in determining the sample size
• the importance of the decision

• the nature of the research
• the number of variables
• the nature of the analysis
• sample sizes used in similar studies
• incidence rates
• completion rates
• resource constraints
Classification of Sampling Techniques
Sampling Techniques
Nonprobability Probability
Sampling Techniques Sampling Techniques
Convenience Judgmental Quota Snowball

Sampling Sampling Sampling Sampling
Simple Random Systematic Stratified Cluster Other Sampling

Sampling Sampling Sampling Sampling Techniques
Simple Random Sampling
Step1. Define the Population.
Step2. Design the Sampling Frame.
Step3. All the units in the sampling frame have equal probability of
being selected into the sample.
Step3. Assign the numbers to all the units in the frame.
Step4. Generate the random numbers based on the sample size using
randbetween in excel.
Step5. For example, if the sample size=25 and population size if 60,
then generate 25 random numbers between 1 and 60
Step6. Select all those units corresponding to the numbers as sample
units.
Example-1
Mr. Arvind is the manager of a store in Mysore. They supply the items
to customers, spread over in that area. He wishes to study the following:
1. Average age of the customer in that area.

2. Average distance travelled by their representatives.
3. Average number of items purchased by a customer.
4. Average number of times the customer visits the store.
The estimated sample size is 42.

Stratified Random Sampling
Step1. Define the population.
Step2. Design the sampling frame.
Step3. Divide the units into groups, called stratum, according to one or
more factors such that, units within the group are homogeneous
and units between the groups are heterogeneous.
Step4. Divide the sample size across the stratum and select the units
from each stratum.
Example-2
ABC’s client has large national and international networks of businesses

and business units, and it relies on ABC to ensure that each part of the
organization receives an adequate amount of customer feedback
within a specified period of time. One of the ways the ABC system
does this is by predicting how many recipients of survey invitations
will choose to complete the survey.
Collect a random sample to study the average number of forms
received and filled as per the brand.
Additional Information
• Population Size (N) =2020
• Required Sample Size (n) =750
• The population is divided into strata
S.No. Brand Places Cost/Unit

1 Double Tree 133 $3
2 Embassy Suites 169 $4
3 Hampton Inn & Suites 1194 $6
4 Hilton Garden Inn 396 $2
5 Homewood Suites 128 $4

Data Description
• DoubleTree by Hilton is a worldwide brand of full service hotels trademarked by
Hilton Worldwide. There are currently more than 325 locations with more than 80,000
rooms on five continents.
• Embassy Suites Hotels is a chain of upscale all-suite hotels trademarked by

Hilton Worldwide. As of Feb. 22, 2011, there are 200 Embassy Suites Hotels in the
United States, plus 8 Embassy Suites Hotels internationally.
• Hilton Garden Inn is a chain of hotels trademarked by the Hilton Worldwide. Hilton

Garden Inns are considered to be upscale mid-priced hotels that are designed for both
business and leisure travellers.
• Hampton Hotels, Hampton Inn, Hampton Inn & Suites, and Hampton by

Hilton are the names of a brand of hotels trademarked by Hilton Worldwide.
• Homewood Suites by Hilton is an American chain of all-suite residential-style hotels

managed by the Hilton Worldwide. As of February 2012, the chain consists of 310
hotels and another 75 under development.
Sampling Design
•Step1.
Divide the population, of size into sub-populations based on a
criterion. Each sub-population is called as Stratum and the collection of
all the sub-populations is called as Strata. Size of each stratum is
denoted by .
Step2. Divide the sample size into sub-sample sizes , using an allocation
method.
Step3. Assign the sub-sample sizes to different stratum.
Step4. Use a simple random sampling to collect the samples from each
stratum.
Allocation Methods
• Method-1: Proportional Allocation
S.No. Stratum
1 Double Tree 133 49
2 Embassy Suites 169 63
3 Hampton Inn & Suites 1194 443
4 Hilton Garden Inn 396 147
5 Homewood Suites 128 48

• Method-2: Optimum Allocation
Step1. Define the cost function C as
where is the overhead cost and

is the cost per unit in the i-th stratum.
Step2. Let C be the given cost then variance of the estimator is minimum
if
: Estimated Value of the Standard deviation.

Optimum Allocation
S.No. Stratum Cost/Unit

1 Double Tree 133 $3 61
2 Embassy Suites 169 $4 53
3 Hampton Inn & Suites 1194 $6 328
4 Hilton Garden Inn 396 $2 250
5 Homewood Suites 128 $4 59

Advantages of Stratified Random Sampling
• If data of known precision are wanted for certain subdivisions of the
population, it is advisable to treat each subdivision as a ''population" in its
own right.
• Administrative convenience may dictate the use of stratification; for

example, the agency conducting the survey may have field offices, each of
which can supervise the survey for a part of the population.
• Sampling problems may differ markedly in different parts of the population.

With human populations, people living in institutions (e.g., hotels, hospitals,
prisons) are often placed in a different stratum from people living in
ordinary homes because a different approach to the sampling is appropriate
for the two situations. In sampling businesses we may possess a list of the
large firms, which are placed in a separate stratum. Some type of area
sampling may have to be used for the smaller firms.
• Stratification may produce a gain in precision in the estimates of
characteristics of the whole population. It may possible to divide a
heterogeneous population into subpopulations, each of which is
internally homogeneous. This is suggested by the name strata, with its
implication of a division into layers. If each stratum is homogeneous,
in that the measurements vary little from one unit to another, a precise
estimate of any stratum mean can be obtained from a small sample in
that stratum. These estimates can then be combined into a precise
estimate for the whole population.
In a given stratum, take a larger sample if

1. The stratum is larger.
2. The stratum is more variable internally.
3. Sampling is cheaper in the stratum.
Systematic Random Sampling
•Step1.
Define the Population.
Step2. Design the Sampling Frame.
Step3. Let the population size be ‘N’ and the sample size be ‘n’.
Step4. Find the value of the pivotal value
Step5. Generate the random numbers between 1 and k.
Step6. For example, if 5, then generate random numbers between 1 and
5. Suppose that the number is 5. We select the 5th , 5+5 =10th , 10+5=15th
,…., till we get 20 elements.
Systematic Sampling
• The sample is chosen by selecting a random starting point and then picking every ith element in
succession from the sampling frame.
• The sampling interval, i, is determined by dividing the population size N by the sample size n and
rounding to the nearest integer.
• When the ordering of the elements is related to the characteristic of interest, systematic sampling
increases the representativeness of the sample.
• If the ordering of the elements produces a cyclical pattern, systematic sampling may decrease the
representativeness of the sample.
For example, there are 100,000 elements in the population and a sample of 1,000 is desired. In
this case the sampling interval, i, is 100. A random number between 1 and 100 is selected. If, for
example, this number is 23, the sample consists of elements 23, 123, 223, 323, 423, 523, and so
on.

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Module-III

Sampling and Sampling

1. Budget Small Large

2. Time available Short Long

3. Population size Large Small

4. Variance in the characteristic Small Large

5. Cost of sampling errors Low High

6. Cost of nonsampling errors High Low

7. Nature of measurement Destructive Nondestructive

8. Attention to individual cases Yes No

Define the Population

Determine the Sampling Frame

Select Sampling Technique(s)

Determine the Sample Size

Execute the Sampling Process

• An element is the object about which or from which the information is

• the importance of the decision

Convenience Judgmental Quota Snowball

Simple Random Systematic Stratified Cluster Other Sampling

1. Average age of the customer in that area.

The estimated sample size is 42.

ABC’s client has large national and international networks of businesses

S.No. Brand Places Cost/Unit

5 Homewood Suites 128 $4

• Embassy Suites Hotels is a chain of upscale all-suite hotels trademarked by

• Hilton Garden Inn is a chain of hotels trademarked by the Hilton Worldwide. Hilton

• Hampton Hotels, Hampton Inn, Hampton Inn & Suites, and Hampton by

• Homewood Suites by Hilton is an American chain of all-suite residential-style hotels

Step3. Assign the sub-sample sizes to different stratum.

5 Homewood Suites 128 48

Step1. Define the cost function C as

where is the overhead cost and

: Estimated Value of the Standard deviation.

S.No. Stratum Cost/Unit

5 Homewood Suites 128 $4 59

• Administrative convenience may dictate the use of stratification; for

• Sampling problems may differ markedly in different parts of the population.

In a given stratum, take a larger sample if

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