Select a Sampling Technique
• Bayesian Versus Traditional approach
• Sampling with or without replacement
• Nonprobability Versus probability
Proportional To Size
• Convenience sampling is done based on
ease of selection of sample. The samples
are chosen simply because they were the
most convenient to choose.
• For purposive sampling, the researcher
chooses the sample based on who they
think would be appropriate for the study.
• Under quota sampling the samples are
selected in quotas from different strata.
• Snowball sampling is non-probability
sampling technique where existing samples
elements recruit future sample elements
from among their acquaintances
Simple Random Sampling
• Simple random sampling is defined by two
properties. First, each member of the
population has an equal and known
probability of being selected in the sample.
Second, each combination of members of
the population has an equal chance of
forming the sample.
• Systematic sampling is also called as
Interval sampling. The sample is chosen by
selecting a random starting point and then
picking every ith element in succession
from the sampling frame.
• For stratified sampling, the population is
divided into homogeneous groups called
Strata. The strata should be mutually
exclusive and collectively exhaustive.
Independent samples are selected from
• In cluster sampling the target population is
first divided into subpopulations called
clusters. The clusters are mutually
exclusive and collectively exhaustive
subpopulations. A random sample of
clusters is selected, using probability
• If clusters are geographic subdivisions, then the
cluster sampling is also referred to as area
sampling. In case the cluster sampling units do
not have the same or approximately same number
of elements, then each cluster being included in
the sample is selected randomly such that the
probability of selection is proportional to the size
of the cluster. This type of cluster sampling is
called Sampling with probability proportional to
Selection of Non-probability versus probability sampling
Selection of non-probabilityversus probability samplingtechnique depends
on many factors. Some key conditionsin favor of probabilityand non-
probability samplingare discussed in below table:
Selection Criteria Favor Non-Probability
Type of Research QualitativeResearch Quantitative
and Non sampling error
Non sampling error is
Population Homogeneity High Low
Statistical Considerations Unfavorable Favorable
Operational Considerations Favorable Unfavorable
Time Availability Low High
Budget Low High
Question for Discussion
• In order to survey the opinions of its
customers, a restaurant chain obtained a
random sample of 30 customers from each
restaurant in the chain. Each selected
customer was asked to fill out a survey.
Which one of the following sampling plans
was used in this survey?
– Cluster sampling
– Stratified sampling
Online Sampling Techniques
• Internet surveys provide an easy and cost
effective method of survey. The online
survey can also provide a much better user
experience while answering the questions
than printed questionnaires.
Important terms and symbols
• Sample Statistic: A sample statistic is a summary
description of a characteristic or measure of the
sample. The sample statistic is used as an
estimate of the population parameter.
• Population Parameter: A population parameter is
a summary description of a fixed characteristic or
measure of the entire target population. A
population parameter indicates the true value
which would be obtained if a census was done
instead of a sample survey.
• Descriptive statistics: The statistics that
describe basic characteristics and
summarize the data in a straightforward
and understandable manner.
• Inferential statistics: The statistics which is
used to make inferences or generalize
results from a sample to an entire
• Proportions: A proportion denotes the
percentage of population elements that
successfully meet some criteria related to a
particular characteristic. A proportion may
be expressed as a percentage (20%), a
fraction (1/5), or a decimal value (0.20)
• Mean: The mean is the arithmetic average.
Researchers generally wish to know the
population mean µ
• The sampling distribution is a distribution
of a sample statistic calculated for each
sample that can be possibly drawn from
the target population
For infinite population, sample size for means is calculated as:
For finite population sample size for means is calculated as:
• A researcher wants to estimate the
population mean of P/E ratio for all stocks
listed on National Stock Exchange with 99
per cent confidence. Suppose the sample
standard deviation of P/E ratios for stocks
listed on the NSE is s = 6.5. How many
stocks should be included in the sample if
margin of error of 2 is desired?
For infinite population, sample size for proportions is calculated as:
For finite population sample size for proportions is calculated as:
For finite population, sample size for means for a stratified sample is
• A warehouse received a shipment of
returned glass bottles. These bottles are to
be sampled to estimate the proportion that
is unusable. From past experience, the
proportion of unusable bottles is estimated
to be 10 per cent. How large a random
2 2 2
=(2.576) (6.5) /(2) =70.09
sample should be taken to estimate the true
proportion of unusable bottles to within 7%
with 90 per cent confidence?
It is given that e= 0.07, 0.10, Confidence level= 90%
α/2 = 1.645 at 90 per cent confidence level
Using the formula for n and substituting the given values, we have
2(0.10*0.90) / (0.07)2 = 49.7025
• For a population of 900, what should be
the sampling size necessary to estimate the
populatin mean at 95 per cent confidence
with a sampling error of 5 and the standard
deviation equal to 15?
• A survey is carried out at a university to estimate the
percentage of undergraduates interested in hostel
accommodation during the current year. The university's
registrar keeps an alphabetical list of all undergraduates,
undergraduates registered in the year during which this
research is conducted. Someone proposes to choose a
number at random between one and one hundred, count
that far down the list, then take that name and every
hundredth name after it for the sample.
– What will the sample size be?
– Is this a probability method? Is it the same as simple random
– Assume now that the registrar's list is not alphabetical, but rather
ordered by their percentage score in previous semester. Would
this method of sampling be adequate?
– Someone else proposes to go out and take the first hundred
undergraduates she sees as the sample. Is this a probability
method? Is it the same as simple random sampling?
– Assume that many students in the university who are from other
cities would have a higher chance of needing hostel. What
sampling method would you recommend?