Sampling

By Rama Krishna Kompella

Learning Objectives
• Understand the identifying the target
respondents
• Sampling and different types of
sampling
• Understanding sample process
• What are the potential errors in
sampling
• Determining Sampling size

Census vs. Sampling
• Two methods of selecting the respondents
– Census
– Sampling
• Census
– When the number of respondents / units of
interest are limited, or
– When it is required to gather data from all the
individuals in the population

Census vs. Sampling
• Sampling
– When the size of the population is too large
– The population is homogeneous
– Considerations of time and cost play a major role
in going for sampling

Sampling Process
• Define the population
• Identify the sampling frame
• Specify the sampling unit
• Selection of sampling method
• Determination of Sampling size
• Specify sampling plan
• Selection of sample

Sampling Process
• The population needs to be defined in terms
of:
Term Example

Element Company’s Product

Sampling Unit Retail outlet, super market

Extent Hyderabad & Secunderabad

Time April 10 – May 25

Sampling Process
• Identify the sampling frame:
– Need to clearly define from which universe will
the sample be picked from
– Ex: When you are studying the purchase
behaviour of consumers buying premium cars,
your sampling frame will be all the premium car
outlets in the city

Sampling Process
• Specify the sampling unit
– We need to decide on whom to contact in order to
obtain the data required
– Need to be careful while selecting the sampling unit,
as we need to be sure of whether we will get the
required data from the respondent or not
– Ex: When studying intention to purchase a car, the
unit of sampling would be people who are employed
and having a steady income. Whereas if we are
studying the trends from a dealer perspective, then
the sampling unit will be the dealers

Sampling process
• Need to select the kind of sampling method
used in order to identify the respondents
• There are two ways of selecting the sample:
– Probability methods
– Non-probability methods

Sampling Process
• Need to decide how many respondents need
to be chosen from the population
• Generally, the sample size depends on the
type of research conducted
• For exploratory research the sample size
tends to be small in number, whereas for
conclusive research the sample size will be
large

Sampling Process
• A sampling plan needs to clearly specify who
is the target population
• Ex: when we are planning to study the
purchase pattern of groceries by households,
we need to clearly specify what “household”
means. Is it a family who have kids, DINKS,
Empty nesters etc.

Sampling Design
within the Research Process

Step 4:
Specifying the sampling method
• Probability Sampling
– Every element in the target population or universe [sampling
frame] has equal probability of being chosen in the sample
for the survey being conducted.
– Scientific, operationally convenient and simple in theory.
– Results may be generalized.
• Non-Probability Sampling
– Every element in the universe [sampling frame] does not
have equal probability of being chosen in the sample.
– Operationally convenient and simple in theory.
– Results may not be generalized.

Types of Sampling Designs
Probability Nonprobability

Simple random Convenience

Complex random Purposive

Systematic Judgment

Cluster Quota

Stratified Snowball

Double

Simple Random Sampling
• In simple random sampling, every item of the
population has equal probability of being
chosen
• Two methods are used in random sampling:
– Lottery method
– Random number table

Simple Random
Advantages Disadvantages
• Easy to implement with • Requires list of
random dialing population elements
• Time consuming
• Uses larger sample sizes
• Produces larger errors
• High cost

14-22

Systematic
• Simple to design • Periodicity within
• Easier than simple random population may skew
• Easy to determine sampling sample and results
distribution of mean or • Trends in list may bias
proportion results
• Moderate cost

14-23

Stratified
• Control of sample size in • Increased error will result if
strata subgroups are selected at
• Increased statistical different rates
efficiency • Especially expensive if
• Provides data to represent strata on population must
and analyze subgroups be created
• Enables use of different • High cost
methods in strata

14-24

Cluster
• Provides an unbiased • Often lower statistical
estimate of population efficiency due to subgroups
parameters if properly being homogeneous rather
done than heterogeneous
• Economically more efficient • Moderate cost
than simple random
• Lowest cost per sample
• Easy to do without list

14-25

Stratified and Cluster Sampling
Stratified Cluster
• Population divided into • Population divided into
few subgroups many subgroups
• Homogeneity within • Heterogeneity within
subgroups subgroups
• Heterogeneity between • Homogeneity between
subgroups subgroups
• Choice of elements • Random choice of
from within each subgroups
subgroup
14-26

Double Sampling
• May reduce costs if first • Increased costs if
stage results in enough discriminately used
data to stratify or
cluster the population

14-28

Nonprobability Samples
No need to
generalize

Limited
Feasibility
objectives

Time Cost

14-29

Nonprobability
Sampling Methods

Convenience

Judgment

Quota

Snowball

14-30

Non-probability samples
• Convenience sampling
– Drawn at the convenience of the researcher. Common in exploratory
research. Does not lead to any conclusion.
• Judgmental sampling
– Sampling based on some judgment, gut-feelings or experience of the
researcher. Common in commercial marketing research projects. If inference
drawing is not necessary, these samples are quite useful.
• Quota sampling
– An extension of judgmental sampling. It is something like a two-stage
judgmental sampling. Quite difficult to draw.
• Snowball sampling
– Used in studies involving respondents who are rare to find. To start with, the
researcher compiles a short list of sample units from various sources. Each of
these respondents are contacted to provide names of other probable
respondents.

Quota Sampling
• To select a quota sample comprising 3000 persons in country X using three control
characteristics: sex, age and level of education.
• Here, the three control characteristics are considered independently of one another. In
order to calculate the desired number of sample elements possessing the various
attributes of the specified control characteristics, the distribution pattern of the general
population in country X in terms of each control characteristics is examined.
Control
Characteristics Population Distribution Sample Elements .

Gender: .... Male ...................... 50.7% Male 3000 x 50.7% = 1521
................. Female .................. 49.3% Female 3000 x 49.3% = 1479

Age: .......... 20-29 years ........... 13.4% 20-29 years 3000 x 13.4% = 402
................. 30-39 years ........... 53.3% 30-39 years 3000 x 52.3% = 1569
................. 40 years & over ..... 33.3% 40 years & over 3000 x 34.3% = 1029

Religion: ... Christianity............ 76.4% Christianity 3000 x 76.4% = 2292
................. Islam ..................... 14.8% Islam 3000 x 14.8% = 444
................. Hinduism ............... 6.6% Hinduism 3000 x 6.6% = 198
................. Others ................... 2.2% Others 3000 x 2.2% = 66
__________________________________________________________________________________

Types of error
• Non-sampling error – Error associated with
collecting and analyzing the data

• Sampling error – Error associated with failing
to interview the entire population

Non-Sampling Error
• Coverage error
– Wrong population definition
– Flawed sampling frame
– Interviewer or management error in following sampling frame
• Response error
– Badly worded question results in invalid or incorrect response
– Interviewer bias changes response
• Non-response error
– Respondent refuses to take survey or is away
– Respondent refuses to answer certain questions
• Processing errors
– Error in data entry or recording of responses
• Analysis errors
– Inappropriate analytical techniques, weighting or imputation are applied

Sampling Error
• Sampling error is known after the data are collected by calculating the
Margin of Error and confidence intervals

• Surveys don’t have a Margin of Error, questions do

• Power analyses use estimates of the parameters involved in calculating the
margin of error

• It is common to see sample sizes of 400 and 1000 for surveys (these are
associated with 5% and 3% margins of error)

• In most cases the size of the population being sampled from is irrelevant

• The margin of error should be calculated using the size of the subgroups
sampled

What’s Next?
• Computation of sample size
• Sampling error

Key Terms
• Area sampling • Multiphase sampling
• Census • Nonprobability sampling
• Cluster sampling • Population
• Convenience sampling • Population element
• Disproportionate • Population parameters
stratified sampling • Population proportion of
• Double sampling incidence
• Judgment sampling • Probability sampling

14-37

Key Terms
• Proportionate stratified • Simple random sample
sampling • Skip interval
• Quota sampling • Snowball sampling
• Sample statistics • Stratified random sampling
• Sampling • Systematic sampling
• Sampling error • Systematic variance
• Sampling frame
• Sequential sampling

14-38

Systematic Random Sampling
• Three steps are followed:
– Select the sampling interval, K
K=Total Population / Desired Sample Size
– Select a unit randomly between the first unit and kth unit
– Add K to the selected number to the randomly chosen
number
– EX: If total population = 1000, desired sample size is 50,
then K = 1000/50 = 20.
– Randomly select a number between 1 and 20
– Let us say, the number is 17, then the sample series will be
17, 37, 57……

Stratified Random Sampling
• Calculate the percentage of population present in
each stratum
• Determine the sample to be drawn from each
stratum
• Randomly select sample from each stratum
• Eg: You need to select 40 people from an office,
which has the following staff
– Male, full time 90
– Male, part time 18
– Female, full time 9
– Female, part time 63

Some Notations to remember
Population Parameters Symbol Sample Notations Symbol
Size N Size n
Mean value μ Mean value x-
Percentage value Percentage value
(population proportion) P (sample proportion) p–
Q or [1 – P] q– or [1 – p–]
Standard deviation σ Estimated standard deviation s–

Variance σ2 Estimated sample s –2
Standard error Estimated standard error
(population parameter) Sμ or SP (sample statistics) Sx – or Sp –
Other Sampling Concepts
Confidence intervals CIx – or CIp –
Tolerance level of error e
Critical z-value ZB
Confidence levels CL
Finite correction factor (the overall
square root of [N – n/N – 1] (also
referred to as “finite multiplier” or
“finite population correction”) fcf

Central Limit Theorem
• The theorem states that for almost all defined target
populations (virtually with disregard to the actual shape of
the original population), the sampling distribution of the
mean (x–) or the percentage ( p–) value derived from a
simple random sample will be approximately normally
distributed, provided that the sample size is sufficiently large
(i.e., when n is greater than or equal to 30).
• In turn, the sample mean value (x–) of that random sample
with an estimated sampling error (Sx–) fluctuates around the
true population mean value (μ) with a standard error of σ/√n
and has an approximately normal sampling distribution,
regardless of the shape of the probability frequency
distribution curve of the overall target population

Sampling Error
• Sampling error is any type of bias that is
attributable to mistakes made in
– either the selection process of prospective
sampling units or
– determining the sample size

Statistical Precision
• Using several statistical methods, the researcher will be
able to specify the critical tolerance level of error (i.e.,
allowable margin of error) prior to undertaking a
research study
• This critical tolerance level of error (e) represents general
precision (S) with no specific confidence level or precise
precision [(S)(ZB,CL)] when a specific level of confidence
is required

• General precision can be viewed as the amount of
general sampling error associated with the given sample
of raw data that was generated through some type of
data collection activity.
• Precise precision represents the amount of measured
sampling error associated with the raw data at a
specified level of confidence

• When attempting to measure the precision of raw data,
researchers must incorporate the theoretical
understanding of the concepts of
– sampling distributions,
– the central limit theorem, and
– estimated standard error in order to calculate the necessary
confidence intervals.

Estimated Standard Error
• Estimated standard error, also referred to as general
precision, gives the researcher a measurement of the
sampling error and an indication of how far the sample
result lies from the actual target population parameter
value estimate.
• The formula to compute the estimated standard
error of a sample mean value (Sx–) is
– Sx– = s – /√n
• where s – = Estimated standard deviation of the
sample mean
• n = Sample size

Confidence Interval
• A confidence interval represents a statistical
range of values within which the true value of
the target population parameter is expected
to lie

Determining Sample Size
Three factors play an important role in determining appropriate
sample sizes:
1. The variability of the population characteristic under
investigation (σμ or σP).
– The greater the variability of the characteristic, the larger the size of
the sample necessary.
2. The level of confidence desired in the estimate (CL).
– The higher the level of confidence desired, the larger the sample size
needed.
3. The degree of precision desired in estimating the population
characteristic (e).
– The more precise the required sample results (i.e., the smaller the e),
the larger the necessary sample size.

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