Methods of sampling

Dr. Shital S. Patil,

Asst. Professor
Dept. Of Community Medicine
Specific Learning Objectives

• At the end of lecture students should be

able to understand:
• Why we use sampling
• Definitions in sampling
• Main methods of sampling
 Why do we use sampling?

Get information from large populations with:

– Reduced costs
– Reduced field time
– Increased accuracy
– Enhanced methods
 Definition of sampling

Procedure by which some members

of a given population are selected as
representatives of the entire population.

Sampling is the use of a subset of the population

to represent the whole population
Definition of sampling terms

Sampling unit (element)

• Subject under observation on which
information is collected
– Example: children <5 years, hospital discharges,
health events…
Sampling fraction
• Ratio between sample size and population
size
– Example: 100 out of 2000 (5%)
Definition of sampling terms

Sampling frame
• List of all the sampling units from which
sample is drawn
– Lists: e.g. children < 5 years of age, households,
health care units…
Sampling scheme
• Method of selecting sampling units from
sampling frame
– Randomly, convenience sample…
 Sampling and representativeness

Sampling
Population
Sample

Target Population

Target Population  Sampling Population  Sample

 Types of sampling

• Non-probability samples

• Probability samples
 Non probability samples
• Convenience samples (ease of access)

• Snowball sampling (friend of

friend….etc.)

• Purposive sampling (judgemental)

• You chose who you think should be in the
study

Probability of being chosen is unknown

Cheaper- but unable to generalise, potential for bias
• Normally sample should reflect the population
structure. A convenience sample does not! In
a convenience sample some persons have a
higher chance of being sampled than others.

• For example, if we choose people on the

main shopping street as a sample for a city
ward, those who are frequently doing their
shopping there are at higher risk of being
chosen than those working during the day,
bedridden

• Examples of nonprobability sampling include:

• Nonprobability sampling techniques cannot
be used to infer from the sample to the
general population. Any generalizations
obtained from a nonprobability sample must
be filtered through one's knowledge of the
topic being studied. Performing nonprobability
sampling is considerably less expensive than
doing probability sampling, but the results are
of limited value.
• Examples of nonprobability sampling include:
• Convenience sampling - members of the population
are chosen based on their relative ease of access.
Like friends, co-workers, or shoppers at a single mall.
• Snowball sampling - The first respondent refers a
friend. The friend also referes a friend, etc.
• Judgmental sampling or Purposive sampling -
The researcher chooses the sample based on who
they think would be appropriate for the study. This is
used primarily when there is a limited number of
people that have expertise in the area being
researched.
• Case study - The research is limited to one group,
often with a similar characteristic or of small size.
• ad hoc quotas - A quota is established (say 65%
women) and researchers are free to choose any
 Probability samples

• Random sampling
– Each subject has a known probability of being
selected
• Allows application of statistical sampling
theory to results to:
– Generalise
– Test hypotheses
Methods used in probability
samples

• Simple random sampling

• Systematic sampling
• Stratified sampling
• Multi-stage sampling
• Multi-phage sampling
• Cluster sampling
• LQAS(lot quality assurance sampling)
 Simple random sampling

• Principle
– Equal chance/probability of drawing each unit

• Procedure
– Take sampling population
– Need listing of all sampling units (“sampling
frame”)
– Number all units
– Randomly draw units
 Simple random sampling

• Advantages
– Simple
– Sampling error easily measured

• Disadvantages
– Need complete list of units
– Does not always achieve best representativeness
– Units may be scattered and poorly accessible
• e.g simple random sampling of telephone
numbers- is everyone in the telephone book?
Are there people without phones? Or non-
functioning phones
• Because units may be scattered may be more
time consuming difficult to involve units
 Simple random sampling
Example: evaluate the prevalence of tooth
decay among 1200 children attending a school

• List of children attending the school

• Children numerated from 1 to 1200
• Sample size = 100 children
• Random sampling of 100 numbers between 1
and 1200

How to randomly select?

Simple random sampling
 Systematic sampling

• Principle
– Select sample at regular intervals based on sampling
fraction
– This is the standard distance between elements
selected in the sample population size/sample size.
• Advantages
– Simple
– Sampling error easily measured
• Disadvantages
– Need complete list of units
– Periodicity
 Systematic sampling

• N = 1200, and n = 60
⇒ sampling fraction = 1200/60 = 20

• List persons from 1 to 1200

• Randomly select a number between 1 and 20

(ex : 8)
⇒ 1st person selected = the 8th on the
list
⇒ 2nd person = 8 + 20 = the 28th etc .....
Systematic sampling
 Systematic Random Sampling

• Provides the benefits of implicit stratification if

the list is grouped
• Runs the risk of error if periodicity in the list
matches the sampling interval
• In this example, every 4th element is red, and red
never gets sampled. If j had been 4 or 8, ONLY
reds would be sampled.
Systematic Random Sampling
 Stratified sampling

• Principle :
– Divide sampling frame into homogeneous
subgroups (strata) e.g. age-group, occupation;

– Draw random sample in each strata.

 Stratified sampling
• Advantages
– Can acquire information about whole population and
individual strata
– Precision increased if variability within strata is
less (homogenous) than between strata
• Disadvantages
– Can be difficult to identify strata
– Loss of precision if small numbers in individual
strata
• resolve by sampling proportionate to stratum
population
 Multiple stage sampling
Principle:
• consecutive sampling
• example :
sampling unit = Farmers of India
– 1st stage: State
– 2nd stage: districts within state
– 3rd stage: talukas within districts
– 4th stage: villages within talukas
– 5th stage: farmers in villages
 Multi-phase sampling
Principle:
• Some information is collected from every unit
and additional from sub-sample.
• Same type of sampling unit is concern at each
phase but some units asked for more
information than other.
 Cluster sampling
• Principle
– Sample units not identified independently but in
a group (or “cluster”)

– Provides logistical advantage.

 Cluster sampling
• Principle
– Whole population divided into groups e.g.
neighbourhoods

– Random sample taken of these groups (“clusters”)

– Within selected clusters, all units e.g. households

included (or random sample of these units)
 Example: Cluster sampling
Section 1 Section 2

Section 3

Section 5

Section 4
 Cluster sampling
• Advantages
– Simple as complete list of sampling units within
population not required
– Less travel/resources required

• Disadvantages
– Potential problem is that cluster members are more
likely to be alike, than those in another cluster
(homogenous)….
– Sampling error difficult to measure
– This “dependence” needs to be taken into account in
the sample size….and the analysis (“design effect”)
 Stratification vs. Clustering
Stratification Clustering
• Divide population into • Divide population into
groups different from each comparable groups:
other: sexes, races, ages schools, cities
• Sample randomly from • Randomly sample some of
each group the groups
• Less error compared to • More error compared to
simple random simple random
• More expensive to obtain • Reduces costs to sample
stratification information only some areas or
before sampling organizations
 Stratified Cluster Sampling

• Reduce the error in cluster sampling by

creating strata of clusters
• Sample one cluster from each stratum
• The cost-savings of clustering with the
error reduction of stratification
 Stratified Cluster Sampling
• Combines elements of stratification and clustering
• First you define the clusters
• Then you group the clusters into strata of clusters,
putting similar clusters together in a stratum
• Then you randomly pick one (or more) cluster
from each of the strata of clusters
• Then you sample the subjects within the sampled
clusters (either all the subjects, or a simple random
sample of them)
Stratified Cluster Sampling
Example: Stratified sampling

• Determine vaccination coverage in a

country
• One sample drawn in each region
• Estimates calculated for each stratum
• Each stratum weighted to obtain estimate
for country (average)
 EPI cluster sampling

To evaluate vaccination coverage:

• Without list of persons
• Total population of villages
• Randomly choose 30 clusters
• 30 cluster of 7 children each= 210 children
 Drawing the clusters
You need :
– Map of the region
– Distribution of population (by villages or area)
– Age distribution (population 12-23 m :3%)

Village Pop. 12-23

A 53000 1600
B 7300 220
C 106000 3200
D 13000 400
E 26500 800
F 6600 200
G 40000 1200
H 6600 200
I 53000 1600
J 13200 400
 Distribution of the clusters

Compute cumulated population

A 1600 1600
B 220 1820
C 3200 5020
D 400 5420
E 800 6220
F 200 6420
G 1200 7620
H 200 7820
I 1600 9420
J 400 9820
Total population = 9820
 Distribution of the clusters

A 1600 IIIII
Then compute sampling fraction :
B 1820 I
9820
K= = 327 C 5020 IIIIIIIII
30
Draw a random number (between 1 and D 5420 I
327) E 6220 II
F 6420 I
G 7620 IIII
Example: 62
H 7820 I
I 9420 IIIII
Start from the village including “62” and
J 9820 I
draw the clusters adding the sampling
fraction
 Drawing households and children

On the spot
Go to the center of the village , choose direction
(random)
Number the houses in this direction
 Ex: 21
Draw random number (between 1 and 21) to identify the
first house to visit

From this house progress until finding the 7 children (

itinerary rules fixed beforehand)
Selecting a sampling method

• Population to be studied
– Size/geographical distribution
– Heterogeneity with respect to variable
• Availability of list of sampling units
• Level of precision required
• Resources available
 Sampling Errors
• If we take repeated samples from the same
population or universe, the results obtained
from one sample will differ to some extent
from the results of another sample.
• This type of variation from one sample to
another is called sampling error.
• It occurs because data were gathered from a
sample rather than from the entire population
of concern.
• Presuming that the sampling procedure is
such that all the individuals in the population
are favoured equally to come to the sample,
the factors that influence the sampling error
are :
• (a) the size of the sample and
• (b) the natural variability of the individual
readings. ·
• As the size of the sample increases, sampling
error will decrease.
• As the individual readings vary widely from
one another, we get more variability from one
sample to another.
 Non-sampling Errors

• An inadequate sampling frame

• Nonresponse from participants
• Field errors
• Response errors
• Coding and data entry errors

• These are often more important than the sampling

errors.
 Conclusions

• Probability samples are the best

• Ensure
– Representativeness
– Precision

• …..within available constraints

Thank You