Samples types, methods of sampling, probability, random, sampling error, sample size

1. Sampling Types and Methods
Professor. Tarek Tawfik Amin
Public Health Dept. Faculty of Medicine
Cairo University
amin55@myway.com

2. Objectives:
By the end of the lectures 4th
yearmedical student should
be able to:
1- Define the indication of using a sample and the whole
population in research.
2- Define the meaning/concepts/rules of probability and
non-probability sampling techniques.
3- Enumerate, define the indication forusing different
types of random techniques and able to use the random
digit table in drawing a simple random sampling.
4- Identify the advantages and uses of non-probability
sampling.

3. In research what we are looking for?
The variable: is a condition, quality or trait that
varies from one case to another
In the target population (population of
interest)
Either the whole
population
SampleOR

4. Theconcept of sampling
Study population:
Samplingunits
You select a few sampling units
from the study population Sample
You collect information
from these people to
find answers to your
research questions.
You make an estimate
“prediction” extrapolated to the
study population
(prevalence, outcomes etc.)

5. Basic Terms and Concepts
Target Population and Sample
A pOpulatiOn is a complete set of units
with a specified set of characteristics while
a sample is a subset of the population.
In research the defining characteristics of
population include geOgRaphic,
clinical, demOgRaphic and
tempORal.

6. Basic Terms and Concept
Clinicalanddemographic characteristics define the
target population, the large set of people
throughout the world to which the results will
be generalized (all teenagers with asthma(.
Example:
The study sample is the subset of the target
population available forstudy (teenagers with
asthma in the investigator’s town in 2005(.

7. Steps in designing the protocol for choosing the
study subjects
Target
population
Specify clinical,
Demographic and then
Geographic and temporal
characteristics
Intended sample
Specify accessible
population and
approach to selecting
the sample
Research question
Truth in the Universe
Study plan
Findings in the study
Design

8. Selection Criteria
 How would you define the population to be
studied?
 Through establishing selection criteria that
include inclusion and exclusion criteria.
 Example:
Demonstrate the selection criteria for subjects to
evaluate the efficacy of calcium supplements for
preventing osteoporosis?

9. Designing selection criteria fora clinical trial of calcium
supplements to prevent osteoporosis
Inclusion
criteria
(be specific(
Specifying the characteristics
that define population that
are relevant to the research
question and efficient for
study:
Demographic: age, sex, and
race.
Clinicalcharacteristics.
Geographic (administrative)
Temporalcharacteristics
A 5-yeartrial of calcium
supplementation forpreventing
osteoporosis might specify the
subject be:
White females 50 to 60 years
old
Ingoodgeneralhealth**
Patients attending clinic at X
Hospital
Between Jan. 1st
and December
31st
of next year.
Considerations Example

10. Designing selection criteria fora clinical trial of calcium
supplements to prevent osteoporosis
Exclusion
Criteria
(be
parsimonious(
Specifying the subsets of the
population that will not be
studied because of:
A high likelihood of being
lost to follow-up.
An inability to provide good
data.
Being at high risk of side
effects.
Characteristics that make it
unethical to withhold the
study treatment
The calcium supplementation
trial might exclude subjects
who are:
oAlcoholic orplan to move of
the country orregion.
oDisoriented orhave a
language barrier.
oSarcoidosis/hypercalcemia
oTaking steroids.
Considerations Example

11. Clinical versus Community populations
If the research question
involves patients with a
disease, hospitalized or
clinic-based patients are
inexpensive and easy to
recruit, but selection factors
that determine who comes
to the hospital orclinic may
have an important effect.
Tertiaryclinics tendto
accumulatepatients with
serious forms of disease.
In choosing the sample in the
community who will
represent a non clinical
population (population-
based)
Samples are difficult and
expensive to recruit, but
they are particularly useful
forguiding public health
and clinical practice in the
community.

12. The Sample Population
Research question
Truth in the universe
Study plan
Truth in the study
Step1
Target population
Specific clinical and
Demographic
characteristics
Step 2
Accessible population
Specific temporal and
geographic
characteristics
Step 3
Sample population
Defined approach
to sampling
Criteria forselection
Suited to research
question
Representative
of target population
Easy to study
Representative
of accessible
population
Easy to do

13. Terms and Concept
 The whole collection of units “universe”from
which a sample may be drawn.
 The samplingunits may be hospitals,
institutions, houses, schools, villages,
records, events and not necessarily
individuals.
 Samplingframe is detailed characteristics of
the study units amenable to sampling.

14.  Adequately representative of the target
population so as to minimize bias (or
systematic error).
 Large enough to minimize random
variation differences that might occur
between the sample and target
populations.
Characteristics Of A Good Sample

15. The whole population
 If we are interested in the characteristics of
each individual, particularly with
descriptive research questions, thereis a
needforgeneralizingthefindings.
 Probability sampling is the goldstandard.
 It provides a rigorous basis forestimating
the fidelityof phenomena observed and for
computing statistical significance and
confidence intervals.

16. The whole population.
A. It is expensive.
B. It is timeconsuming.
C. Highererrorchances because of the
many persons, equipments and wide
geographic area covered.
Study of the whole population is carried
out in censuses.

17. Sampling
Resorted to if we are interested in studying the prevalence of
a problem, associations or intervention effect,…..etc
A. It is less expensive.
B. It is less time consuming.
C. It has lower error chances because of less
persons, equipments and geographic area
covered.
D. It allows for continuous study of the
population (longitudinal study).
Study of a sample is carried out in the majority
of researches.

18. Principlesof sampling
I. In a majority of cases of sampling there will be a
difference between the sample statistics and the true
population mean, which attributable to the selection of
the units in the sample “sampling error”.
II. The greaterthe sample size, the more accurate will be
the estimate of the true population mean “reduction in
sampling error”
III. The greaterthe difference in the variable
“heterogeneous variable” understudy in a population
fora given sample size, the greaterwill be the
difference between the sample statistics and the true
population mean “the largerthe sampling error”.

19. Sampling error
Fourindividuals A, B, C, D
A = 18 years
B= 20 years
C= 23 years
D= 25 years
Theirmean age is = 18+20+23+ 25=
86/4= 21.5 years (population mean).

20. Probability of sampling two individuals: (6 probabilities)
A+B=18+20= 38/2=19.0 years
A+C= 18+23=20.5 years.
A+D=18+25=21.5 years.
B+C=20+23=21.5 years.
B+D=20+25=22.5 years.
C+D=23+25=24.0 years.
Probability of sampling three individuals: (4 probabilities)
A+B+C=18+20+23/3=20.33 years.
A+B+D=18+20+25=21.00 years.
A+C+D=18+23+25=22.00 years.
B+C+D=20+23+25=22.67 years.
If C=32 years and D=40 years: sampling of 2 will include a sampling
errorof -7.00 to +7.00 and in case of 3 individuals it will be -3.67
to +3.67 years.
Sampling error= population mean-sample mean
= ranges from -2.5 to +2.5 years.
Sampling error= population mean-sample mean
= ranges from -1.17 to +1.17 years.
The greaterthe difference (variability) of a given variable
the largerthe sampling errorfora given sample size.

21. Typesof sampling
Random/probability Non-random/probability Mixed sampling
Simple Stratified
Proportionate
Disproportionate
Cluster
Single
Doublestage Multi-stage
Quota
Accidental
Judgmental
Snowball
Systematic
sampling

22. Types of Samples
Probability samples:
Units are selected according to probability laws
i.e. everyoneintheunderlyingpopulationhas an
equal(aspecified)andindependentchanceof
appearinginthatsample.
Non-probability (convenience) samples:
Units are selected based on known factors.
In clinical research the study sample is usually made
up of people who meet the inclusion criteria and are
easily accessible to the investigator.

23. Probability Samples
In orderto be able to inferfrom sample results to the
underlying population, that sample should be a
representative sample.
i.e. it should represent the population from which
it is drawn in every respect.
Becausewecannotanticipateallcharacteristics of the
populationthatthesampleshouldrepresent, wechosea
probability (random)sample.

24. How to draw aprobability Sample?
I. Identify the study units (individuals,
villages, houses, …etc).
II. Make a complete list of the study units in
the underlying population. That complete
list is known as the samplingframe.
III. Each of these units is given a number.
IV. Then select the required numberof units
(sample size) at random from that frame.

25. The selection of units can be made either
by:
1. The lottery method “fishbowl draw” (the
numbers of frame units are written on
identical pieces of papers, mixed
thoroughly in a bowl and the required
number is blindly picked up).
2. Through the use of random numbers
tables.
3. Computer generated random numbers.
Two systems o f drawing a rando m sample:
Sampling witho ut replacement.
Sampling withreplacement.

26. Random number table

27. Random Sampling Techniques
1-Simple random sample
2-Stratified random sample
3-Systematic random sample
4-Clusterrandom sample
5-Multistage random sample

28. 1-Simple random sample
We prepare a complete and up-to-date list of the underlying
population (sample frame). The specified sample size is drawn
from that frame at random.
Disadvantages:
 Suitable forhomogenous population (single sex).
 Largersample size is required.
 More expensive as we have to get the cases from
widely scattered areas.
 Time consuming and more laborious.
 Some groups might not be represented in the
sample.
 Extreme values can occurby chance.

29. Example of Simple random sample using random digit table.
Draw at random a sample size of 50 from a
population of 10,000.
Prepare the sampling frame and each subject received a number.
A. The size of the population is 10,000 i.e. it is formed of 5
digits.
B. Select at random a page from the random numbers tables.
C. Select 5 adjacent columns (5 digits).
D. Proceed from up down (blindly), any value falling between
00001 and 10,000 is chosen and so on until you completed
your50 cases.
E. Duplicate numbers are left aside
F. Individuals with those 50 numbers compose oursample.

30. Simplerandom sampling
26804 00010 93445
90720 12805 58563
85027 32242 86468
09362 16212 00128
64590 75362 32348
29273 34703 23763
96215 01556 63708
59207 22211 48522
49674 01534 98685
04104 00047 14986
Samplingframe
Random table

31. 2-Stratified random sampling
o Based upon thelogic of heterogeneity of the
included variables(variationsin population
characteristicsand distribution which may
result in dominanceof somestrataand
ignoring others).
o Ensurehomogeneity of sub-population though
ranking them into strata.

32. 2-Stratified random sample
 Ensures representativeness with regard to important
characteristics as age, sex, educational orsocio-
economic levels.
 The population is divided into strata (subgroups)
according to the different levels of the important
variable. The population in each stratum is
homogenous so sampling accuracy is increased.
 We choose a simple random sample from each
stratum, the size of which is proportionateto the size
of that stratum.
In otherwords the sampling fraction is the same foreach
stratum and the total sample.
3
3
2
2
1
1
N
n
N
n
N
n
N
n
===

33. Example of Stratified random sample
A town with a total population of 12,000 was classified into 4
homogenous socioeconomic strata. The population in each
stratum was 2,000 (class I), 4,000 (class II), 5,000 (class III)
and 1,000 (class IV) respectively. A sample size of 600 is to
be drawn from the town. Calculate the number of
individuals to be drawn at random from each of the 4 strata?
501000
2505000
2004000
1002000
20
1
20
1
20
1
20
1
20
1
000,12
600
==
==
==
==
==
xsampleStratum4
xsampleStatum3
xsampleStratum2
xsampleStratum1
fractionSampling

34. 3-Systematic random sample
1. The underlying population is classified into
intervals:
Thesizeof intervals = thesizeof thepopulation÷the
requiredsamplesize. (indicatedinsmallfullyidentified
populations).
2. The first case is selected at random from the first
stratum (interval) and the others are selected by
adding systematically the size of each interval.
3. Accordingly we are taking each (nth) individual. n
is the size of the interval. If the latteris 10 we
take every tenth observation

35. Example of systematic random sample
1000 patients visit Kasr AlAiny outpatient clinics every day.
We need a systematic random sample of 100 patients.
Explain how should we proceed in selecting those 100
patients composing our sample?
Weclassifythepatients into100intervals andselecta
patientfromeach.
Sizeof eachinterval=1000/100= 10
Chooseatrandomanumberthatlies between1and10say
9.
Choosefromthesecondintervalpatientnumber19th
.
Choosefromthethirdintervalobservationnumber 29th
.
th291019ORth2910x29 =+=+
th19109ORth191x109 =+=+

36. Systematic sampling

37. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
31 32 33 34 35 36 37 38 39 40 41 42 43 44 45
16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
46 47 48 49 50 51 52 53 54 55 56 57 58 59…..
First interval (pick one at random)
Addtheintervaltoselectthesubsequentsubjects

38. 4-Cluster random sample
۞ In this method, the sampling units are clusters
(groups) of individuals – (incomplete sampling frame
and/orthe total sampling population is large) rather
than individuals.
۞ The clusters (schools, houses, villages, …etc.) form
the sampling frame, from which the required number
of clusters is selected at random.
۞ All individuals in a cluster, a specific group, ora
random sample of them are included.
۞ Very useful when the population is widely dispersed,
and it is impractical to list and sample from all its
elements.

39. Example of random cluster sample
The objective of ourstudy was to define the
prevalence of Obesity among primary school
children in Giza There are 150 primary schools
in Giza. The estimated sample size is 20
clusters.
Describe how would you proceed in drawing such
sample?
A. Listall200schools
B. Giveeachanumber
C. Usetherandomnumbers tables inselectingthe20
schools whosenumbers willfallbetween001and
200.

40. Example: Clustersampling
Section 4
Section 5
Section 3
Section 2Section 1

41. 5-Multistagerandom sample
We use this method if the target population is
spread overwide geographic area and there is
limited budget orresources (in community-
based surveys).
In this method, the sample is drawn in many
stages.
The area is divided into smallerclusters, the
clusters are divided into smallerclusters and so
on.
Random selection is carried out at each level
successively.

42. Country
Provinces
Sampling units: province
Cities
Districts
Households
Person
Sampling unit: city
Sampling unit: district
Sampling unit: household
Sampling unit: person
Multi stage sampling

43. Youwereaskedtoheadaresearchteamtoinvestigate
theproblemof hypertensioninEgypt
Howwouldyouproceedindrawingyoursample?
List all governorates (provinces).
 Select 4 governorates (provinces) at random
 List the districts in each of the 4 governorates
 Select a district from each governorate at random
 List all villages and urban areas in each districts.
 Select a village and an urban centre from each
district randomly
 Study all or sub-sample of individuals in the
selected villages and urban centres

44. II-Non-probability (convenience) samples
 A convenience sample can minimize volunteerism and
otherselection biases by consecutively selecting every
accessible person who meets the inclusion criteria.
 A consecutive sample is specially desirable when it
mounts to taking the entire accessible population over
a long enough period to include seasonal variation or
otherchanges overtime that considered important to
research question.
 Representativness is a matterof judgment.

45. Non-probability samples
These designs are used when the number
of elements in a population is either
unknown orcan not be individually
identified.
Quota sampling.
Accidental sampling.
Judgmental orpurposive sampling.
Snowball sampling.

46. Non-probability (convenience) samples
1-Purposive sample:
Chosen according to the investigator’s judgement
in such a way that maximizes the chances of
proving the study hypothesis. “selecting patients
with ESRD”
2-Quota sample:
Involves only few strata e.g. men and women
>20 years. The enumerators select any individual
belonging to those strata from whom they get the
required information in an easy, quick and
accessible way.

47. Thankyou