Sampling Types and Methods

Professor. Tarek Tawfik AminPublic Health Dept. Faculty of Medicine

Cairo University

amin55@myway.com

Objectives: By the end of the lectures 4th year medical 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 for using

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.

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

The concept of sampling

Study population:Sampling units

You select a few sampling unitsfrom the study population Sample

You collect informationfrom these people to find answers to your research questions.

You make an estimate “prediction” extrapolated to the study population

(prevalence, outcomes etc.)

Basic Terms and ConceptsTarget 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.

Basic Terms and Concept

Clinical and demographic 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 for study (teenagers with asthma in the investigator’s town in 2005).

Steps in designing the protocol for choosing the study subjects

Target populationSpecify clinical ,

Demographic and thenGeographic and temporal

characteristics

Intended sampleSpecify accessible population and

approach to selecting the sample

Research question

Truth in the Universe

Study plan

Findings in the study

Design

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?

Designing selection criteria for a 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.Clinical characteristics.Geographic (administrative)

Temporal characteristics

A 5-year trial of calcium supplementation for preventing osteoporosis might specify the subject be:

White females 50 to 60 years oldIn good general health**

Patients attending clinic at X HospitalBetween Jan. 1st and December 31st of next year.

Considerations Example

Designing selection criteria for a 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 or plan to move of the country or region.oDisoriented or have a language barrier.oSarcoidosis/hypercalcemia

oTaking steroids.

Considerations Example

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 or clinic may have an important effect.

Tertiary clinics tend to accumulate patients 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 for guiding public health and clinical practice in the community.

The Sample PopulationResearch question

Truth in the universe

Study planTruth in the study

Step1 Target populationSpecific clinical and

Demographic characteristics

Step 2Accessible populationSpecific temporal and

geographic characteristics

Step 3Sample population

Defined approach to sampling

Criteria for selection

Suited to researchquestion

Representativeof target population

Easy to study

Representative of accessible populationEasy to do

Terms and Concept

The whole collection of units “universe” from which a sample may be drawn.

The sampling units may be hospitals, institutions, houses, schools, villages, records, events and not necessarily individuals.

Sampling frame is detailed characteristics of the study units amenable to sampling.

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

The whole population

If we are interested in the characteristics of each individual, particularly with descriptive research questions, there is a need for generalizing the findings.

Probability sampling is the gold standard.

It provides a rigorous basis for estimating the fidelity of phenomena observed and for computing statistical significance and confidence intervals.

The whole population.

A.It is expensive. B.It is time consuming.C. Higher error chances because

of the many persons, equipments and wide geographic area covered.

Study of the whole population is carried out in censuses.

SamplingResorted 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.

Principles of 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 greater the sample size, the more accurate will be the estimate of the true population mean “reduction in sampling error”

III. The greater the difference in the variable “heterogeneous variable” under study in a population for a given sample size, the greater will be the difference between the sample statistics and the true population mean “the larger the sampling error”.

Sampling error

Four individuals A, B, C, DA = 18 yearsB= 20 yearsC= 23 yearsD= 25 yearsTheir mean age is = 18+20+23+

25= 86/4= 21.5 years (population mean).

Probability of sampling two individuals: (6 probabilities)

A+B=18+20= 38/2=19.0 yearsA+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 error of -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 greater the difference (variability) of a given variablethe larger the sampling error for a given sample size.

Types of sampling

Random/probability Non-random/probability Mixed sampling

Simple Stratified

Proportionate

Disproportionate

Cluster

Single

Double stage

Multi-stage

Quota

Accidental

Judgmental

Snowball

Systematicsampling

Types of SamplesProbability samples:

Units are selected according to probability laws i.e. everyone in the underlying population has an equal (a specified) and independent chance of appearing in that sample.

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.

Probability Samples

In order to be able to infer from 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.

Because we can not anticipate all characteristics of the population that the

sample should represent, we chose a probability (random) sample.

How to draw a probability 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 sampling frame.

III. Each of these units is given a number. IV. Then select the required number of units

(sample size) at random from that frame.

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 of drawing a random sample: Sampling without replacement. Sampling with replacement.

Random number table

Random Sampling Techniques

1-Simple random sample2-Stratified random sample3-Systematic random sample4-Cluster random sample5-Multistage random sample

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 for homogenous population (single sex).

Larger sample 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 occur by chance.

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 your 50 cases.

E. Duplicate numbers are left aside F. Individuals with those 50 numbers compose our

sample.

Simple random sampling26804 00010 9344

5

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

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fram

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Random table

2-Stratified random sampling

o Based upon the logic of heterogeneity of the included variables (variations in population characteristics and distribution which may result in dominance of some strata and ignoring others).

o Ensure homogeneity of sub-population though ranking them into strata.

2-Stratified random sample Ensures representativeness with regard to

important characteristics as age, sex, educational or socio-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 proportionate to the size of that stratum.

In other words the sampling fraction is the same for each stratum and the total sample.  

3

3

2

2

1

1

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n

N

n

N

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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

201

201

201

201

201

000,12600

x sampleStratum4

x sampleStatum3

x sampleStratum2

x sampleStratum1

fraction Sampling

3-Systematic random sample

1. The underlying population is classified into intervals:

The size of intervals = the size of the population ÷ the required sample size. (indicated in small fully identified 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 latter is 10 we take every tenth observation

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? 

We classify the patients into 100 intervals and select a patient from each.

Size of each interval =1000/100 = 10Choose at random a number that lies

between 1 and 10 say 9. Choose from the second interval patient

number 19th. Choose from the third interval observation

number 29th.

th 29 10 19 OR th 29 10 x 2 9

th 19 10 9 OR th 19 1x10 9

Systematic sampling

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)A

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4-Cluster random sample

۞ In this method, the sampling units are clusters (groups) of individuals – (incomplete sampling frame and/or the 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, or a 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.

Example of random cluster sample The objective of our study 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.  List all 200 schoolsB. Give each a numberC. Use the random numbers tables in

selecting the 20 schools whose numbers will fall between 001 and 200.

Example: Cluster sampling

Section 4

Section 5

Section 3

Section 2Section 1

5-Multistagerandom sample

We use this method if the target population is spread over wide geographic area and there is limited budget or resources (in community-based surveys). In this method, the sample is drawn in many stages.

The area is divided into smaller clusters, the clusters are divided into smaller clusters and so on. Random selection is carried out at each level successively.

Country

ProvincesSampling units: province

Cities

Districts

Households

Person

Sampling unit: city

Sampling unit: district

Sampling unit: household

Sampling unit: person

Multi stage sampling

You were asked to head a research team to investigate the problem of hypertension in Egypt

How would you proceed in drawing your sample?

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

II-Non-probability (convenience) samples

A convenience sample can minimize volunteerism and other selection 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 other changes over time that considered important to research question.

Representativness is a matter of judgment.

Non-probability samples

These designs are used when the number of elements in a population is either unknown or can not be individually identified.

Quota sampling.Accidental sampling. Judgmental or purposive sampling.Snowball sampling.

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.

Thank you