1. 17th EPIET introductory course Lazareto, Menorca, Spain
Sampling
17th EPIET introductory course
Lazareto, Menorca, Spain
Ioannis Karagiannis & Biagio Pedalino
Based on previous EPIET intro courses

2. Objectives: sampling To understand: Why we use sampling
Definitions in sampling
Concept of representativity
Main methods of sampling
Sampling errors

3. Definition of sampling
Procedure by which some members
of a given population are selected as representatives of the entire population in terms of the desired characteristics
Sampling is the use of a subset of the population to represent the whole population, in order to extrapolate the study results to the population from which the sample is drawn.

4. Why bother in the first place?
Get information from large populations with:
Reduced costs
Reduced field time
Increased accuracy
Why do we use sampling?
We want to obtain information from large populations at:
Reduced costs
Reduced field time
Increased accuracy

5. 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%)
There are several terms used in sampling which are important to understand:
First the sampling unit or element of sampling:
The sampling unit is the subject under observation on which information is collected, for example: children <5 years, hospital discharges, health events…
Secondly, the sampling fraction is the ratio between sample size and population size, for example: 100 out of 2000 (5%)

6. Definition of sampling terms
Sampling frame
List of all the sampling units from which sample is drawn
Lists: e.g. all children < 5 years of age, households, health care units…
Sampling scheme
Method of selecting sampling units from sampling frame
Randomly, convenience sample…
To choose the sampling units you will need a sampling frame, which is a list of all the sampling units from which sample is drawn, for example all children < 5 years of age, households, health care units…
And finally the sampling scheme is the method of selecting sampling units from sampling frame, for example randomly, convenience sample…

7. Survey errors Systematic error (or bias) Sampling error (random error)
Representativeness (validity)
Information bias
Sampling error (random error)
Precision
Before I will present the different sampling schemes or methods, I would like to mention some of the survey errors.
First of all, your study can have a systematic error (or bias). This would be the case when your sample is not typical of the population you are looking at. This could happen through obtaining inaccurate response (information bias) or selecting people not representative of the population you are studying.
A Sampling error or random error could also be possible.

8. Validity
Sample should accurately reflect the distribution of relevant variable in population
Person (age, sex)
Place (urban vs. rural)
Time (seasonality)
Representativeness essential to generalise
Ensure representativeness before starting
Confirm once completed
Our sample should accurately reflect the distribution of relevant variables in the population, regarding person (age, sex), place e.g. urban vs. rural and time e.g. seasonality. Is this the case for my example?
The representativeness is essential to be able to generalise our results.
We should ensure that our sample is representative before starting and confirm once completed the sampling

9. Information bias Systematic problem in collecting information
Inaccurate measuring
Scales (weight), ultrasound, lab tests (dubious results)
Badly asked questions
Ambiguous, not offering right options…
Systematic problem in collecting information
Inaccurate measuring
Scales, ultrasound, lab tests…
Badly asked questions
Ambiguous, not offering right options…

10. Sampling error (random error)
No sample is an exact mirror image of the population
Standard error depends on
size of the sample
distribution of character of interest in population
Size of error
can be measured in probability samples
standard error
Even if we have made sure that we have a representative sample, we can have a sampling error.
Was does this mean?
We should not forget that our sample is just a gross reflection of the reality. There will always be a random difference between our sample and the population from which the sample was drawn. This is also what we mean with precision.
So the five persons I have chosen as my sample might not completely reflect all participants. Even if I have about the same age and gender distribution, it will not be exactly the same.
We can measure the size of the sampling error in probability samples, and this is expressed by standard error of mean, proportion, differences, etc
The size of the sampling error depends on the sample size (the bigger the sample, the smaller the error).
Also the sampling error depends upon how often a characteristic is present in the population. For very rare characteristics we might need to aim for a better sample error or precision.

11. Survey errors: example
Measuring height:
Measuring tape held differently by different investigators
→ loss of precision
→ large standard error
Tape too short
→ systematic error
→ bias (cannot be corrected retrospectively)
Just to illustrate this by an example: We would like to measure the height of all participants of this course.
We have one tape which we would use. All facilitators will be asked to measure the height of the participants in their group. Some facilitators will hold the tape to the right, the others to the left, so that even when they take the height of the same person, they would end up having different numbers. This would correspond to the standard error.
However, if some of us are using an incorrect tape, which is actually not 2 m but only 1,98 m we will have a systematic error and our results will be biased in one direction. We will not be able to correct this after we took the measurements.
Is that clear?

12. Types of sampling Non-probability samples Probability samples
Convenience samples
Biased
Subjective samples
Based on knowledge
In the presence of time/resource constraints
Probability samples
Random
only method that allows valid conclusions about population and measurements of sampling error
There are two types of sampling, the non-probability samples and the probability samples which ensures each sampling unit has the same chance to be selected. In this presentation, we will focus on probability sampling techniques. 12

13. 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
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
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. To sample friends, co-workers, or shoppers at a single mall, are all examples of convenience sampling.
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 respondent they wish as long as the quota is met
Even studies intended to be probability studies sometimes end up being non-probability studies due to unintentional or unavoidable characteristics of the sampling method. In public opinion polling by private companies (or organizations unable to require response), the sample can be self-selected rather than random. This often introduces an important type of error: self-selection error. This error sometimes makes it unlikely that the sample will accurately represent the broader population. Volunteering for the sample may be determined by characteristics such as submissiveness or availability. The samples in such surveys should be treated as non-probability samples of the population, and the validity of the estimates of parameters based on them unknown
Probability of being chosen is unknown
Cheaper- but unable to generalise, potential for bias

14. Example of a non-probability sample
Take a sample of the population of a Greek island to ask about possible exposures following a gastroenteritis outbreak
Sampling frame: people walking around the port at high noon on a Monday

15. …we ended up interviewing only two locals!

16. Probability samples Random sampling
Each unit has a known probability of being selected
Allows application of statistical sampling theory to results in order to:
Generalise
Test hypotheses
Let’s look at the 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

17. Methods used in probability samples
Simple random sampling
Systematic sampling
Stratified sampling
Multi-stage sampling
Cluster sampling
There are several ways of performing random sampling and I will present you the following:
Simple random sampling
Systematic sampling
Stratified sampling
Multi-stage sampling
Cluster sampling

18. Simple random sampling
Principle
Equal chance/probability of each unit being drawn
Procedure
Take sampling population
Need listing of all sampling units (“sampling frame”)
Number all units
Randomly draw units
Simple random sampling
In a simple random sampling, there is an equal chance/probability of drawing each unit. X has the same probability as y to be chosen.
The Procedure is simple: Take the sampling population, establish a listing of all sampling units (“sampling frame”), number all units and randomly draw units

19. Simple random sampling
Advantages
Simple
Sampling error easily measured
Disadvantages
Need complete list of units
Units may be scattered and poorly accessible
Heterogeneous population  important minorities might not be taken into account
The advantages are that the method is simple and the sampling error easily measured.
The disadvantages are that you need complete list of units. This can be a problem. Here in the course we have the total list, but what when you need to sample from a larger population? Where do you get the listing from?
Also, this method does not always achieve the best representativeness, e.g telephone numbers- is everyone in the telephone book? Are there people without phones? Or non-functioning phones… Or the population registry. Is it up to date?
If we are not using telephones but door-to-door interviews: The units may be scattered and poorly accessible. Because units may be scattered may be more time consuming to perform the study.

20. Systematic sampling Principle Procedure
Select sampling units at regular intervals (e.g. every 20th unit)
Procedure
Arrange the units in some kind of sequence
Divide total sampling population by the designated sample size (eg 1200/60=20)
Choose a random starting point (for 20, the starting point will be a random number between 1 and 20)
Select units at regular intervals (in this case, every 20th unit), i.e. 4th, 24th, 44th etc.
For convenience, selection from the sampling frame is sometimes carried out systematically rather than randomly, by taking individuals at regular intervals down the list. The principle of systematic sampling is to select sampling units at regular intervals.
The process for drawing a systematic sample is as follows:
You arrange the units in some kind of sequence
Divide the total sampling population by the sample size (say 1200/60=20)
Choose a random starting point (e.g. for 20 the starting point will be chosen randomly from 1 to 20)
Select units at regular intervals (for 20 this will be every 20th unit).
The advantages are that it is simple to do and the sampling error can be easily measured.
The disadvantages are that you need a complete list of units. If this list of units is not well mixed and there may be an underlying pattern in the sampling frame, eg. if we choose every second person in this room and men-women are always seated in the same order, the second person will be only eg. women. So if the sampling units are grouped such that particular characteristics occur at regular intervals, bias can occur. 20

21. Systematic sampling Advantages Disadvantages
Ensures representativity across list
Easy to implement
Disadvantages
Need complete list of units
Periodicity-underlying pattern may be a problem (characteristics occurring at regular intervals)
The advantages are that the method is simple and the sampling error easily measured.
-The disadvantages are that you need complete list of units. This can be a problem eg in a country with no census data or central population register.
-The population may be widely dispersed and so a simple random sample would be impractical, time-consuming and costly (e.g. in an Afriacan country with remote villages and bad roads, a simple random sample would require much travelling to sample a few individuals from many remote villages).
-If the population is made up of different types of groups (eg small minorities, a simple random will not be representative of the population- unless you have a very large number)
Also, this method does not always achieve the best representativeness, e.g telephone numbers- is everyone in the telephone book? Are there people without phones? Or non-functioning phones… Or the population registry. Is it up to date? 21

22. More complex sampling methods

23. Stratified sampling When to use Procedure
Population with distinct subgroups
Procedure
Divide (stratify) sampling frame into homogeneous subgroups (strata) e.g. age-group, urban/rural areas, regions, occupations
Draw random sample within each stratum
Stratified sampling is used when the population is made up of groups with different characteristics and expected big differences in the feature under study (eg minorities, urban/rural areas). Simple random sample will not be representative of the population, unless you have a very large sample.This is because the big differences that may occur between the separate groups will cause more variation in the overal estimate and it will be less precise. Eg. to estimate the prevalence of nosocomial infections, I can stratify by wards which have different levels of risk for hospital-acquired infections.
We divide the sampling frame into homogeneous subgroups (strata) that have common characteristics e.g. age-group, occupation, area of residence;
We draw a random sample in each stratum.
In most situations, the number of people in each subgroup will not be the same. To ensure that all subjects have the same chance of being selected, the same proportion of subjects should be sampled from each group. In other words, the same sampling fraction is used in each stratum. 23

24. Selecting a sample with probability proportional to size
Stratified sampling
Selecting a sample with probability proportional to size
Area Population Proportion Sample size Sampling
size fraction
Urban %
1000 x 0.7 = 700
10 %
Rural %
1000 x 0.3 = 300
10 %
1000
Total 24

25. Stratified sampling Advantages Disadvantages
Can acquire information about whole population and individual strata
Precision increased if variability within strata is smaller (homogenous) than between strata
Disadvantages
Sampling error is difficult to measure
Different strata can be difficult to identify
Loss of precision if small numbers in individual strata (resolved by sampling proportional to stratum population)
The advantages of stratified sampling are that you can acquire information about whole population and individual strata.
The precision will increase 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 25

27. Multiple stage sampling
Principle:
Consecutive sampling
Example : sampling unit = household
1st stage: draw neighbourhoods
2nd stage: draw buildings
3rd stage: draw households
Principle:
consecutive sampling
example : sampling unit = household
1st stage: draw neighborhoods
2nd stage: draw buildings
3rd stage: draw households 8

28. Cluster sampling Principle
Whole population divided into groups e.g. neighbourhoods
A type of multi-stage sampling where all units at the lower level are included in the sample
Random sample taken of these groups (“clusters”)
Within selected clusters, all units e.g. households included (or random sample of these units)
Provides logistical advantage
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)

34. Stage 3: Selection of the sampling unit
Second-stage units => Households
Third-stage unit => Individuals 34

35. All third-stage units might be included in the sample
Stage 3: Selection of the sampling unit
All third-stage units might be included in the sample 35

36. Cluster sampling Advantages
Simple as complete list of sampling units within population not required
Less travel/resources required
Disadvantages
Cluster members may be more alike than those in another cluster (homogeneous)
this “dependence” needs to be taken into account in the sample size and in the analysis (“design effect”)
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 (homogeneous)….
This “dependence” needs to be taken into account in the sample size….and the analysis (“design effect”)

37. 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
Which one is the right sampling method?
This depends first on the population to be studied: How large is the target population? Small population you can use a simple random sampling, for a large population you mkight need more sophisticated methods. Also, a population scattered in remote areas will require a different sampling method that the population of a large city.
If you expect a large heterogeneity regarding your variable of interest, you may have to choose a stratified sample.
It also depends on the availability of a list of sampling units, the level of precision required and last but not least the resources available.

38. Conclusions Probability samples are the best Ensure
Validity
Precision
…..within available constraints

39. Conclusions
If in doubt…
Call a statistician !!!!

40. Acknowledgements Thomas Grein Denis Coulombier Philippe Sudre
Mike Catchpole
Denise Antona
Brigitte Helynck
Philippe Malfait
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