Sampling

Sources: -EPIET Introductory course, Thomas Grein, Denis Coulombier, Philippe Sudre, Mike Catchpole-IDEA Brigitte Helynck, Philippe Malfait, Institut de veille sanitaire

Modified: Denise Antona, EPIET 2003

Objectives of presentation

• Definition of sampling• Why do we use samples?• Concept of representativeness• Main methods of sampling• Sampling error• Sample size calculation

Definition of sampling

Procedure by which some members

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

Definition of sampling terms

• Sampling unit– Subject under observation on which information is

collected

• Sampling fraction– Ratio between the sample size and the population

size

• Sampling frame – Any list of all the sampling units in the population

• Sampling scheme– Method of selecting sampling units from sampling

frame

Why do we use samples ?

Get information from large populations

– At minimal cost

– At maximum speed

– At increased accuracy

– Using enhanced tools

Sampling

PrecisionCost

What we need to know

• Concepts

– Representativeness

– Sampling methods

– Choice of the right design

• Calculations

– Sampling error

– Design effect

– Sample size

Sampling and representativeness

Sample

Target Population

SamplingPopulation

Target Population Sampling Population Sample

Representativeness

• Person• Demographic characteristics (age, sex…)• Exposure/susceptibility

• Place (ex : urban vs. rural)• Time

• Seasonality• Day of the week• Time of the day

Ensure representativeness before starting, confirm once completed !!!!!!

Types of samples

• Non-probability samples

• Probability samples

Non probability samples

• Quotas • Sample reflects population structure• Time/resources constraints

• Convenience samples (purposive units)• Biased• Best or worst scenario

Probability of being chosen : unknown

Probability samples

• Random sampling

• Each subject has a known probability of being chosen

• Reduces possibility of selection bias

• Allows application of statistical theory to results

Sampling error

• No sample is the exact mirror image of the population

• Magnitude of error can be measured in probability samples

• Expressed by standard error– of mean, proportion, differences, etc

• Function of– amount of variability in measuring factor of interest– sample size

Methods used in probability samples

• Simple random sampling• Systematic sampling• Stratified sampling• Multistage sampling• Multiphase sampling• Cluster sampling

Quality of an estimate

Precision & validity

No precision

Random error !

Precision butno validity

Systematicerror (Bias) !

Simple random sampling

• Principle–Equal chance of drawing each unit

• Procedure–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

Example: evaluate the prevalence of tooth decay among the 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

Simple random sampling

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Table of random numbers

EPITABLE: random number listing

EPITABLE: random number listing

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

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 ……..

Systematic samplingExample: systematic sampling

Stratified sampling

• Principle :

–Classify population into internally homogeneous subgroups (strata)

–Draw sample in each strata–Combine results of all strata

Stratified sampling

• Advantages– More precise if variable associated with

strata– All subgroups represented, allowing

separate conclusions about each of them

• Disadvantages– Sampling error difficult to measure– Loss of precision if very small numbers

sampled in individual strata

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)

Multiple stage sampling

Principle

• = consecutive samplings

• example : sampling unit = household

– 1rst stage : drawing areas or blocks – 2nd stage : drawing buildings, houses – 3rd stage : drawing households

Cluster sampling

• Principle

– Random sample of groups (“clusters”)

of units– In selected clusters, all units or

proportion (sample) of units included

Example: Cluster sampling

Section 4

Section 5

Section 3

Section 2Section 1

Cluster sampling

• Advantages– Simple as complete list of sampling units

within population not required– Less travel/resources required

• Disadvantages– Imprecise if clusters homogeneous and

therefore sample variation greater than population variation (large design effect)

– Sampling error difficult to measure

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%)

1600

220

3200

400

800

200

1200

200

1600

400

53000

7300

106000

13000

26500

6600

40000

6600

53000

13200

A

B

C

D

E

F

G

H

I

J

12-23Pop.Village

Distribution of the clusters

ABCDEFGHI

J

1600220

3200400800200

1200200

1600400

1600182050205420622064207620782094209820

Total population = 9820

Compute cumulated population

Distribution of the clusters

Then compute sampling fraction :

K= = 327

Draw a random number (between 1 and 327)

Example: 62

Start from the village including “62” and draw the clusters adding the sampling fraction

982030

A

B

C

D

E

F

G

H

I

J

1600

1820

5020

5420

6220

6420

7620

7820

9420

9820

I I I I

I

I I I I I I I I I I

I

I I

I

I I I I

I

I I I I I

I

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)

EPITABLE: Calculating design effect

Selecting a sampling method

• Population to be studied– Size/geographical distribution– Heterogeneity with respect to variable

• Level of precision required

• Resources available

• Importance of having a precise estimate of the sampling error

Steps in estimating sample size

• Identify major study variable• Determine type of estimate (%, mean, ratio,...) • Indicate expected frequency of factor of interest• Decide on desired precision of the estimate• Decide on acceptable risk that estimate will fall outside its

real population value• Adjust for estimated design effect• Adjust for expected response rate• (Adjust for population size? In case of small size population

only)

Sample size formula indescriptive survey

z: alpha risk express in z-score

p: expected prevalence

q: 1 - p

d: absolute precision

g: design effect

z² * p * q 1.96²*0.15*0.85n = -------------- ---------------------- = 544

d² 0.03²

Cluster sampling

z² * p * q 2*1.96²*0.15*0.85n = g* -------------- ------------------------ = 1088d² 0.03²

Simple random / systematic sampling

EPITABLE: cluster sample size calculation

Place of sampling in descriptive surveys

• Define objectives• Define resources available• Identify study population• Identify variables to study• Define precision required• Establish plan of analysis (questionnaire)• Create sampling frame• Select sample• Pilot data collection• Collect data• Analyse data• Communicate results• Use results

Conclusions

• Probability samples are the best

• Beware of …– refusals– absentees– “do not know”

Conclusions

• If in doubt…

Call a statistician !!!!