SamplingSamplingVorasith Sornsrivichai, M.D., FETP Cert.

Epidemiology Unit, Faculty of Medicine, PSU

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ObjectivesObjectives1. Explain the need for survey sampling2. Define the following terms:

– Reference population, study population, study sample

– Internal validity, external validity– Probability sampling, equal probability

selection method, disproportionate sampling– Stratification, design effect

3. Describe principles of & steps in sampling for a household survey

– Simple, systematic, stratified random sampling, cluster sampling

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Outline of PresentationOutline of Presentation• Population & sample• Validity, precision, representativeness• Non-probability VS probability sample• Proportionate VS disproportionate

sampling• Sampling error, sampling variation,

sampling bias• Methods in probability sampling

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POPULATION

SAMPLE

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Population (N)Population (N)• The whole collection of units (the

“universe”), from which a sample may be drawn

• The units may be records or events, not necessarily a population of persons

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Sample (n)Sample (n)• A selected subset of a population

– Random or nonrandom– Representative or nonrepresentative

• The sample is intended to give results that are representative of the whole population

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Population (N=100)Population (N=100)0

2040

6080

100

y

0 20 40 60 80 100x

Wisdom Score

Age (yr)

Does wisdom come with age?

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Sample (n=10)Sample (n=10)0

2040

6080

100

y

0 20 40 60 80 100x

Wisdom Score

Age (yr)

Does wisdom come with age?

9

Population (N=100)Population (N=100)0

2040

6080

100

y

0 20 40 60 80 100x

Wisdom Score

Age (yr)

Does wisdom come with age?

““ Pain makes man think.Pain makes man think.Thought makes man wise.Thought makes man wise.

Wisdom makes life endurable."Wisdom makes life endurable."~ John Patrick ~~ John Patrick ~

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Why Do We Sample Populations?Why Do We Sample Populations?

• Get accurate information from large populations

• Efficiency of study

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Hierarchy of PopulationHierarchy of Population• Target population: The general

population you want to know about• Sample: The part of target population

you collect the data• We use the estimate from the sample to

estimate the parameter in the target population

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Hierarchy of PopulationHierarchy of PopulationReference/external

population

Study/target population

Actual population

Study sample/population

(Sample)

Statistical inferenceIssue of chance

Internal validityIssue of bias

External Validity(Generalizability)

Issue of population difference

Sampling

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Validity & PrecisionValidity & Precision

Valid,

and precise

Valid,

not precise

Not valid,

but precise

Not valid,

not precise

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Validity & PrecisionValidity & Precision• Validity

– Measurement reflects true value of population

– Improved by good design, sampling scheme, quality assurance

• Precision– The measurement results conform to

themselves– Improved by increasing the sample size

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Truth is (almost) EverythingTruth is (almost) Everything• A small sample that gives a true

estimate of the target population is better than a big sample that gives a precise but false estimate

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RepresentativenessRepresentativeness• Persons

• Demographic: age, sex, race• Socioeconomic: SES• Cultural

• Place• Geographical: country, region• Sociological: urban VS rural

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

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Type of SamplesType of Samples• Non-probability samples : probability of being

selected is unknown – Convenience or accidental or haphazard samples

e.g. Man-in-the-street surveys, grab sample• Biased

– Purposive or subjective samples e.g. expert sample, quota sample

• Based on knowledge• Time/resources constraints

• Probability (random) samples: every unit in the population has a known probability of being selected

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Probability SampleProbability Sample• All individuals have a known chance of

selection– May have an equal chance of being

selected– Or, if a stratified sampling method is

used, the chance of being selected can be varied

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Probability SampleProbability Sample• Created by

– Assigning an identity (label, number) to all individuals in the population

– Arranging them in alphabetical order and numbering in sequence, or simply assigning a number to each, or by grouping according to area of residence and numbering the groups

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Probability SampleProbability Sample– Select individuals (or groups) for

study by a random procedure such as use of a table of random numbers (or comparable procedure) to ensure that the chance of selection is known

"To conquer fear is the beginning of wisdom." "To conquer fear is the beginning of wisdom." ~ Bertrand Russell ~~ Bertrand Russell ~

Any questions? :-)

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SamplingSampling• The process of selecting a number of

subjects from all the subjects in a particular group– Conclusions based on sample results

may be attributed only to the population sampled

– Any extrapolation to a larger or different population is a judgment or a guess and is not part of statistical inference

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Definition of Sampling TermsDefinition of Sampling Terms• Sampling frame

– Any list of all the sampling units in the population

• Primary Sampling Unit (PSU)– Sample drawn from sampling frame in the

first stage of sample selection• Sampling scheme

– Method of selecting sampling units from sampling frame

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EPSMEPSM• “Equal Probability of Selection Method":

A sample that each final unit of selection in the population has an equal probability of selection– Simple random sampling, systematic

random sampling are EPSM samples

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Disproportionate SamplingDisproportionate Sampling• May be used for

– Cost efficiency– Important small subgroup population

• Stratified sampling are not EPSM, if the sampling fraction or probability of selection (n/N) is not the same for all strata

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Sampling ErrorSampling Error• That part of the total estimation error of

a parameter caused by the random nature of the sample

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

• Is a function of– Sample size– Amount of variability in measuring

factor of interest

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Sampling VariationSampling Variation• Since the inclusion of individuals in a

sample is determined by chance, the result of analysis in two or more samples will differ, purely by chance

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Sampling BiasSampling Bias• Systematic error due to study of a

nonrandom sample of a population

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E+D+

E+D-

E-D+

E-D-

E+D+

E+D-

E-D+

E-D-

E+D+

E+D-

E-D+

E-D-

E+D+

E+D-

E-D+

E-D-

Selection BiasSelection Bias

n

N

"Mistakes are "Mistakes are the usual bridge the usual bridge

between between inexperienceinexperienceand wisdom." and wisdom."

~ Phyllis Theroux ~~ Phyllis Theroux ~

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Selecting a Sampling MethodSelecting a Sampling Method• Population to be studied

– Heterogeneity with respect to variable of interest

– Size/geographical distribution• Resources available • Importance of precision of estimate or

sampling error

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Methods in Probability SamplingMethods in Probability Sampling• Simple random sampling• Systematic sampling• Stratified sampling• Cluster sampling• Multistage sampling

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Simple Random Simple Random Sampling (SRS)Sampling (SRS)• Principle

– Each person has an equal chance of being selected from the entire population

• Procedure– Assign each person a number, starting with

1, 2, 3, and so on – Numbers are selected at random until the

desired sample size is attained

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Random TableRandom TableRow <--------- uniform random digits --------------------------> 1 57245 39666 18545 50534 57654 25519 35477 71309 12212 98911 2 42726 58321 59267 72742 53968 63679 54095 56563 09820 86291 3 82768 32694 62828 19097 09877 32093 23518 08654 64815 19894 4 97742 58918 33317 34192 06286 39824 74264 01941 95810 26247 5 48332 38634 20510 09198 56256 04431 22753 20944 95319 29515 6 26700 40484 28341 25428 08806 98858 04816 16317 94928 05512 7 66156 16407 57395 86230 47495 13908 97015 58225 82255 01956 8 64062 10061 01923 29260 32771 71002 58132 58646 69089 63694 9 24713 95591 26970 37647 26282 89759 69034 55281 64853 50837 10 90417 18344 22436 77006 87841 94322 45526 38145 86554 42733 11 78886 86557 11295 07253 29289 44814 58898 36929 66839 81250 12 39681 54696 38482 48217 73598 93649 92705 34912 18981 74299 13 38265 45196 31143 82190 27279 79883 20219 38823 84543 22119 14 34270 41885 00079 63600 59152 10670 27951 77830 05368 58315 15 73869 34748 75787 88844 89522 71436 04166 06246 20952 56808 16 21732 36017 69149 70330 90500 73110 92908 55789 73450 68282

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Simple Random SamplingSimple Random Sampling1 Albert D.2 Richard D.3 Belle H.4 Raymond L.5 Stéphane B.6 Albert T.7 Jean William V.8 André D.9 Denis C.10 Anthony Q.11 James B.12 Denis G.13 Amanda L.14 Jennifer L.15 Philippe K.16 Eve F.17 Priscilla O.18 Frank V.L.19 Brian F.20 Hellène H.21 Isabelle R.22 Jean T.23 Samanta D.24 Berthe L.

25 Monique Q.26 Régine D.27 Lucille L.28 Jérémy W.29 Gilles D.30 Renaud S.31 Pierre K.32 Mike R.33 Marie M.34 Gaétan Z.35 Fidèle D.36 Maria P.37 Anne-Marie G.38 Michel K.39 Gaston C.40 Alain M.41 Olivier P.42 Geneviève M.43 Berthe D.44 Jean Pierre P.45 Jacques B.46 François P.47 Dominique M.48 Antoine C.

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Simple Random Simple Random SamplingSampling• Advantages

– Simple– Sampling error easily measured

• Disadvantages– Need complete & up-to-date list of units– For a wide geographic area, travel costs is

often the most expensive component– Does not always achieve best

representativeness

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Systematic Systematic SamplingSampling• Principle

– Units drawn with a constant interval between successive units

– Equal chance of being selected for each unit

• Procedure– Calculate sampling interval (k = N/n)– Draw a random number (≤ k) for random

starting point– Draw every kth units from first unit

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Systematic SamplingSystematic Samplingf=11/93

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Systematic SamplingSystematic Sampling

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Systematic Systematic SamplingSampling• Advantages

– Provide better spread, ensures representativeness across list

– Can improve precision – Easy to implement

• Disadvantages– Dangerous if list has cycles or periodic– Travel cost

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Systematic SamplingSystematic Samplingf=7/93

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Stratified SamplingStratified Sampling• Principle

– Dividing the population into subgroups according to some important characteristic e.g. age

– Selecting a random sample out of each subgroup– If proportion of the sample drawn from each strata is

the same as the proportion of the population in each stratum (Probability Proportional to Size-PPS) then all strata will be fairly represented with the sample

• Procedure– Classify population into homogeneous subgroups

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

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Stratified Sampling with PPSStratified Sampling with PPS

Stratification

Sampling

15 10

N=25

n=5

3 2

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Stratified SamplingStratified Sampling• Advantages

– More precise if interesting 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

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Cluster Cluster SamplingSampling• Principle

– Each unit selected is a group of units (a village, an ED. etc.) rather than an individual

• Procedure– Random sample of groups (“clusters”) of

units– In selected clusters, all units or proportion

(sample) of units included– Sampling within cluster may be simple

random or systematic

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EPI 30 Clusters SurveyEPI 30 Clusters SurveyCommunity Pop. size Cum. pop. size

1 110 110

2 100 210

3 130 340

4 100 440

5 120 560

6 80 640

7 160 800

8 110 910

| | |

50 300 4000

1. Divide total population of the communities (4000) by the number of clusters to be selected (30) = sampling interval (133)

2. Choose a random number between 1 and 133 (118.) Since 118 lies between 110 and 210, community 2 will be chosen

3. Now add the sampling interval: 118 + 133 = 251, so community 3 is chosen and so on

4. In each cluster choose 7 children (total sample size/no. of clusters = 210/30 = 7)

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Cluster SamplingCluster Sampling

Section 4

Section 5

Section 3

Section 2Section 1

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Cluster SamplingCluster Sampling• Advantages

– 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

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Steps in Cluster SamplingSteps in Cluster Sampling• Clarify the rationale• Set up specific objective. This technique is

suitable for survey for estimating proportion not so good for testing hypothesis

• Define study population particularly geographic definition such as rural/urban area in the specific province(s)

• Define eligibility of the informant• Calculate sample size and estimate number

of households to be visited

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Steps in Cluster SamplingSteps in Cluster Sampling• Obtain the enumeration district (ED), a list of districts

and villages in the study province(s). Each village should have the most recent number of population or household.

• Assuming the proportion of population among different districts in the study province is relative stable over time, this enumeration table (with name of village in the first and its population size in the second column) will be use as sampling frame. In the first stage of sampling, the PSU is village

• Calculate cumulative population for each village. Place the number in the third column

• Calculate sampling interval if the no. of cluster is 30 then sampling interval = total pop. / 30 = i

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Steps in Cluster SamplingSteps in Cluster Sampling• Select a random start which must fall between

1 to the sampling interval. Say r• The first village is the village with cumulative

population is just over r• The second village is the village with cumulative

population is just over r + i• The third village is the village with cumulative

population is just over r + 2 i• The other consecutive village can be sampled

similarly• At the end, there will be 30 selected villages

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Steps in Cluster SamplingSteps in Cluster Sampling• Prepare the questionnaire• Prepare initial field visit with the responsible

officers. Check information related to transportation, security and availability of other facilities: shelters, food

• Make an appointment with key persons in each selected village. Have an initial visit. Employ 1-2 locals to facilitate the survey. Make sure that there would be no serious problem during the day of survey

• Pre-test the questionnaire and train the interviewers in a non-selected village

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Steps in Cluster SamplingSteps in Cluster Sampling• Visit the village on the day of appointment.

Choose a random starting point and visit consecutive nearest household. Ask for eligible subject. Conduct interview

• When a sample size in that cluster reach the desire number, check the completeness of the questionnaire and leave the village

• Continue until all 30 clusters are finished

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Design EffectDesign EffectGlobal variance

p(1-p)Var srs = ----------n

Cluster variance

p= global proportionpi= proportion in each stratumn= number of subjectsk= number of strata

Σ (pi-p)²Var clust = -------------

k(k-1)

Design effect = ------------------Var srs

Var clust

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Design EffectDesign Effect= Actual sample size (SS) / Effective SS

e.g. cluster sampling SS / SRS SS= 1+(m−1)ρ

If m = cluster size k = no. of clusterρ = Intracluster correlation coefficient

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The The IntraclusterIntracluster Correlation Correlation Coefficient (ICC, Coefficient (ICC, ρρ--rhorho))

• A measure of the relatedness of clustered data; by comparing the variance within clusters with the variance between clusters.

• Mathematically, it is the between-cluster variability divided by the sum of the within-cluster and between-cluster variabilities.ICC (ρ) = Sb

2

(Sb2 + Sw

2)

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Effective Sample SizeEffective Sample Size• If we have 4 physicians recruiting 32 patients

each (total 128 patients.) Given ρ = 0.017, what is the effective sample size (ESS) after adjusting for clustering?

• Design Effect = Actual SS / Effective SS• ESS = m k / 1+(m−1)ρ

If m = cluster size = 32, k = no. of cluster = 4, ρ = 0.017

• ESS = 32x4 / 1+0.017(32-1) = 84

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Multistage SamplingMultistage Sampling• Principle

– Several chained samples– Several statistical units

• Advantages– No complete listing of population required– Most feasible approach for large

populations• Disadvantages

– Several sampling lists– Sampling error difficult to measure

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Example: Multistage SamplingExample: Multistage Sampling• Determine hepatitis A susceptibility

among school children in a country– Sample of regions drawn from country– Sample of provinces drawn from each

selected region– Sample of schools drawn in each selected

province– Sample children within selected schools

"A prudent question is one half of wisdom.""A prudent question is one half of wisdom."

~ Francis Bacon ~~ Francis Bacon ~

Any questions? :-)

"The rain is famous for falling"The rain is famous for fallingon the just and unjust alike, on the just and unjust alike,

but if I had the managementbut if I had the managementof such affairsof such affairs

I would rain softly and sweetlyI would rain softly and sweetlyon the just,on the just,

but if I caught a sample ofbut if I caught a sample ofthe unjust outdoorsthe unjust outdoors

I would drown himI would drown him““

~ Mark Twain ~~ Mark Twain ~