Shooting right

Sampling methods

FETP India

Competency to be gained from this lecture

Select a sample from a population to generate precise and valid estimates

Key issues

• Sampling• Sampling error• Validity and precision• Sample size calculation

Definition of sampling

Procedure by which some members of the population are selected as representatives

of the entire population

Sampling

Sample

Population

Study population

The study population is the population to which the results of the study will be

inferred

Sampling

The study population depends upon the research question

• How many injections do people receive each year in India? Study population: Population of India

• How many needle-sticks to health care workers experience each year in India? Study population: Health care workers of

India

• How many hospitals have a needle-stick prevention policy in India? Study population: Hospitals of India

Sampling

The sample needs to be representative of the population in

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

Sampling

The sample needs to be representative of the population in

terms of place• Urban• Rural

Sampling

The sample needs to be representative of the population in

terms of persons• Age• Sex• Other demographic characteristics

Sampling

Definition of sampling terms

• Sampling unit (Basic sampling unit, BSU) Elementary unit that will be sampled

• People• Health care workers• Hospitals

• Sampling frame List of all sampling units in the population

• Sampling scheme Method used to select sampling units from

the sampling frame

Sampling

Why do we sample populations?

• Obtain information from large populations

• Ensure the efficiency of a study• Obtain more accurate information

Sampling

Population Sample

•Infinite/finite size•Characterized by unknown parameters

•Finite size•Characterized by measurable parameters (e.g., mean, standard dev.)

A sample is a part of the population, selected by the investigator to gather information (measures) on certain characteristics

of the original population Sampling

Practical example

• The Ministry of Health of a country X wants to estimate the proportion of children in elementary schools who have been immunized against childhood infectious diseases

• The task must be completed in one month

• The objective is to estimate the proportion of immunized children

Sampling

Planning and implementing a sample survey

• Sampling plan Methodology used for selecting the sample

from the population

• Estimation procedures Algorithms or formulas used for obtaining

estimates of population values from the sample data and for estimating the reliability of these population estimates

Sampling

The various steps of a survey (1/2)

1.Describe the objective of the survey2.Define the target population3.Prepare a “sampling frame” 4.Analysis plan: Develop “table shells” for

the results 5.Choose the sampling method 6.Calculate the sample size (s)

Sampling

The various steps of a survey (2/2)

7. Develop, field test and revise data collection instrument(s)

8. Train the data collectors 9. Conduct the survey10.Monitor the field work11.Tabulate, analyze and interpret the

results12.Use the results

Sampling

Collaborative sample design for steps 5 and 6

The statistician, the epidemiologist, and those who will use the data from the survey work together to choose the

right sample design

Sampling

Taking several samples

• If you take repeated samples out of a population, each result will be a little different

• Their distribution is called a sampling distribution

Sampling error

Population mean

A sampling distribution

A sample mean

1 Standard Error

Sampling error

MeanSD 95% 99%

The standard normal curve

What is the value of mean and standard deviation?

Properties of the standard normal curve

• If every member of the population has an equal chance to be in the sample We can plot our results on the normal curve

by calculating a z score

• This tells us how likely the results are due to chance

• Example: 95% of the sample means will be within two

standard deviations of the population mean

Sampling error

Chance

• How likely is the result due to chance?• Measured by the confidence level,

example 95% or 0.95• We are 95% confident the population

mean is within the confidence interval around our sample mean

Sampling error

Sampling error

• The validity and reliability of these extrapolations depend on: How well the sample was chosen How well the measurements were made

• Although hypothesis can be tested based on data collected on sample surveys, the primary objective is always estimation

Sampling error

Quality of the measures: The precision

• If the results are precise, they do not vary if the measures are repeated

• Precision is expressed by the confidence we have in the results

• Precision is estimated by the confidence interval around the measureWe can estimate the variability by

computing the confidence interval

True value

Precision, validity

The sample size increases precision and reduces the confidence interval

Lower limit

Upper limit

x

Precision, validity

Estimating precision

• If every member of the target population had an equal chance of being in the sample

• Confidence interval provides an estimate of how closely the sample population proportion estimates the target population Example: ± 10%.

Precision, validity

Quality of the measures: The validity

• Absence of systematic error

• A valid measure reflects the true value in the population

• In contrast, a biased measure gives an unreliable “point of view”

True Observed

Precision, validity

Appropriate study design and sampling frame lead to valid results

True

ObservedPrecision, validity

Assuring validity

• Good design• Interviewer training• Quality assurance

Precision, validity

10%5%

A valid and precise measure

Precision, validity

10%5%

A precise measure that is not valid

Precision, validity

10%5%

A valid measure that is not precise

Precision, validity

10%5%

A measure that is not valid nor precise

Precision, validity

Truth is everything

• It is easier to control bias and errors in a small sample than in a big one

• Better have: A small sample that gives a true estimate

• Than: A large sample that gives a false estimate

Precision, validity

Type of samples

• Non-probability samples Probability of being selected is unknown Convenience samples

• Biased• Best or worst scenario

Subjective samples • Based on knowledge• Time/resource constraints

• Probability samples

Sampling techniques

Type of samples

• Non-probability samples• Probability samples

Every unit in the population has a known probability of being selected

Only sampling method that allows to draw valid conclusions about population

Sampling techniques

Random sampling in probability samples

• Removes the possibility of bias in selection of subjects

• Ensures that each subject has a known probability of being chosen

• Allows application of statistical theory

Sampling techniques

Sampling error

• No sample is a perfect mirror image of the population

• Magnitude of error can be measured in probability samples

• Expressed by standard error of mean, proportion, differences…

• Function of: Sample size Variability in measurement

Sampling techniques

Methods used in probability samples

1. Simple, random sampling2. Systematic sampling3. Stratified sampling4. Cluster sampling5. Multistage sampling

Sampling techniques

1. Simple, random sampling

• Principle Equal chance for each statistical unit

• Procedure Number all units Randomly draw units

• Advantages Simple Sampling error easily measured

• Disadvantages Need complete list of units Does not always achieve best representativity

Sampling techniques

Example of simple, random sampling

1 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.

Numbers are selected at random

2. Systematic sampling

• Principle A unit drawn every k units Equal chance of being drawn for each unit

• Procedure Calculate sampling interval (k = N/n) Draw a random number ( k) for starting Draw every k units from first unit

• Advantages Ensures representativity across list Easy to implement

• Disadvantage Dangerous if list has cycles

Sampling techniques

Example of systematic samplingExample: systematic sampling

Every eighth house is selected

3. Stratified sampling

• Principle Classify population into homogeneous subgroups

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

• Advantage 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 small numbers sampled in

individual strata

Sampling techniques

Example of stratified sampling

• Estimate vaccination coverage in a country

• One sample drawn from each region• Estimates calculated for each stratum• Each strata weighted to obtain estimate

for country

Sampling techniques

4. Cluster sampling

• Principle Random sample of groups (“clusters”) of

units All or proportion of units included in selected

clusters• Advantages

Simple: No list of units required Less travel/resources required

• Disadvantages Imprecise if clusters homogeneous (Large

design effect) Sampling error difficult to measure

Sampling techniques

Cluster sampling

• The sampling unit is not a subject, but a group (cluster) of subjects.

• It is assumed that: The variability among clusters is minimal The variability within each cluster is what is

observed in the general population

Sampling techniques

The two stages of a cluster sample

1. First stage: Probability proportional to size• Select the number of clusters to be included • Compute a cumulative list of the populations in each unit

with a grand total• Divide the grand total by the number of clusters and

obtain the sampling interval• Choose a random number and identify the first cluster• Add the sampling interval and identify the second cluster• By repeating the same procedure, identify all the clusters

2. Second stage• In each cluster select a random sample using a sampling

frame of subjects (e.g. residents) or households

Sampling techniques

Self-weighting in cluster samples

• Stage one: The larger units are more likely to be selected in the first round Unit B twice as large as unit A will have twice the

chance of being selected

• Stage two: Individuals in larger unit selected are less likely to be selected in the second round Individual in unit B will have half the chance of being

selected within the unit

• The two effects cancel each other and each person in the population has the same probability of being sampled

30 x 7 cluster sampling in the expanded programme of

immunizationProcedure: list of all villages (areas) with total population

Village Inhabitants Cumulative1 34 342 60 943 30 1244 76 2005 315 515.. 4,715

Divide the cumulative total by 30 clusters we wish to select

4,715 : 30= 157.1Sampling techniques

30 x 7 cluster sampling in the expanded programme of immunization

Find a random number with three digits (= Sampling interval) e.g. 123

Choose from the cumulative distribution the clustersby adding 157 (sampling interval) 4 124 124 * 1st cluster5 76 200 6 315 515 ** 2nd 123+157=280

In each village (area) choose 7 children

Total sample 30 X 7= 210 Sampling techniques

Design effect (Use Epitable software)Global 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 clus = -------------

k(k-1)

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

Var clust

Sampling techniques

Example of cluster sampling

Section 4

Section 5

Section 3

Section 2Section 1

Sampling techniques

5. Multistage 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

Sampling techniques

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)

Sampling techniques

Sample size formula in descriptive survey(Use Epitable)

z: alpha risk expressed 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

Sampling techniques

Remember

• Probability samples are the best • Beware of …

Refusals Absentees “Do not know”

Sampling techniques

Summary of methods used in probability samples

1. Simple, random sampling• Draw subjects from list with random number

2. Systematic sampling• Draw every xth subject

3. Stratified sampling• Take one sample for each strata

4. Cluster sampling• Select clusters and then select individuals

5. Multistage sampling• Sample stage by stage

Sampling techniques

Key issues

• We cannot study the whole population so we sample it

• Taking a sample leads to sampling error, which is measurable

• Good design and quality assurance ensure validity and while appropriate sample size will ensure precision

• Probability samples are the only ones that allow use of statistics as we know them