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United Nations Workshop on the 2010 World Programme on Population and Housing Censuses: Census Evaluation and Post Enumeration Surveys, Amman, Jordan, 21-24 November, 2010
Sampling Frames andSample Design
Pres. 5
United Nations Workshop on the 2010 World Programme on Population and Housing Censuses: Census Evaluation and Post Enumeration Surveys, Amman, Jordan, 21-24 November, 2010
Sample Frames & Sample Design
Objectives: Important to define objectives before designing a sample
Items to estimate – coverage error, duplication, omissions, etc.
Geographic level – national, sub-national (province or district, urban/rural, etc.)
Demographic characteristics – sex, age, person, household, etc.
Confidence levelMargin of error
United Nations Workshop on the 2010 World Programme on Population and Housing Censuses: Census Evaluation and Post Enumeration Surveys, Amman, Jordan, 21-24 November, 2010
Sample Frames & Sample Design
Frames: Material from which a sample is drawn
Each unit to be included in the universeThere should be no duplicatesEach unit should be well defined and distinguishable
from other units (it should be unique)Should be updated
United Nations Workshop on the 2010 World Programme on Population and Housing Censuses: Census Evaluation and Post Enumeration Surveys, Amman, Jordan, 21-24 November, 2010
Sampling Strategies
Probability household surveys It is usual to make inferences in a PES for a number of analytical
domains Relatively large samples necessary in each domain for reliable
estimates Stratified cluster sample design-common First-stage units or Primary Sampling Units (PSUs) - many countries use
geographically contiguous land areas usually called area clusters or EAs PPS systematic sample selection Second-stage, common to canvass all persons in selected households
United Nations Workshop on the 2010 World Programme on Population and Housing Censuses: Census Evaluation and Post Enumeration Surveys, Amman, Jordan, 21-24 November, 2010
Importance of Stratification
Population subdivided into heterogeneous groups that are internally homogenous
Stratification based on variables correlated with the extent of coverage-geopolitical subdivisions
Internal homogeneity can be maintained with regard to socio-demographic variables e.g. urban stratum
Common strata may include: rural, urban, provinces etc.
United Nations Workshop on the 2010 World Programme on Population and Housing Censuses: Census Evaluation and Post Enumeration Surveys, Amman, Jordan, 21-24 November, 2010
Multi-stage Cluster Sampling
Usually used when sampling hierarchical populations The hierarchical levels are called stages First stage units are called primary sampling units (PSUs) e.g.
EAs Second stage units are called secondary sampling units
(SSUs) e.g. households Last stage units are called ultimate sampling units (USUs) e.g.
persons within households which can be selected from EAs
United Nations Workshop on the 2010 World Programme on Population and Housing Censuses: Census Evaluation and Post Enumeration Surveys, Amman, Jordan, 21-24 November, 2010
Why Area sampling?
At national level only a frame of EAs is required Data collection is more efficient Lower costs compared to simple random sampling (SRS) Supervision is easier However, estimates are prone to higher variability
compared to SRS
United Nations Workshop on the 2010 World Programme on Population and Housing Censuses: Census Evaluation and Post Enumeration Surveys, Amman, Jordan, 21-24 November, 2010
Choices of PSUs
Must have clearly identifiable and stable boundaries Must completely cover the relevant population Preferably must have measures of size They should be mapped Must cover the whole country The number of PSUs must be relatively large
United Nations Workshop on the 2010 World Programme on Population and Housing Censuses: Census Evaluation and Post Enumeration Surveys, Amman, Jordan, 21-24 November, 2010
Common problems with EAs
Incomplete coverage Inadequate maps Poor measures of size or lack of them
United Nations Workshop on the 2010 World Programme on Population and Housing Censuses: Census Evaluation and Post Enumeration Surveys, Amman, Jordan, 21-24 November, 2010
PES sample design
A single-stage stratified clustered sample design is commonly adopted
When the PSUs i.e. EAs are selected all households in selected EAs are canvassed, or more rarely only a sample (e.g. 1 every 5).
This is beneficial for matching operation
United Nations Workshop on the 2010 World Programme on Population and Housing Censuses: Census Evaluation and Post Enumeration Surveys, Amman, Jordan, 21-24 November, 2010
Sample Size
Sample size depends on estimate requirementsGeographic level (national, province, urban/rural)Demographic (sex, age)ReliabilityConfidence level
United Nations Workshop on the 2010 World Programme on Population and Housing Censuses: Census Evaluation and Post Enumeration Surveys, Amman, Jordan, 21-24 November, 2010
Sample Size
To estimate sample size in the case of proportions you must: Know the occurrence of the event in the population by
domain of estimation
Specify a confidence interval (e.g 95%)
Specify the margin of error or precision (e.g 1%)
United Nations Workshop on the 2010 World Programme on Population and Housing Censuses: Census Evaluation and Post Enumeration Surveys, Amman, Jordan, 21-24 November, 2010
Sample Size (contd.)
To estimate sample size in the case of proportions, the following formula can be used:
estimate toproportion theof varianceestimated )(
population totalof size
curveon distributi normal a of in tails area % cuts that of value
size sample
valueestimated
)1()(
)1(
2
1
2
1
n
ys
N
tt
n
Y
n
ys
N
ntYP
United Nations Workshop on the 2010 World Programme on Population and Housing Censuses: Census Evaluation and Post Enumeration Surveys, Amman, Jordan, 21-24 November, 2010
Sample size (contd.)
From that it is deduced :
212
2
2
1
then
11
ondistributi binomial ,)(
% of pointsin precision theis )(
)1(
m
pqtn
N
n
pqys
n
ys
N
ntm
United Nations Workshop on the 2010 World Programme on Population and Housing Censuses: Census Evaluation and Post Enumeration Surveys, Amman, Jordan, 21-24 November, 2010
Sample Size (contd.)
Example: To estimate percentage of households omitted in the census
(expected about 5%); confidence interval at 95% (t=1.96) for a margin of error of 2 %
The sample size works out to be:
4562
955)96.1(
22
22
x
m
pqtnh
United Nations Workshop on the 2010 World Programme on Population and Housing Censuses: Census Evaluation and Post Enumeration Surveys, Amman, Jordan, 21-24 November, 2010
Sample Size (contd.)
Adjusting for non-response, e.g. 10%:
Adjusting for the design effect for a complex sample
design Design effect of 2 is a default value : 2 x 507 =1,014 This may apply to each province (analysis) domains. If they
are five provinces Sample size will be 5 x 1,014 = 5,070
50790.0
456
United Nations Workshop on the 2010 World Programme on Population and Housing Censuses: Census Evaluation and Post Enumeration Surveys, Amman, Jordan, 21-24 November, 2010
Sample selection procedures
For greater convenience and efficiency, the sample of PSUs should be selected using a systematic procedure.
If there are good measures of size, probability proportional to size (PPS) should be used to increase the efficiency of the sample design.
Otherwise, the selection should be made with equal probabilities
United Nations Workshop on the 2010 World Programme on Population and Housing Censuses: Census Evaluation and Post Enumeration Surveys, Amman, Jordan, 21-24 November, 2010
Sample selection procedures -- PPS
1) Order the EAs geographically (and, if applicable, by other stratification characteristic) to allow implicit stratification
2) Record for each EA i of the stratum h the measure of size Mhi, typically the number of households or persons from the census mapping operation
3) Cumulate the size measures down the list of EAs, the last cumulated number will be equal to the total number of households (or persons) in stratum h (Mh)
4) Determine the number of EAs (nh) to be selected in a stratum according to the allocation
United Nations Workshop on the 2010 World Programme on Population and Housing Censuses: Census Evaluation and Post Enumeration Surveys, Amman, Jordan, 21-24 November, 2010
Sample selection procedures –- PPS (contd.)
5) Determine the sampling interval (Ih) by:
6) Obtain a random number (Ah) between 1 and Ih inclusively;
7) Determine the selected EAs as follows: Shi=Ah + (i-1) x Ih, for i = 1,...,nh, rounded up to the next integer
The i-th EA selected will be the one for which the cumulated measure is closest to Shi without exceeding it.
United Nations Workshop on the 2010 World Programme on Population and Housing Censuses: Census Evaluation and Post Enumeration Surveys, Amman, Jordan, 21-24 November, 2010
Illustration: Selection of Eight EAs with probability Proportional to size
United Nations Workshop on the 2010 World Programme on Population and Housing Censuses: Census Evaluation and Post Enumeration Surveys, Amman, Jordan, 21-24 November, 2010
Sample Allocation – 2009 Kenyan PES