Sampling Frames and Sample Design Pres. 5

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Sampling Frames andSample DesignPres. 5
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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 level
• Margin of error

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Sample Frames Sample Design

• Frames Material from which a sample is drawn
• Each unit to be included in the universe
• There should be no duplicates
• Each unit should be well defined and
  distinguishable from other units (it should be
  unique)
• Should be updated

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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

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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.

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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

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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

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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

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Common problems with EAs

• Incomplete coverage
• Inadequate maps
• Poor measures of size or lack of them

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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

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Sample Size

• Sample size depends on estimate requirements
• Geographic level (national, province,
  urban/rural)
• Demographic (sex, age)
• Reliability
• Confidence level

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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)

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Sample Size (contd.)

• To estimate sample size in the case of
  proportions, the following formula can be used

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Sample size (contd.)

• From that it is deduced

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Sample Size (contd.)

• Example
• To estimate percentage of households omitted in
  the census (expected about 5) confidence
  interval at 95 (t1.96) for a margin of error of
  2
• The sample size works out to be

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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

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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

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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

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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
•  ShiAh (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.

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Illustration Selection of Eight EAs with
probability Proportional to size
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Sample Allocation 2009 Kenyan PES
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