Sampling-big picture

1
Sampling-big picture

• Want to estimate a characteristic of population
  (population parameter).
• Estimate a corresponding sample statistic
• Sample must be representative of population on
  variable(s) of interest
• Sampling error is probability of getting an
  un-representative sample by chance
• Sample may be biased if not drawn properly

2
Sampling

• Always define study population first
• Use element/unit/extent/time for complete
  definition
• element - who is interviewed
• sampling unit - basic unit containing elements
• extent - limit population (often spatially)
• time - fix population in time

3
Exampleselement, unit, extent, time

• Adults 12 and older
• in vehicles
• entering Yogi Bear Park
• between July 1 and Aug 31, 1998

• Teenagers (13-18)
• in households
• in Lansing, MI
• during May 1996

4
Steps in Sampling

• Define study population
• Specify sampling frame and unit
• Specify sampling method
• Determine sample size
• Specify sampling plan
• Choose sample

5
Sampling methods

• Probability vs non-probability (Does each element
  of population have known chance of being
  selected?)
• Simple random sample or Systematic sample
  (equal probability) (choose
  every nth element)
• Stratified vs Cluster
  Samplegroup elements and sample from groups
• stratified choose some from every group
• cluster only some groups sampled

6
Non-probability sampling

• Convenience
• Judgement
• Purposive
• Quota
• Snowball

7
Prob or Non-prob Sample?

• Project/generalize results to population - prob
• Quantitative estimate of sampling error - prob
• Accuracy needed relative magnitude of sampling
  vs other kinds of errors
• Homo- or hetero-geneous population
• Overall Costs vs benefits

8
Stratify vs Cluster

• Stratify to ensure enough samples from subgroups
  to lower sampling error
• Cluster primarily to reduce costs of gathering
  the data
• Form homogeneous groups when stratifying,
  heterogeneous when clustering
• Proportionate vs disproportionate sample
• Stratification variables

9
Sample size

• Based on four factors
• Cost/budget
• Accuracy desired
• variance in popln on variable of interest
• subgroup analysis planned
• Formula n Z2 ?2 / e 2
• n sample size
• Z indicates confidence level (95 1.96)
• ? standard deviation of variable in population
• e sampling error

10
Sampling error formula

• n Z2 ?2 / e 2
• 1. Solve for e to express error as a function of
  sample size, confidence level, and variance
• e (Z ?) / SQRT ( n )
• 2. For binomial, ? sqrt (p(1-p)) , where p
  is proportion for yes in
• the population
• Generate numbers in binomial sampling error
  table as
• 1.96 sqrt( p (1-p)) / sqrt (n)

11
Sampling errors for binomial (95 confidence
interval)percent distribution in population
12
Computing 95 confidence interval

• N 100 , sample mean 46, use p 50/50,
• sampling error from table 10
• 95 CI is 46 or - 10 (36, 56)
• N1,000 sample mean 22
• sampling error from table 2.5
• 95 CI is 22 or - 2.5 (19.5, 24.5)