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. Examples element, 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. Stratified vs Cluster Sample group elements and sample from groups
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 Sample group 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 Proportionate vs disproportionate sample
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 Formula: n= Z2 2 / e 2 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)
N=1,000 sample mean =22%
sampling error from table = 2.5%
95% CI is 22% + or - 2.5% = (19.5, 24.5)