Introduction to Survey Sampling

1
Introduction to Survey Sampling

• Linda Owens
• Survey Research Laboratory
• University of Illinois

2
Why Sample?

• Complete enumeration often impossible
• Greater speed, scope, accuracy
• Provide statistical data on wide range of
  subjects
• Classical statistical inference based on
  assumption of random sample

3
Developing and Evaluating Sample Designs

• How good must the sample be?
• Use of biased samples for screening

4
Defining the Target Population

• What is the unit?
• Individuals or households, etc.
• Geography
• Age
• Other demographic variables

5
Defining the Target Population (cont.)

• Sampling Frame
• Source from which sample will be drawn
• Examples
• Lists
• Phone numbers
• Maps
• Be aware of deficiencies

6
Simple and Pseudo-Simple Random Sampling

• Probability samplesmeasurable chance of
  selection
• Simple random sample
• p of selection equal for all elements
• sampling done in one stage
• Random numbers and their use
• random ? haphazard
• random well-designed probability mechanism

7
Simple and Pseudo-Simple Random Sampling (cont.)

• Random number tables
• Systematic Sampling
• How?
• calculate sampling interval
• pick random start
• take every ith case
• length measures
• periodicity

8
Stratified Sampling

• Divide population into subgroups
• Sample from each subgroup
• Need population totals for each stratum
• Major use is comparison of subgroups
• Homogeneous subgroups

9
Stratified Sampling (cont.)

• Poor uses of stratification
• Quota samples
• Make up for poor response in one stratum
• Post-stratification
• Weights

10
Cluster Sampling

• Typically used in face to face surveys
• Sample population elements that are in close
  proximity
• Reasons for cluster sampling
• Reduction in cost
• No satisfactory sample frame available
• Clusters small enough to provide savings

11
Multistage Samples

• Several stages of selection
• Area sampling
• face to face
• based on geography
• Selection of PSUs (primary sampling units)
• problems with random selection
• cant control sample size
• varying PSU sizes increase sampling variance

12
Multistage Samples

• Sampling with probabilities proportionate to size
• Sampling PPS at several stages

13
Random Sample of PSU's County Population
Sample Size 1 1000 2 5000 x
37 3 1500 4 9000 5 7500 6 15000
x 112 7 3500 8 6000 9 7400 10 500
x 4 11 35000 12 4400 13 8600 14 2400
x 18 15 9500 16 12500 17 65000
18 14700 x 110 19 21500 20 38000 Total
Population 268000 281 Select 5
PSU's Sample Size 500 Sample Interval
1 in 536 Sample Rate w/i each selected
county1/134 (1/41/1341/536)
Example
14
Example
15
How Big Should the Sample Be?

• Depends on variation in subject of interest
• Sample size not dependent on population size
• Formula for simple random samples
• based on confidence interval of proportion
• precisionCI(pq/n)1/2
• e.g. .051.96((.5.5)/n))1/2

16
How Big Should the Sample Be (cont.)?

• Finite population correction (1-n/N)
• Design effects
• ratio of variance of a design to variance of SRS
• Analysis of subgroups
• Increase size to accommodate non-response
• Budget constraints

17
Sampling Variance

• What are sampling variances?
• Repeated samples
• Variance between values of statistics observed on
  separate samples
• Sampling method affects size of variance
• Many software packages underestimate
• Wesvar, Sudaan, Stata can estimate