1. Probability Sampling

2. Types of Probability Sampling Designs
Simple random sampling
Stratified sampling
Systematic sampling
Cluster (area) sampling
Multistage sampling

3. Some Definitions N = the number of cases in the sampling frame
n = the number of cases in the sample
NCn = the number of combinations (subsets) of n from N
f = n/N = the sampling fraction

4. Simple Random Sampling
Objective: Select n units out of N such that every NCn has an equal chance.
Procedure: Use table of random numbers, computer random number generator or mechanical device.
Can sample with or without replacement.
f=n/N is the sampling fraction.

5. Simple Random Sampling
Example:
Small service agency.
Client assessment of quality of service.
Get list of clients over past year.
Draw a simple random sample of n/N.

6. Simple Random Sampling
List of clients

7. Simple Random Sampling
List of clients
Random subsample

8. Stratified Random Sampling
Sometimes called "proportional" or "quota" random sampling.
Objective: Population of N units divided into nonoverlapping strata N1, N2, N3, ... Ni such that N1 + N Ni = N; then do simple random sample of n/N in each strata.

9. Stratified Sampling - Purposes:
To insure representation of each strata, oversample smaller population groups.
Administrative convenience -- field offices.
Sampling problems may differ in each strata.
Increase precision (lower variance) if strata are homogeneous within (like blocking).

10. Stratified Random Sampling
List of clients

11. Stratified Random Sampling
List of clients
African-American
Hispanic-American
Others
Strata

12. Stratified Random Sampling
List of clients
African-American
Hispanic-American
Others
Strata
Random subsamples of n/N

13. Proportionate vs. Disproportionate Stratified Random Sampling
Proportionate: If sampling fraction is equal for each stratum
Disproportionate: Unequal sampling fraction in each stratum
Needed to enable better representation of smaller (minority groups)

14. Systematic Random Sampling
Procedure:
Number units in population from 1 to N.
Decide on the n that you want or need.
N/n=k the interval size.
Randomly select a number from 1 to k.
Take every kth unit.

15. Systematic Random Sampling
Assumes that the population is randomly ordered.
Advantages: Easy; may be more precise than simple random sample.
Example: The library (ACM) study.

16. Systematic Random Sampling
N = 100

17. Systematic Random Sampling
N = 100
Want n = 20

18. Systematic Random Sampling
N = 100
want n = 20
N/n = 5

19. Systematic Random Sampling
N = 100
Want n = 20
N/n = 5
Select a random number from 1-5: chose 4

20. Systematic Random Sampling
N = 100
Want n = 20
N/n = 5
Select a random number from 1-5: chose 4
Start with #4 and take every 5th unit

21. Cluster (Area) Random Sampling
Procedure:
Divide population into clusters.
Randomly sample clusters.
Measure all units within sampled clusters.

22. Cluster (Area) Random Sampling
Advantages: Administratively useful, especially when you have a wide geographic area to cover.
Examples: Randomly sample from city blocks and measure all homes in selected blocks.

23. Multi-Stage Sampling
Cluster (area) random sampling can be multi-stage.
Any combinations of single-stage methods.

24. Example: Choosing students from schools
Multi-Stage Sampling
Example: Choosing students from schools
Select all schools; then sample within schools.
Sample schools; then measure all students.
Sample schools; then sample students.