1. © 2007 Thomson, a part of the Thomson Corporation. Thomson, the Star logo, and Atomic Dog are trademarks used herein under license. All rights reserved. Probability Sampling

2. © 2007 Thomson, a part of the Thomson Corporation. Thomson, the Star logo, and Atomic Dog are trademarks used herein under license. All rights reserved. Types of Probability Sampling Designs l Simple random sampling l Stratified sampling l Systematic sampling l Cluster (area) sampling l Multistage sampling

3. © 2007 Thomson, a part of the Thomson Corporation. Thomson, the Star logo, and Atomic Dog are trademarks used herein under license. All rights reserved. Some Definitions l N = the number of cases in the sampling frame l n = the number of cases in the sample l N C n = the number of combinations (subsets) of n from N l f = n/N = the sampling fraction

4. © 2007 Thomson, a part of the Thomson Corporation. Thomson, the Star logo, and Atomic Dog are trademarks used herein under license. All rights reserved. Simple Random Sampling Objective: Select n units out of N such that every N C n 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. © 2007 Thomson, a part of the Thomson Corporation. Thomson, the Star logo, and Atomic Dog are trademarks used herein under license. All rights reserved. Simple Random Sampling l Small service agency. l Client assessment of quality of service. l Get list of clients over past year. l Draw a simple random sample of n/N. Example:

6. © 2007 Thomson, a part of the Thomson Corporation. Thomson, the Star logo, and Atomic Dog are trademarks used herein under license. All rights reserved. Simple Random Sampling List of clients

7. © 2007 Thomson, a part of the Thomson Corporation. Thomson, the Star logo, and Atomic Dog are trademarks used herein under license. All rights reserved. Simple Random Sampling List of clients Random subsample

8. © 2007 Thomson, a part of the Thomson Corporation. Thomson, the Star logo, and Atomic Dog are trademarks used herein under license. All rights reserved. Stratified Random Sampling Sometimes called "proportional" or "quota" random sampling. Objective: Population of N units divided into nonoverlapping strata N 1, N 2, N 3,... N i such that N 1 + N 2 +... + N i = N; then do simple random sample of n/N in each strata.

9. © 2007 Thomson, a part of the Thomson Corporation. Thomson, the Star logo, and Atomic Dog are trademarks used herein under license. All rights reserved. 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. © 2007 Thomson, a part of the Thomson Corporation. Thomson, the Star logo, and Atomic Dog are trademarks used herein under license. All rights reserved. Stratified Random Sampling List of clients

11. © 2007 Thomson, a part of the Thomson Corporation. Thomson, the Star logo, and Atomic Dog are trademarks used herein under license. All rights reserved. Stratified Random Sampling List of clients Strata African-AmericanOthersHispanic-American

12. © 2007 Thomson, a part of the Thomson Corporation. Thomson, the Star logo, and Atomic Dog are trademarks used herein under license. All rights reserved. Stratified Random Sampling List of clients Random subsamples of n/N Strata African-AmericanOthersHispanic-American

13. © 2007 Thomson, a part of the Thomson Corporation. Thomson, the Star logo, and Atomic Dog are trademarks used herein under license. All rights reserved. Proportionate vs. Disproportionate Stratified Random Sampling l Proportionate: If sampling fraction is equal for each stratum l Disproportionate: Unequal sampling fraction in each stratum l Needed to enable better representation of smaller (minority groups)

14. © 2007 Thomson, a part of the Thomson Corporation. Thomson, the Star logo, and Atomic Dog are trademarks used herein under license. All rights reserved. Systematic Random Sampling l Number units in population from 1 to N. l Decide on the n that you want or need. l N/n=k the interval size. l Randomly select a number from 1 to k. l Take every kth unit. Procedure:

15. © 2007 Thomson, a part of the Thomson Corporation. Thomson, the Star logo, and Atomic Dog are trademarks used herein under license. All rights reserved. Systematic Random Sampling l Assumes that the population is randomly ordered. l Advantages: Easy; may be more precise than simple random sample. l Example: The library (ACM) study.

16. © 2007 Thomson, a part of the Thomson Corporation. Thomson, the Star logo, and Atomic Dog are trademarks used herein under license. All rights reserved. Systematic Random Sampling 1265176 2275277 3285378 4295479 5305580 6315681 7325782 8335883 9345984 10356085 11366186 12376287 13386388 14396489 15406590 16416691 17426792 18436893 19446994 20457095 21467196 22477297 23487398 24497499 255075100 N = 100

17. © 2007 Thomson, a part of the Thomson Corporation. Thomson, the Star logo, and Atomic Dog are trademarks used herein under license. All rights reserved. Systematic Random Sampling 1265176 2275277 3285378 4295479 5305580 6315681 7325782 8335883 9345984 10356085 11366186 12376287 13386388 14396489 15406590 16416691 17426792 18436893 19446994 20457095 21467196 22477297 23487398 24497499 255075100 N = 100 Want n = 20

18. © 2007 Thomson, a part of the Thomson Corporation. Thomson, the Star logo, and Atomic Dog are trademarks used herein under license. All rights reserved. Systematic Random Sampling 1265176 2275277 3285378 4295479 5305580 6315681 7325782 8335883 9345984 10356085 11366186 12376287 13386388 14396489 15406590 16416691 17426792 18436893 19446994 20457095 21467196 22477297 23487398 24497499 255075100 N = 100 want n = 20 N/n = 5

19. © 2007 Thomson, a part of the Thomson Corporation. Thomson, the Star logo, and Atomic Dog are trademarks used herein under license. All rights reserved. Systematic Random Sampling 1265176 2275277 3285378 4295479 5305580 6315681 7325782 8335883 9345984 10356085 11366186 12376287 13386388 14396489 15406590 16416691 17426792 18436893 19446994 20457095 21467196 22477297 23487398 24497499 255075100 N = 100 Want n = 20 N/n = 5 Select a random number from 1-5: chose 4

20. © 2007 Thomson, a part of the Thomson Corporation. Thomson, the Star logo, and Atomic Dog are trademarks used herein under license. All rights reserved. Systematic Random Sampling 1265176 2275277 3285378 4295479 5305580 6315681 7325782 8335883 9345984 10356085 11366186 12376287 13386388 14396489 15406590 16416691 17426792 18436893 19446994 20457095 21467196 22477297 23487398 24497499 255075100 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. © 2007 Thomson, a part of the Thomson Corporation. Thomson, the Star logo, and Atomic Dog are trademarks used herein under license. All rights reserved. Cluster (Area) Random Sampling l Divide population into clusters. l Randomly sample clusters. l Measure all units within sampled clusters. Procedure:

22. © 2007 Thomson, a part of the Thomson Corporation. Thomson, the Star logo, and Atomic Dog are trademarks used herein under license. All rights reserved. Cluster (Area) Random Sampling l Advantages: Administratively useful, especially when you have a wide geographic area to cover. l Examples: Randomly sample from city blocks and measure all homes in selected blocks.

23. © 2007 Thomson, a part of the Thomson Corporation. Thomson, the Star logo, and Atomic Dog are trademarks used herein under license. All rights reserved. Multi-Stage Sampling l Cluster (area) random sampling can be multi-stage. l Any combinations of single-stage methods.

24. © 2007 Thomson, a part of the Thomson Corporation. Thomson, the Star logo, and Atomic Dog are trademarks used herein under license. All rights reserved. Multi-Stage Sampling l Select all schools; then sample within schools. l Sample schools; then measure all students. l Sample schools; then sample students. Example: Choosing students from schools