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Probability Sampling

Probability Sampling. Types of Probability Sampling Designs. Simple random sampling Stratified sampling Systematic sampling Cluster (area) sampling Multistage sampling. Some Definitions. N = the number of cases in the sampling frame n = the number of cases in the sample

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Probability Sampling

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  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 + N2 + ... + 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 1 26 51 76 2 27 52 77 3 28 53 78 4 29 54 79 5 30 55 80 6 31 56 81 7 32 57 82 8 33 58 83 9 34 59 84 10 35 60 85 11 36 61 86 12 37 62 87 13 38 63 88 14 39 64 89 15 40 65 90 16 41 66 91 17 42 67 92 18 43 68 93 19 44 69 94 20 45 70 95 21 46 71 96 22 47 72 97 23 48 73 98 24 49 74 99 25 50 75 100 N = 100

  17. Systematic Random Sampling 1 26 51 76 2 27 52 77 3 28 53 78 4 29 54 79 5 30 55 80 6 31 56 81 7 32 57 82 8 33 58 83 9 34 59 84 10 35 60 85 11 36 61 86 12 37 62 87 13 38 63 88 14 39 64 89 15 40 65 90 16 41 66 91 17 42 67 92 18 43 68 93 19 44 69 94 20 45 70 95 21 46 71 96 22 47 72 97 23 48 73 98 24 49 74 99 25 50 75 100 N = 100 Want n = 20

  18. Systematic Random Sampling 1 26 51 76 2 27 52 77 3 28 53 78 4 29 54 79 5 30 55 80 6 31 56 81 7 32 57 82 8 33 58 83 9 34 59 84 10 35 60 85 11 36 61 86 12 37 62 87 13 38 63 88 14 39 64 89 15 40 65 90 16 41 66 91 17 42 67 92 18 43 68 93 19 44 69 94 20 45 70 95 21 46 71 96 22 47 72 97 23 48 73 98 24 49 74 99 25 50 75 100 N = 100 want n = 20 N/n = 5

  19. Systematic Random Sampling 1 26 51 76 2 27 52 77 3 28 53 78 4 29 54 79 5 30 55 80 6 31 56 81 7 32 57 82 8 33 58 83 9 34 59 84 10 35 60 85 11 36 61 86 12 37 62 87 13 38 63 88 14 39 64 89 15 40 65 90 16 41 66 91 17 42 67 92 18 43 68 93 19 44 69 94 20 45 70 95 21 46 71 96 22 47 72 97 23 48 73 98 24 49 74 99 25 50 75 100 N = 100 Want n = 20 N/n = 5 Select a random number from 1-5: chose 4

  20. Systematic Random Sampling 1 26 51 76 2 27 52 77 3 28 53 78 429 54 79 5 30 55 80 6 31 56 81 7 32 57 82 8 33 58 83 934 59 84 10 35 60 85 11 36 61 86 12 37 62 87 13 38 63 88 1439 64 89 15 40 65 90 16 41 66 91 17 42 67 92 18 43 68 93 1944 69 94 20 45 70 95 21 46 71 96 22 47 72 97 23 48 73 98 244974 99 25 50 75 100 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. 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.

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