Probability Sampling. Types of Probability Sampling Designs l Simple random sampling l Stratified...
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Transcript of Probability Sampling. Types of Probability Sampling Designs l Simple random sampling l Stratified...
Probability SamplingProbability SamplingProbability SamplingProbability Sampling
Types of Probability Sampling Types of Probability Sampling DesignsDesigns
Types of Probability Sampling Types of Probability Sampling DesignsDesigns
Simple random samplingSimple random sampling Stratified samplingStratified sampling Systematic samplingSystematic sampling Cluster (area) samplingCluster (area) sampling Multistage samplingMultistage sampling
Some DefinitionsSome DefinitionsSome DefinitionsSome Definitions
N = the number of cases in the N = the number of cases in the sampling framesampling frame
n = the number of cases in the samplen = the number of cases in the sample
NNCCnn = the number of combinations = the number of combinations
(subsets) of n from N(subsets) of n from N f = n/N = the sampling fractionf = n/N = the sampling fraction
Simple Random SamplingSimple Random SamplingSimple Random SamplingSimple 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.
Simple Random SamplingSimple Random SamplingSimple Random SamplingSimple Random Sampling
Small service agency.Small service agency. Client assessment of quality of service.Client assessment of quality of service. Get list of clients over past year.Get list of clients over past year. Draw a simple random sample of n/N.Draw a simple random sample of n/N.
Example:Example:Example:Example:
Simple Random SamplingSimple Random SamplingSimple Random SamplingSimple Random Sampling
List of clientsList of clientsList of clientsList of clients
Simple Random SamplingSimple Random SamplingSimple Random SamplingSimple Random Sampling
List of clientsList of clientsList of clientsList of clients
Random subsampleRandom subsampleRandom subsampleRandom subsample
Stratified Random SamplingStratified Random SamplingStratified Random SamplingStratified 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.
Stratified Sampling - Purposes:Stratified Sampling - Purposes:Stratified Sampling - Purposes: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).
Stratified Random SamplingStratified Random SamplingStratified Random SamplingStratified Random Sampling
List of clientsList of clientsList of clientsList of clients
Stratified Random SamplingStratified Random SamplingStratified Random SamplingStratified Random Sampling
List of clientsList of clientsList of clientsList of clients
StrataStrataStrataStrata
African-AmericanAfrican-American OthersOthersHispanic-AmericanHispanic-American
Stratified Random SamplingStratified Random SamplingStratified Random SamplingStratified Random Sampling
List of clientsList of clientsList of clientsList of clients
Random subsamples of n/NRandom subsamples of n/NRandom subsamples of n/NRandom subsamples of n/N
StrataStrataStrataStrata
African-AmericanAfrican-American OthersOthersHispanic-AmericanHispanic-American
Proportionate vs. Disproportionate Stratified Proportionate vs. Disproportionate Stratified Random SamplingRandom Sampling
Proportionate vs. Disproportionate Stratified Proportionate vs. Disproportionate Stratified Random SamplingRandom Sampling
Proportionate: If sampling fraction is Proportionate: If sampling fraction is equal for each stratumequal for each stratum
Disproportionate: Unequal sampling Disproportionate: Unequal sampling fraction in each stratumfraction in each stratum
Needed to enable better representation Needed to enable better representation of smaller (minority groups)of smaller (minority groups)
Systematic Random SamplingSystematic Random SamplingSystematic Random SamplingSystematic Random Sampling
Number units in population from 1 to N.Number units in population from 1 to N. Decide on the n that you want or need.Decide on the n that you want or need. N/n=k the interval size.N/n=k the interval size. Randomly select a number from 1 to k.Randomly select a number from 1 to k. Take every kth unit.Take every kth unit.
Procedure:Procedure:Procedure:Procedure:
Systematic Random SamplingSystematic Random SamplingSystematic Random SamplingSystematic Random Sampling
Assumes that the population is Assumes that the population is randomlyrandomly ordered. ordered.
Advantages: Easy; may be more Advantages: Easy; may be more precise than simple random sample.precise than simple random sample.
Example: The library (ACM) study.Example: The library (ACM) study.
Systematic Random SamplingSystematic Random SamplingSystematic Random SamplingSystematic Random Sampling1 26 51 762 27 52 773 28 53 784 29 54 795 30 55 806 31 56 817 32 57 828 33 58 839 34 59 8410 35 60 8511 36 61 8612 37 62 8713 38 63 8814 39 64 8915 40 65 9016 41 66 9117 42 67 9218 43 68 9319 44 69 9420 45 70 9521 46 71 9622 47 72 9723 48 73 9824 49 74 9925 50 75 100
N = 100N = 100N = 100N = 100
Systematic Random SamplingSystematic Random SamplingSystematic Random SamplingSystematic Random Sampling1 26 51 762 27 52 773 28 53 784 29 54 795 30 55 806 31 56 817 32 57 828 33 58 839 34 59 8410 35 60 8511 36 61 8612 37 62 8713 38 63 8814 39 64 8915 40 65 9016 41 66 9117 42 67 9218 43 68 9319 44 69 9420 45 70 9521 46 71 9622 47 72 9723 48 73 9824 49 74 9925 50 75 100
N = 100N = 100N = 100N = 100
Want n = 20Want n = 20Want n = 20Want n = 20
Systematic Random SamplingSystematic Random SamplingSystematic Random SamplingSystematic Random Sampling1 26 51 762 27 52 773 28 53 784 29 54 795 30 55 806 31 56 817 32 57 828 33 58 839 34 59 8410 35 60 8511 36 61 8612 37 62 8713 38 63 8814 39 64 8915 40 65 9016 41 66 9117 42 67 9218 43 68 9319 44 69 9420 45 70 9521 46 71 9622 47 72 9723 48 73 9824 49 74 9925 50 75 100
N = 100N = 100N = 100N = 100
want n = 20want n = 20want n = 20want n = 20
N/n = 5N/n = 5N/n = 5N/n = 5
Systematic Random SamplingSystematic Random SamplingSystematic Random SamplingSystematic Random Sampling1 26 51 762 27 52 773 28 53 784 29 54 795 30 55 806 31 56 817 32 57 828 33 58 839 34 59 8410 35 60 8511 36 61 8612 37 62 8713 38 63 8814 39 64 8915 40 65 9016 41 66 9117 42 67 9218 43 68 9319 44 69 9420 45 70 9521 46 71 9622 47 72 9723 48 73 9824 49 74 9925 50 75 100
N = 100N = 100N = 100N = 100
Want n = 20Want n = 20Want n = 20Want n = 20
N/n = 5N/n = 5N/n = 5N/n = 5
Select a random number from 1-5: Select a random number from 1-5: chose 4chose 4
Select a random number from 1-5: Select a random number from 1-5: chose 4chose 4
Systematic Random SamplingSystematic Random SamplingSystematic Random SamplingSystematic Random Sampling1 26 51 762 27 52 773 28 53 784 29 54 795 30 55 806 31 56 817 32 57 828 33 58 839 34 59 8410 35 60 8511 36 61 8612 37 62 8713 38 63 8814 39 64 8915 40 65 9016 41 66 9117 42 67 9218 43 68 9319 44 69 9420 45 70 9521 46 71 9622 47 72 9723 48 73 9824 49 74 9925 50 75 100
N = 100N = 100N = 100N = 100
Want n = 20Want n = 20Want n = 20Want n = 20
N/n = 5N/n = 5N/n = 5N/n = 5
Select a random number from 1-5: Select a random number from 1-5: chose 4chose 4
Select a random number from 1-5: Select a random number from 1-5: chose 4chose 4
Start with #4 and take every 5th unitStart with #4 and take every 5th unitStart with #4 and take every 5th unitStart with #4 and take every 5th unit
Cluster (Area) Random SamplingCluster (Area) Random SamplingCluster (Area) Random SamplingCluster (Area) Random Sampling
Divide population into clusters.Divide population into clusters. Randomly sample clusters.Randomly sample clusters. Measure all units within sampled Measure all units within sampled
clusters.clusters.
Procedure:Procedure:Procedure:Procedure:
Cluster (Area) Random SamplingCluster (Area) Random SamplingCluster (Area) Random SamplingCluster (Area) Random Sampling
Advantages: Administratively useful, Advantages: Administratively useful, especially when you have a wide especially when you have a wide geographic area to cover.geographic area to cover.
Examples: Randomly sample from city Examples: Randomly sample from city blocks and measure all homes in blocks and measure all homes in selected blocks.selected blocks.
Multi-Stage SamplingMulti-Stage SamplingMulti-Stage SamplingMulti-Stage Sampling
Cluster (area) random sampling can be Cluster (area) random sampling can be multi-stage.multi-stage.
Any combinations of single-stage Any combinations of single-stage methods.methods.
Multi-Stage SamplingMulti-Stage SamplingMulti-Stage SamplingMulti-Stage Sampling
Select all schools; then Select all schools; then samplesample within within schools.schools.
Sample schools; then measure Sample schools; then measure allall students.students.
Sample schools; then Sample schools; then samplesample students. students.
Example: Choosing students from schoolsExample: Choosing students from schoolsExample: Choosing students from schoolsExample: Choosing students from schools
