EMR 6500: Survey Research
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Transcript of EMR 6500: Survey Research
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EMR 6500:Survey Research
Dr. Chris L. S. CorynKristin A. Hobson
Spring 2013
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Stratified Random Sampling
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Stratified Random Sampling• A stratified random sample is one in
which some form of random sampling is applied in each of a set of separate groups formed from all entries on a sampling frame from which a sample is to be drawn
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Strata• In stratified random sampling, strata
are nonoverlapping groups separating population elements
• By strategically forming these groups, stratification becomes a feature of the sample design that can improve the statistical quality of survey estimates
Discrete
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Notation for Stratified Random Sampling
Need at least 2
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Allocation to Strata• Deciding how a stratified sample will
be distributed among all strata is called stratum allocation
• The most appropriate allocation method depends on how the stratification will be used
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Equal Allocation• If the main purpose of stratification is to
control subgroup sample sizes for important population subgroups, stratum sample sizes should be sufficient to meet precision requirements for subgroup analysis
• An important part of the analysis is to produce comparisons among all subgroup strata
• In this instance, equal allocation (i.e., equal sample sizes) would be appropriate
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Proportionate Allocation• Proportionate allocation is a prudent choice
when the main focus of the analysis is characteristics of several subgroups or the population as a whole and where the appropriate allocations for these analyses are discrepant
• Proportionate allocation involves applying the same sampling rate to all strata, thus implying that the percent distribution of the selected sample among strata is identical to the corresponding distribution for the population can miss some strata
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Optimum Allocation• Optimum allocation, in which the most
cost-efficient stratum sample sizes are sought, can lead to estimates of overall population characteristics that are statistically superior to those from proportionate allocations
• When all stratum unit costs are the same, the stratum sampling rates that yield the most precise sample estimates are proportional to the stratum-specific standard deviations (Neyman allocation)
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Estimation of a Population Mean and Total
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Estimate of Population MeanSt stratified
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Example for a Population Mean
N n M SDTown A 155 20 33.90 5.95Town B 62 8 25.12 15.25Rural 93 12 19.00 9.36
93
precision
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Example for a Population Mean
.871 same size samples
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Estimate of Population Total
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Example for Population Total
310 total of means
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Selecting the Sample Size for Estimating Population Means and Totals
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Sample Size for Estimating Population Means and Totals
A allocation method
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Example for a Population Mean
1/3 Equal allocation
Square root
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Example for a Population Mean
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Example for a Population Mean
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Example for a Population Mean
Need a total sample size of 57, each 19
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Neyman AllocationOptimum – smallest allocation
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Neyman Allocation
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Neyman Allocation
Determine sampling fractions
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Neyman Allocation
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Neyman Allocation
summation
Changed slightly from previous ex
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Proportionate Allocation
NOT N-SQUARED
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Proportionate Allocation
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Proportionate Allocation
76 QUITE DIFFERENT ALLOCATION FROM 57
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Proportionate AllocationVERY DIFFERENT ALLOCATION,ADEQUATE SAMPLES FROM EACH SUBGROUP
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Comparison of Allocation Methods
Proportionate
Neyman
General framework