Post on 22-Feb-2016
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EMR 6500:Survey Research
Dr. Chris L. S. CorynKristin A. Hobson
Spring 2013
Stratified Random Sampling
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
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
Notation for Stratified Random Sampling
Need at least 2
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
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
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
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)
Estimation of a Population Mean and Total
Estimate of Population MeanSt stratified
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
Example for a Population Mean
.871 same size samples
Estimate of Population Total
Example for Population Total
310 total of means
Selecting the Sample Size for Estimating Population Means and Totals
Sample Size for Estimating Population Means and Totals
A allocation method
Example for a Population Mean
1/3 Equal allocation
Square root
Example for a Population Mean
Example for a Population Mean
Example for a Population Mean
Need a total sample size of 57, each 19
Neyman AllocationOptimum – smallest allocation
Neyman Allocation
Neyman Allocation
Determine sampling fractions
Neyman Allocation
Neyman Allocation
summation
Changed slightly from previous ex
Proportionate Allocation
NOT N-SQUARED
Proportionate Allocation
Proportionate Allocation
76 QUITE DIFFERENT ALLOCATION FROM 57
Proportionate AllocationVERY DIFFERENT ALLOCATION,ADEQUATE SAMPLES FROM EACH SUBGROUP
Comparison of Allocation Methods
Proportionate
Neyman
General framework