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