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EMR 6500: Survey Research

EMR 6500: Survey Research. Dr. Chris L. S. Coryn Kristin A. Hobson Spring 2013. Stratified Random Sampling. Stratified Random Sampling.

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EMR 6500: Survey Research

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  1. EMR 6500:Survey Research Dr. Chris L. S. Coryn Kristin A. Hobson Spring 2013

  2. Stratified Random Sampling

  3. Stratified Random Sampling Astratified 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

  4. Strata Discrete 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

  5. Notation for Stratified Random Sampling Need at least 2

  6. 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

  7. 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

  8. 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

  9. 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)

  10. Estimation of a Population Mean and Total

  11. Estimate of Population Mean St stratified

  12. Example for a Population Mean 93 precision

  13. Example for a Population Mean .871 same size samples

  14. Estimate of Population Total

  15. Example for Population Total 310 total of means

  16. Selecting the Sample Size for Estimating Population Means and Totals

  17. Sample Size for Estimating Population Means and Totals A allocation method

  18. Example for a Population Mean Square root 1/3 Equal allocation

  19. Example for a Population Mean

  20. Example for a Population Mean

  21. Example for a Population Mean Need a total sample size of 57, each 19

  22. Neyman Allocation Optimum – smallest allocation

  23. Neyman Allocation

  24. Neyman Allocation Determine sampling fractions

  25. Neyman Allocation

  26. Neyman Allocation summation Changed slightly from previous ex

  27. Proportionate Allocation NOT N-SQUARED

  28. Proportionate Allocation

  29. Proportionate Allocation 76 QUITE DIFFERENT ALLOCATION FROM 57

  30. Proportionate Allocation VERY DIFFERENT ALLOCATION, ADEQUATE SAMPLES FROM EACH SUBGROUP

  31. Comparison of Allocation Methods Proportionate Neyman General framework

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