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STRATIFIED SAMPLING

STRATIFIED SAMPLING. STRATIFIED SAMPLING. 1. Stratification : The elements in the population are divided into layers/groups/ strata based on their values on one/several auxiliary variables. The strata must be non-overlapping and together constitute the whole population.

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STRATIFIED SAMPLING

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  1. STRATIFIED SAMPLING

  2. STRATIFIED SAMPLING 1.Stratification: The elements in the population are divided into layers/groups/ strata based on their values on one/several auxiliary variables. The strata must be non-overlapping and together constitute the whole population. 2.Sampling within strata:Samples are selected independently from each stratum. Different selection methods can be used in different strata.

  3. Ex. Stratification of individuals by age group

  4. Ex. Regional stratification Stratum 1: Northern Sweden Stratum 2: Mid-Sweden Stratum 3: Southern Sweden

  5. Ex. Stratification of individuals by age group and region

  6. WHY STRATIFY? • Gain in precision.If the strata are more homogenous with respect to the study variable(s) than the population as a whole, the precision of the estimates will improve. • Strata = domains of study. Precision requirements of estimates for certain subpopulations/domains can be assured by using domains as strata.

  7. WHY STRATIFY?, cont’d • Practical reasons. For instance nonresponse rates, method of measurement and the quality of auxiliary information may differ between subpopulations, and can be efficiently handled by stratification. • Administrative reasons. The survey organization may be divided into geographical districts that makes it natural to let each district be a stratum.

  8. ESTIMATION Assume a population divided into H strata of sizes . Independently, a sample of size nh is selected from each stratum. = y-value for element j in stratum h = population total for stratum h = sample mean for stratum h

  9. ESTIMATION OF A TOTAL Assume: SRS within all strata.

  10. ESTIMATION OF A TOTAL Assume: SRS within all strata. In general: What is the variance of this estimator?

  11. VARIANCE OF THE ESTIMATOR OF A TOTAL Principle: Add the variances of the estimators for each stratum. A legitimate approach since samples are selected independently from each stratum. Remember: if X, Y are independent random variables.

  12. VARIANCE OF THE ESTIMATOR OF A TOTAL, cont’d One term per stratum Result: Finite population correction (one per stratum!) where

  13. ESTIMATION OF THE VARIANCE OF THE ESTIMATOR OF A TOTAL Principle: Estimate what’s unknown in the variance formula. where

  14. ESTIMATORS FOR A MEAN Note: Start from the estimators for a total!

  15. ESTIMATORS FOR A MEAN, cont’d Note: Start from the estimators for a total!

  16. ESTIMATORS FOR A PROPORTION Note: Like the estimators for a mean, only with y a 0/1-variable!

  17. IMPORTANT DESIGN CHOICES IN STRATIFIED SAMPLING • Stratification variable(s) • Number of strata • Sample size in each stratum (allocation) • Sampling design in each stratum • Estimator for each stratum

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