Chapter 5 Stratified Random Sampling n Advantages of stratified random sampling n How to select stratified random sample n Estimating population mean and.

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Presentation transcript:

Chapter 5 Stratified Random Sampling n Advantages of stratified random sampling n How to select stratified random sample n Estimating population mean and total n Determining sample size, allocation n Estimating population proportion; sample size and allocation n Optimal rule for choosing strata

Stratified Random Sampling n The ultimate function of stratification is to organize the population into homogeneous subsets and to select a SRS of the appropriate size from each stratum.

Stratified Random Sampling n Often-used option –May produce smaller BOE than SRS of same size –Cost per observation may be reduced –Obtain estimates of population parameters for subgroups n Useful when the population is heterogeneous and it is possible to establish strata which are reasonably homogeneous within each stratum

Chapter 5 Stratified Random Sampling Improved Sampling Designs with Auxiliary Information Chapter 6 Ratio and Regression Estimators Stratified Random Sampling

Stratified Random Sampling: Notation

Stratified Random Sampling

Stratified Random Sampling: Estimate of Mean 

Stratified Random Sampling: Estimate of Mean , BOE

Stratified Random Sampling: Estimate of Population Total 

Stratified Random Sampling: BOE for Mean  and Total , t distribution n When stratum sample sizes are small, can use t dist.

Degrees of Freedom(worksheet cont.)

Compare BOE in Stratified Random Sample and SRS (worksheet cont.) Strat. random sample has more precision

Approx. Sample Size to Estimate 

Approx. Sample Size to Estimate 

Summary: Approx. Sample Size to Estimate , 

Example: Sample Size to Estimate  (worksheet cont.)

Example: Sample Size to Estimate  (worksheet cont.)

5.5 Allocation of the Sample n Objective: obtain estimators with small variance at lowest cost. n Allocation affected by 3 factors: 1.Total number of elements in each stratum 2.Variability in each stratum 3.Cost per observation in each stratum

5.5 Allocation of the Sample: Proportional Allocation n If don’t have variability and cost information for the strata, can use proportional allocation. In general this is not the optimum choice for the stratum sample sizes.

Directly proportional to stratum size and stratum variability

n Worksheet 11

Directly proportional to stratum size and stratum variability Inversely proportional to stratum cost/obs

n Worksheet 12