Chapter 5 Stratified Random Sampling

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## Chapter 5 Stratified Random Sampling

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**Chapter 5Stratified Random Sampling**• Advantages of stratified random sampling • How to select stratified random sample • Estimating population mean and total • Determining sample size, allocation • Estimating population proportion; sample size and allocation • Optimal rule for choosing strata**Stratified Random Sampling**• 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.**Warmup**You are doing a project to study grade inflation in the STEM disciplines. A quick internet search shows that average GPA differs by STEM major. In addition, overall GPA differs by school, so you don’t want to limit your sample to “convenient” schools.**Warmup**(cont.) • Data from the National Center for Education Statistics results in the following percentages of majors among STEM disciplines: • Computer Science24% • Engineering 21% • Bio/Life Sciences 17% • Math/Stat 15% • Technology 12% • Chemistry 7% • Physics 4% • Approximately 15 million students are in public colleges and 5 million are in private colleges. • Suppose you would like to use a sample size of n = 1,000 students.**Stratified Random Sampling**• Often-used option b/c … • May produce smaller BOE than SRS of same size • Cost per observation may be reduced • Obtain estimates of population parameters for subgroups • Useful when the population is heterogeneous and it is possible to establish strata which are reasonably homogeneous within each stratum**Chapter 5Stratified Random Sampling**Improved Sampling Designs with Auxiliary Information Chapter 5 Stratified Random Sampling Chapter 6 Ratio and Regression Estimators**Warmup**(cont.) • Selecting the stratified random sample. • Recall: • approximately 15 million students are in public colleges and 5 million are in private colleges. • Suppose you would like to use a sample size of n = 1,000 students.**Stratified Random Sampling: BOEfor Mean and Total , t**distribution • When stratum sample sizes are small, can use t dist.**Compare BOE in Stratified Random Sample and SRS (worksheet**cont.) Strat. random sample has more precision**5.5 Allocation of the Sample**• Objective: obtain estimators with small variance at lowest cost. • Allocation affected by 3 factors: • Total number of elements in each stratum • Variability in each stratum • Cost per observation in each stratum**5.5 Allocation of the Sample: Proportional Allocation**• 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**Directly proportional to**stratum size and stratum variability Inversely proportional to stratum cost/obs