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Unformatted text preview: Stratified Random Sampling Scheaffer et al. in Chapter 5 of their book considered the following case study as an application of stratified sampling. An important problem of national concern involves the estimation of the health care cost. These costs are studied by government agencies and private sectors alike. Government need estimates of these costs for policy decisions, and business sector needs them for business decisions, such as rates for insurance policies. Shuster and Scheaffer (1984) considered a method of estimating hospital costs for treatment of kidney stones in white adult males. In their work, these authors considered two regions of the United States, the Carolinas and the Rocky Mountain states. A sample of n 1 = 363 kidney stone patients in the Carolinas had an average cost for first hospitalization of $ 1350; a sample of n 2 = 258 kidney stone patients in the Rockies had an average cost for first hospitalization of $ 1150. Can we estimate the total annual hospitalization costs for this disease for both regions combined? Example 1: Estimating the assets of a failed bank The Federal Deposit Insurance Corporation (FDIC) supervises banks, and insures de- posits at member banks up to a specified limit. When a bank fails, the FDIC acquires the assets from that bank to pay the insured depositors. Valuing the assets is time- consuming, so the FDIC selects a sample of the assets in order to estimate total amount may be recovered from the failed institutions. These assets fall into several categories: (1) consumer loans, (2) commercial loans, (3) securities, (4) real estate mortgages, (5) other owned real estate, (6) other assets, and (7) net investments in subsidiaries. An SRS of assets may result in an imprecise estimate of the total amount recovered. Con- sumer loans tend to be more in number but much smaller on average than assets in other classes, so the sample variance can be very large. Moreover, an SRS may not contain any assets from one or more of the asset types; if category (2) assets tend to have the most monetary value (but less in numbers) and the sample has no assets from category (2), that sample may result in an estimate of total assets that is too small. It would be desirable to have a method for sampling that prevents samples we know would produce bad estimates, and that increases the precision of estimators. Stratified sampling can accomplish these goals. Why Stratified Sampling? The purpose of sample survey design is to maximize the amount of information for a given cost. Simple random sampling, the basic sampling design, often provides good estimates of population quantities at low cost. However this design may be less effective if the population is large and heterogeneous. In this case, stratified random sampling may be more effective....
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- Spring '11