STAT 344 Chapter Notes - Chapter unit 3 summary: Simple Random Sample, Bias Of An Estimator
6 Feb 2018
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Strati ed sampling refers to partitioning the population into h mutually exclusive and exhaustive subsets or strata. Partitioning a population according to geographic regions would be the poster-child for strati cation. In the h-th stratum, a simple random sample of nh out of nh stratum members is drawn. + nh of the n = n1 + . We think about combining what we learn from each stratum to draw inference about the population as a whole, e. g. , we want to estimate yp, the population mean of y . Since each sample stratum mean ysh estimates the corresponding population stratum mean. N (cid:19) ysh is a sensible estimator of yp. Going beyond intuition, we can think about the sampling distribution of ystr. We can verify we have an unbiased estimator, that is e( ystr) = yp. And, upon noting that the stratum-speci c means are reasonably assumed to be independent of one another, we can derive:
