Handout3-W09

Handout3-W09 - STAT 454/854 Winter 2009 Handout #3...

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STAT 454/854 Winter 2009 Handout #3 Single-stage Cluster Sampling (1) Single-stage cluster sampling with clusters of equal sizes We have M i = M , i = 1 , ··· ,N and K = NM . The population mean is μ y = N - 1 N i =1 μ i , where μ i = M - 1 M j =1 y ij . Under single-stage cluster sampling with clus- ters selected by SRSWOR, an unbiased estimator of μ y is given by ¯ y = n - 1 n i =1 μ i , with theoretical variance V y ) = ± 1 - n N ² σ 2 M n , where σ 2 M = ( N - 1) - 1 N i =1 ( μ i - μ y ) 2 . An unbiased variance estimator is given by v y ) = ± 1 - n N ² s 2 M n , where s 2 M = ( n - 1) - 1 i s ( μ i - ¯ y ) 2 . (2) Intra-cluster correlation coefficient Suppose that we randomly select a cluster from the population, and then randomly select two elements without replacement in the selected cluster, and let z 1 and z 2 be the respective y -value of the two selected elements. Define the intra-cluster correlation coefficient as ρ = Cov ( z 1 ,z 2 ) / { V ( z 1
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This note was uploaded on 11/23/2010 for the course STAT 454 taught by Professor Da during the Fall '09 term at Waterloo.

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Handout3-W09 - STAT 454/854 Winter 2009 Handout #3...

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