Sample Survey Methods
Sample Survey Methods STAT 422
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This 2 page Class Notes was uploaded by Mr. Alex Berge on Friday October 23, 2015. The Class Notes belongs to STAT 422 at University of Idaho taught by Staff in Fall. Since its upload, it has received 15 views. For similar materials see /class/227943/stat-422-university-of-idaho in Statistics at University of Idaho.
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Date Created: 10/23/15
Twostage cluster sampling unbiased estimation of a population mean and total Twostage cluster sampling In this chapter we examine two stage cluster sampling7 a very simple kind of multi stage sampling ln real life surveys7 it is common to have several levels of sampling7 including use of strati cation and ratio estimators Here we will consider two stage cluster sampling where a simple random sample of clusters is taken7 then a simple random sample of elements in the selected clusters is taken One example would be to estimate the proportion of US college students who like Korean food by taking a SRS of Us colleges7 then taking a SRS of students in each selected college Notation The extra stage of sampling here gives us notation that is slightly changed from that used for single stage cluster sampling N the number of clusters in the population 71 the number of clusters selected in a SRS Ml the number of elements in cluster 239 ml the number of elements selected in a SRS from cluster 239 M 2 M1 the number of elements in the population i1 MN the average cluster size for the population yij the jth observation in the sample from the 2th cluster 7 i yij the sample mean for the 2th cluster 2 F1 Unbiased estimation of the population mean M In single stage V L cluster sampling the unbiased estimator of 739 was Z yi where the yi term i was the total of observations in the 2th cluster We are now sampling from each cluster7 so we do not know these totals However7 we can estimate the cluster total by multiplying the cluster average by the number of elements in the cluster We can divide by M to estimate M Then we have N r r N 7 A N 7 1 i1 l m 1 yi 1s estlmated by m 1 MZyi7 so u m E Miyl T and the estimated variance is Emmi 7 Mg 2 1w 7 a 5127 l1 1 and s 71 n In the variance estimator7 5127 measures variation between clusters7 and 5 measures variation within cluster 239 We can obtain an unbiased estimator of 739 and a variance estimator by multiplying the above expressions by M Ai MiaNL T 11 n 7 with variance estimator A N771 25127 N 2 Miimi s V TNMi T a where 5127 and s are de ned as above See the text and SAS code on the web for example calculations
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