Sample Survey Methods
Sample Survey Methods STAT 422
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This 6 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 Christopher Williams in Fall. Since its upload, it has received 43 views. For similar materials see /class/227939/stat-422-university-of-idaho in Statistics at University of Idaho.
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Date Created: 10/23/15
O U S house 93 errorsq 1 066260 188238 140660 149084 414122 1 016565 MOOOMMO 316484 NU 1 003460 OWQC U39IFPUDNH 0010U1HgtL L 1 1 035165 H D 1 O 039438 The MEANS Procedure Variable Sum house 550000000 m 270000000 a 110000000 errorsq 136947610 Plot of am Legend A 1 obs B 2 obs etc Ratio Estimate of Population R Simple Random Sample Design Response Variable a Auxilialy Variable m Standard Sample Estimate Error Bound srquot2 Size 040741 013959 027919 152202 10 Twostage cluster sampling Ratio estimation of a population mean or proportion Ratio estimation of a population mean The unbiased estimator of the population mean that we recently introduced for two stage cluster sam pling requires that we know M the number of elements in the population note however that the unbiased estimator of 739 does not require this in formation ln many cases we do not know M and so an alternative ratio estimator of u can be used with an estimated variance of A N771 1 52 1 n Mim 52 VAT 7 L M 71 l 71 M lt N M2nnNM2Z 1 Mi m where Z Mi2i r Mi ry 2 7 l 1 ST 7 n 7 1 n 7 1 The estimator is biased but the bias is small when n is large In cases where we do know M it often turns out that is more ef cient than the unbiased estimator particularly when the cluster sizes M vary Note that when the cluster sizes M are all equal then and the unbiased estimator are identical See the SAS code on the web for example calculations comparing the two methods for estimating a population mean Ratio estimation of a population proportion Since the number of elements in the population M is usually unknown when estimating a proportion we will use a ratio estimator to estimate p Let be the pro portion of elements in the sample from cluster 239 that are fall into the category of interest The ratio estimator of p is n ZMipi A i1 1077 Mi H l 1 with an estimated variance of VtltN gtlt2gti N M n nNM 11 where 2 MRI 7 I372 20 MW 2 7 11 7 i1 A i A 57 andqiilipi n 7 1 n 7 1 There is a SAS example on the website