Transcription of Chapter 4 Stratified Sampling - IIT Kanpur
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Chapter 4 Stratified Sampling - IIT Kanpur
Sampling Theory| Chapter 4 | Stratified Sampling | Shalabh, IIT Kanpur Page 1 Chapter 4 Stratified Sampling An important objective in any estimation problem is to obtain an estimator of a population parameter which can take care of the salient features of the population. If the population is homogeneous with respect to the characteristic under study, then the method of simple random Sampling will yield a homogeneous sample and in turn, the sample mean will serve as a good estimator of population mean. Thus, if the population is homogeneous with respect to the characteristic under study, then the sample drawn through simple random Sampling is expected to provide a representative sample. Moreover, the variance of sample mean not only depends on the sample size and Sampling fraction but also on the population variance. In order to increase the precision of an estimator, we need to use a Sampling scheme which can reduces the heterogeneity in the population.
st i i i k ii ii i ii Es S s yy n Nn Var y s Nn Var y w Var y Nn ws Nn Note: If SRSWR is used instead of SRSWOR for drawing the samples from each stratum, then in this case 1 2 222 11 22 1 22 1 1 () 1 where ( ). i k st i i i st kk ii st i i i iiii i k ii st i i N iiji i j ywy Ey Y N Var y w S w Nn n ws Var y n yy n
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