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SAMPLING METHODS Stratification and Clustering Richard L. Scheaffer University of Florida RLS907@bellsouth.net http://courses.ncssm.edu/math/Stat_Inst/Notes.htm

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The Sampling Process Population Sampling Unit Sampling Frame Sampling Design Sample

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…and Process Failures Sampling errors Non-sampling errors*

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PSI Example

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SIMPLE RANDOM SAMPLING

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STRATIFIED RANDOM SAMPLING Stratified sampling designs: Convenience (administration efficiency) Estimates desired for each of the strata Reduced variation (statistical efficiency)

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CLUSTER SAMPLING Commonly used when: Frame for elements is relatively difficult to obtain Frame for clusters of elements of elements is relatively easy to obtain Examples: Classrooms versus students City blocks versus residents Cartons of items stored in a warehouse versus individual items

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Examples of Clusters Polls (home or workplace) Crop yield surveys (trees, corn, sugar cane) Animal studies (traps, colonies) Systematic sample

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Two-stage cluster sampling with equal cluster sizes

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FIGURE 1: Distribution of class GPA s

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FIGURE 2: Distribution of sample means from simple random sampling

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FIGURE 3: GPA S by gender

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FIGURE 4: Distribution of sample means from stratified random sampling

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FIGURE 5: Distribution of sample means from cluster sampling; ordered clusters

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FIGURE 6: Distribution of sample means from cluster sampling; random clusters

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FIGURE 7: Distribution of sample means from cluster sampling; systematic clusters

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Summary Chart

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Names to Explore P. C. Mahalanobis –"The I.S.I. has taken the lead in the original development of the technique of sample surveys, the most potent fact finding process available to the administration". R. A. Fisher Walter Shewhart Jerzy Neyman William Cochran Edwards Deming Warren Mitofsky

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References Groves, Robert; Dillman, Donald; Eltinge, John; and Little, Roderick, editors. 2002. Survey Nonresponse. New York: Wiley. Lohr, S. 1999. Sampling: Design and Analysis, Pacific Grove, CA: Brooks Cole. Scheaffer, Richard; Mendenhall, William; and Ott, R. Lyman. 1996. Elementary Survey Sampling, 5 th ed. Belmont,CA: Duxbury Press.

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EXTRAS!

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Equal cluster sizes- comparison to SRS

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For a random sample of size mn,

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