SAMPLING METHODS Stratification and Clustering Richard L. Scheaffer University of Florida

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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

The Sampling Process Population Sampling Unit Sampling Frame Sampling Design Sample

…and Process Failures Sampling errors Non-sampling errors*

PSI Example

SIMPLE RANDOM SAMPLING

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

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

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

Two-stage cluster sampling with equal cluster sizes

FIGURE 1: Distribution of class GPA s

FIGURE 2: Distribution of sample means from simple random sampling

FIGURE 3: GPA S by gender

FIGURE 4: Distribution of sample means from stratified random sampling

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

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

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

Summary Chart

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

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.

EXTRAS!

Equal cluster sizes- comparison to SRS

For a random sample of size mn,

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