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Sample Allocation and Stratification

William E. Winkler



This overview covers stratification and sample allocation for one-variable and multi-variable selection schemes. For the multi-variable problem, the methods employ a generalization of iterative proportional fitting (Winkler 1990) and a computationally tractable extension of the methods of Causey, Cox, and Ernst (1985) to more than two dimensions. With the defined probability structures, the methods allow straightforward variance estimation based on ideas of Rao (1975). Unlike alternatives, the methods do not require numerical approximations during optimization that can bias estimates (possibly) severely.

CITATION: Winkler, William E. (2009). Sample Allocation and Stratification. Statistical Research Division Research Report Series (Statistics #2009-08). U.S. Census Bureau. Available online at <>.

Source: U.S. Census Bureau, Statistical Research Division

Published online: November 16, 2009
Last revised: March 4, 2004

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Source: U.S. Census Bureau | Statistical Research Division | (301) 763-3215 (or |   Last Revised: October 08, 2010