The Equivalence of Neyman Optimum Allocation for Sampling and Equal Proportions for Apportioning the U.S. House of Representatives |
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| Authors: | Tommy Wright |
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| Affiliation: | Center for Statistical Research and Methodology , U.S. Bureau of the Census , Washington , DC , 20233 |
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| Abstract: | We present a surprising though obvious result that seems to have been unnoticed until now. In particular, we demonstrate the equivalence of two well-known problems—the optimal allocation of the fixed overall sample size n among L strata under stratified random sampling and the optimal allocation of the H = 435 seats among the 50 states for apportionment of the U.S. House of Representatives following each decennial census. In spite of the strong similarity manifest in the statements of the two problems, they have not been linked and they have well-known but different solutions; one solution is not explicitly exact (Neyman allocation), and the other (equal proportions) is exact. We give explicit exact solutions for both and note that the solutions are equivalent. In fact, we conclude by showing that both problems are special cases of a general problem. The result is significant for stratified random sampling in that it explicitly shows how to minimize sampling error  | |
| Keywords: | Apportionment Fractional parts Neyman allocation Probability sampling Stratification |
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