Utah v. Evans, 536 U.S. 452, 14 (2002)

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Cite as: 536 U. S. 452 (2002)

Opinion of the Court

siders it feasible, authorize the use of the statistical method known as 'sampling' . . . ." 13 U. S. C. 195.

We have previously read this language as forbidding apportionment-related use of "the statistical method known as 'sampling.' " Department of Commerce v. United States House of Representatives, 525 U. S. 316, 343 (1999). Utah claims that imputation, as practiced by the Census Bureau, is a form of that forbidden "sampling" method.

The Government argues that imputation is not "sampling." And it has used a simplified example to help explain why this is so. Imagine a librarian who wishes to determine the total number of books in a library. If the librarian finds a statistically sound way to select a sample (e. g., the books contained on every 10th shelf) and if the librarian then uses a statistically sound method of extrapolating from the part to the whole (e. g., multiplying by 10), then the librarian has determined the total number of books by using the statistical method known as "sampling." If, however, the librarian simply tries to count every book one by one, the librarian has not used sampling. Nor does the latter process suddenly become "sampling" simply because the librarian, finding empty shelf spaces, "imputes" to that empty shelf space the number of books (currently in use) that likely filled them—not even if the librarian goes about the imputation process in a rather technical way, say, by measuring the size of nearby books and dividing the length of each empty shelf space by a number representing the average size of nearby books on the same shelf.

This example is relevant here both in the similarities and in the differences that it suggests between sampling and imputation. In both, " 'information on a portion of a population is used to infer information on the population as a whole.' " Brief for Appellants 18. And in Utah's view, and that of Justice O'Connor, see post, at 482-483 (opinion concurring in part and dissenting in part), that similarity brings


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