Utah v. Evans
Utah v. Evans, 536 U.S. 452 (U.S. 2002) is the leading court case about the use of Hot-Deck Imputation in the United States Census. After the use of Hot-Deck techniques in the 2000 census, one of Utah's congressional seats was appointed to North Carolina. Utah challenged this, on the grounds that Hot-Deck Imputation is a form of sampling, and "violated various statutory provisions and the Constitution." The Supreme Court affirmed the judgment of the Second Circuit Court of Appeals (see below).
Justice Breyer wrote in the opinion "The question before us is whether the Census Bureau's use in the year 2000 census of a methodology called "hot-deck imputation" either (1) violates a statutory provision forbidding use of "the statistical method known as 'sampling'" or (2) is inconsistent with the Constitution's statement that an "actual Enumeration" be made. 13 U.S.C. section 195; U.S. Const., Art. I, � 2, cl. 3. We conclude that use of "hot-deck imputation" violates neither the statute nor the Constitution."
To illustrate why imputation is not sampling, the opinion uses the following metaphor:
"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."
But people are not nearly as simple as books. Depending on how missing data is filled in, hot-deck imputation can cause bias.
After establishing the difference between hot-deck imputation and sampling, the Court discussed the Constitutional requirement for Actual Enumeration. The Court argued that "The textual word "actual" refers in context to the enumeration that will be used for apportioning the Third Congress, succinctly clarifying the fact that the constitutionally described basis for apportionment will not apply to the First and Second Congresses. The final part of the sentence says that the "actual Enumeration" shall take place "in such Manner as" Congress itself "shall by Law direct," thereby suggesting the breadth of congressional methodological authority, rather than its limitation."
The Court concluded, "We need say only that in this instance, where all efforts have been made to reach every household, where the methods used consist not of statistical sampling but of inference, where that inference involves a tiny percent of the population, where the alternative is to make a far less accurate assessment of the population, and where consequently manipulation of the method is highly unlikely, those limits are not exceeded."
Utah v. Evans, 182 F. Supp. 2d 1165 (2001).
The Court stated "We begin by noting that section 195 does not preclude the Census Bureau from the use of every type of statistical methodology in arriving at apportionment figures during a decennial census. Instead, it prohibits only "the use of the statistical method known as 'sampling.'" Section 195 is part of the Census Act, and states, "Except for the determination of population for purposes of apportionment of Representatives in Congress among the several States, the Secretary shall, if he considers it feasible, authorize the use of the statistical method known as "sampling" in carrying out the provisions of this title." This section has been interpreted to prohibit the use of sampling for apportionment. (See, for example, Department of Commerce v. United States House of Representatives)
"[H]ot deck imputation is not sampling. Sampling is the selection of a subset of units from a larger population in such a way that each unit of the population has a known chance of selection. Sampling is used where a scientifically selected set of units can be used to represent the entire population from which they are drawn."
The Court concluded "that the Constitution does not prohibit the use of narrowly tailored statistical methodologies, such as hot deck imputation, for the purpose of improving the accuracy of the decennial census and furthering "the constitutional goal of equal representation."