The census will be wrong. We could fix it.

I have an op/ed in tomorrow’s Washington Post about statistical sampling and the census.  It boils down to the claim that by failing to use the best statistical techniques we have to enumerate the population accurately, we’re getting the answer wrong on purpose in order to avoid getting it wrong by accident, and possibly violating the Constitution as a result.  And that estimating an unmeasured quantity to be zero is a really bad estimate.

The book Who Counts?  The Politics of Census-Taking In Contemporary America, by Margo Anderson and Stephen Fienberg, was an invaluable resource for the piece — highly recommended.

One argument I cut for space involves Kyllo vs. US, in which the Supreme Court ruled, in an opinion written by Antonin Scalia, that the use of a thermal imaging device to detect heat coming off the exterior wall of a house, and thus to infer the presence of a drug operation inside, can constitute a “search” for Fourth Amendment purposes.  On the other hand, Scalia questions the constitutionality of statistical adjustment of the census, expressing doubt that such a procedure would still be an “actual enumeration” as required by the Constitution.  So, for Scalia:

  • “Search,” in 2010, includes a scenario in which something of interest inside the house is not seen or otherwise sensed by any person or people, but is inferred by means of a scientific instrument that didn’t exist in Constitutional times.
  • But “enumeration,” in 2010, does NOT include a scenario in which the population is not counted one by one by any person or people, but is inferred by means of a statistical instrument that didn’t exist in Constitutional times.

Is that a problem?

Update (4 May):  It turns out I’m not the first arithmetic geometer to weigh in on census adjustment.  Brian Conrad in the New York Times, August 1998 does in three sentences what took me 1000 words:

Human intelligence plus a little brute force is often far more efficient and accurate than brute force alone. This is why statistical sampling is the superior way to carry out an ”actual enumeration” of a large population. Just ask any Republican who relies on a poll or who takes a blood test rather than drain every drop from his body.

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8 thoughts on “The census will be wrong. We could fix it.

  1. Bisi Agboola says:

    Jordan, could you perhaps post the first version (before you had to cut it for space reasons) of the article somewhere?

  2. Lior says:

    Regarding the constitutional question, the issue turns on meaning of “enumeration”. It can mean “making a list of people” or “determining their number”. That is, statistical estimation certainly does not produce a list of people who have been counted but it does provide a more accurate determination of the number of people.

    In either case I don’t think there’s a dispute you can use modern technology to achieve the enumeration, whatever that means.

  3. JSE says:

    Bisi: Actually, the Post edited it quite lightly; the stuff there wasn’t room for was stuff I didn’t actually write, just thought about. In any event, I’m pretty sure it would violate my agreement with the Post to post “director’s cuts” on the blog!

    Lior: Re the meaning of “enumeration” — I didn’t get a chance to put this in the article, but I think Breyer’s majority opinion in Utah v. Evans makes a good case that “actual enumeration” means “as opposed to the total guesses we used in the previous paragraph to apportion the first Congress,” not as a methodological demand on the Census.

  4. […] an unrelated link, Jordan Ellenberg has just written a piece for the Washington Post on statistical sampling and how it could make the […]

  5. harrison says:

    I’m not a constitutional lawyer, but I’ve read up on the subject as a hobby since I was about 12, and one crucial thing that I’d point out that wasn’t mentioned in the article is the following:

    “The actual Enumeration shall be made within three Years after the first Meeting of the Congress of the United States, and within every subsequent Term of ten Years, in such Manner as they shall by Law direct.

    Maybe this refers to the time periods, but if it refers to the “actual Enumeration” that seems to me (and again, IANACL) to be a pretty strong constitutional basis for sampling.

    Although, you have the following, from the most important Amendment of all, the Fourteenth: “Representatives shall be apportioned among the several States according to their respective numbers, counting the whole number of persons in each State…” OTOH, the Constitution doesn’t actually specify the method of apportionment, other than the 1/30000*population upper bound for the size of Congress, and the method of apportionment has changed a number of times — and the Court has ruled these changes constitutional. As such, it seems like it’d be perfectly legitimate to apply a statistical adjustment before apportioning seats. And when it’s just reporting data, the Census Bureau can pretty much do whatever, right?

  6. Susan Holmes says:

    It was interesting to see this complement to your oped, so you did in fact read some statistics papers. But it seems that you didn’t read both points of view on subject.
    You might consider reading the other side:
    D.A. Freedman and K.W. Wachter. “On the likelihood of improving the accuracy of the census through statistical adjustment.” In Science and Statistics: A Festschrift for Terry Speed. Institute of Mathematical Statistics Monograph 40 (2003) pp. 197–230. D. R. Goldstein, ed.
    It is a paper you can find on David Freedman’s website – he was a well known statistician and co-authored many papers with mathematicians such as Persi Diaconis, …..
    There is actually a serious discussion among statisticians about whether the census should be adjusted and maybe it would be worth exploring all the complexities as a professional statistician myself, I haven’t made up my mind because of the complexities so I found your take on it a little naive.

  7. JSE says:

    Susan: I read the Freedman-Wachter paper. I don’t have enough statistical power to assess the merits of their argument on my own; I relied on testimony from various people I interviewed that Freedman and Watcher’s views on this are serious, but decidedly in the minority. But you’re right, of course, that the form of an op/ed sort of forbids doing very much “on the one hand, on the other hand…” and a more thorough treatment of the issue would address this question more directly and more deeply.

  8. Susan Holmes says:

    I wonder what the sample size was for your interviewing process,
    I know a large number of serious statisticians who were on David’s side of the argument.

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