Applied Statistics

Mark Rank and Thomas Hirschl recently published an estimate that 50% of American kids are on food stamps at some point during their first twenty years of life. Their estimate is based on an analysis of data from the Panel Study of Income Dynamics, from 1968 through 1997.

This news article by Lindsey Tanner provides a good overview.

The survey followed up families annually, thus there are kids in the study who were included at age 1, 2, . . ., 20. From this you can easily just count the proportion who were never on food stamps, the proportion who were on food stamps for one year during the first 20 years of their lives, the proportion who were on food stamps for exactly two years, etc.

Rank and Hirschl don’t quite do this; instead they use all their data to estimate the probability of being on food stamps at age 1; then they use all the kids who were in the study for ages 1-2 to estimate the prob of being on food stamps at age 2, if they were not on food stamps at age 1; . . . and for their last step, they use the subset of kids who were in the study continuously for ages 1-20 to estimate the prob of being on food stamps at age 20, for kids who were not on food stamps for the first 19 years. Put these together and you can figure out the probability of ever having food stamps.

This is all fine–it’s an efficient use of the data they have–but I’d feel a bit more confidence in Rank and Hirschl’s estimates if they would cross-check by doing some raw-data calculations based on the subset of kids who were in the study continuously for ages 1-20. That’s a crucial component in any applied statistical analysis–the continuous thread connecting the raw numbers to the final estimate–and I always like to see it, especially for a politically-charged subject such as this one. But really this isn’t much different from my comment on the basketball halftime study: I’ll believe the fancy analysis a lot more if I see the connection to the data.

Here are the key results from the study:

(from Table 1): 12% of newborns were on food stamps. 49% of kids were on food stamps for at least one year between ages 1-20. 23% of kids were on food stamps for at least 5 years.

(from Table 2); 8% of white newborns and 33% of black newborns were on food stamps. 37% of white kids and 90% of black kids were on food stamps for at least one year between ages 1-20.

(from Table 3): Among the black kids of unmarried parents where the head of household did not graduate from high school, 99.6% were on food stamps.

Again, I don’t know how much to believe these numbers, but I assume that they’re not too far from what was really happening in those years.

Also, whassup with those superfluous decimal places? “22.8%” and all the rest? Doesn’t anybody teach these people about sampling variation and significant digits? (I guess I should let them off the hook, given that the entire economics profession seems to have this problem too.)

Comments

  1. #1 Rosie Redfield
    November 28, 2009

    The problem of superfluous decimal places isn’t limited to economists. Many biologists who should know better (including those with very strong math backgrounds) publish , data with 4, 5, 6 and even 7 ‘significant figures’ (e.g. 3.253297 ± 0.182736), where clearly only 2 are genuinely significant. I keep pointing this problem out to them and their students, and they just shrug and carry on.

    (I blame this on the use of calculators. In the olden days, when we used slide rules, we could never get more than 3 significant figures.)

  2. #2 dean
    November 28, 2009

    “Mark Rank and Thomas Hirschl recently published …”

    When I try the link given at the “recently published” point of this sentence I’m taken to a Columbia University log-in site.

    Is that what was intended?

  3. #3 Andrew Gelman
    November 29, 2009

    Rosie: What I tell people is that, just as you never want to write a sentence that nobody will read, you never want to include a number that nobody will read. But it really is a hard message to get across.

    Dean: Link fixed; thanks.

  4. #4 ZBicyclist
    November 29, 2009

    What Dean said. Link doesn’t work. Andrew, maybe it works for you because your computer has various Columbia cookies that I don’t have??

    Attempting to find the article directly, I see from Google that a similar study was getting press in 2004, although SFGate says “half of adult Americans”, not half of all American children.

    http://www.sfgate.com/cgi-bin/article.cgi?f=/c/a/2004/09/05/MNGUK8J29C1.DTL&type=printable

    Does anyone else find it odd that the researchers find “half of all adults 20 to 65″ and “half of all children to age 20″?

  5. #5 Andrew Gelman
    November 30, 2009

    I fixed the link again; this time it should work.