Back in October I offered five guidelines on “how to be a better guesstimater,” ways to hone your skills at guessing and estimation — guesstimation — that will help us minimize innumeracy.
A recent Washington Post article—“Majority of U.S. public school students are in poverty”—shows how applying these five tips could prevent people from falling for obviously inaccurate reporting. Here is the main claim of the article:
For the first time in at least 50 years, a majority of U.S. public school students come from low-income families, according to a new analysis of 2013 federal data, a statistic that has profound implications for the nation.
The Southern Education Foundation reports that 51 percent of students in pre-kindergarten through 12th grade in the 2012-2013 school year were eligible for the federal program that provides free and reduced-price lunches. The lunch program is a rough proxy for poverty, but the explosion in the number of needy children in the nation’s public classrooms is a recent phenomenon that has been gaining attention among educators, public officials and researchers.
Are those numbers accurate or even plausible? Let’s see how we could apply the tools of guesstimation to this claim.
Choose (and know) your reference points — The article claims that 51 percent of public school students are in poverty. Therefore the two main reference points we need are (1) the number of children in public schools, and (2) the number of children in America. Take a moment to estimate both numbers.
Now let’s look at the actual figures. In the fall 2014, about 49.8 million students will attend public elementary and secondary schools. Fifty-one percent of 49.9 million is 25.5 million. The U.S population in 2013 was 316,128,839 and 23 percent (about 73 million) were under the age of 18. Let’s assume that last figure didn’t count children under 5 (which it does). It would mean that 33 percent of all children (25.5 million out of 75 million) are in poverty. Does that seem even remotely plausible?
Translate into both percentages and fractions — A lot of guesstimation problems occur when we use percentages without translating them into their equivalent fraction. In the figure above, the claim 51 percent refers to 1 out of 2 public school children, and one 1 out of 3 of every child in America. Does it seem possible that every other kid sitting in a public school classroom is in poverty?
Think outside your circles — If you are a teacher in an inner city school in Chicago, 51 percent of the children you teach may actually live in poverty. But why would the rest of us make that assumption? Think about everyone you come in contact that has children in public schools. Is it likely that half of those children live in households in poverty?
Ask, “Is that a big number? — Earlier we calculated that the claim as stating that 25.5 million are in poverty. Even in a country of 315 million, that is a huge number. Is it plausible that so many children are being affected and yet no one noticed until this study was pointed out in the Washington Post?
You don’t have to go through all these steps to come up with a rough “guestimation” of the accuracy of this claim. It seems implausible even with rough, back-of-the envelope calculations. So what went wrong with the report. As economist Alex Tabarrok explains:
Eligibility for free and reduced-price lunches, however, depends on eligibility rules and not just income levels let alone poverty rates. The New York Times article on the study is much better: “Children who are eligible for such lunches do not necessarily live in poverty. Subsidized lunches are available to children from families that earn up to $43,568, for a family of four, which is about 185 percent of the federal poverty level.”
Frankly I suspect that this study was intended to confuse the media by conflating “low-income” with “below the poverty line”. Indeed, why did this study grab headlines except for the greater than 50% statistic? It is very easy to find official numbers of the number of students in poverty according to the federal poverty standard.
According to the National Center for Education Statistics, in 2012 (the date of most recent data), approximately 21 percent of school-age children in the United States were in families living in poverty. There is no disputing that 21 percent is still way too high. It is scandalously high. But there is a huge difference between 1 out of 5 students (21 percent) and 1 out of 2 students (51 percent).
Such innumerate claims are not only misleading, they hurt the cause of poverty-reduction. As Tabarrok says, “we won’t get very far understanding the issue by shifting definitions and muddying the waters with misleading but attention grabbing statistics.”