As a 6-foot-2 graduate of the New York City elementary school system, I apparently have P.S. 166 to thank for my extra-long legs. At least, that’s the suggestion of a new working paper distributed by the National Bureau of Economic Research. The authors took the teacher value added measures commonly used to assess the effect of teachers on student academic achievement and applied them to student height.

The findings show that high-value teachers seem to produce increased height in the same way they seem to deliver higher SAT scores.

Sound crazy? Bear with me.

If we could replicate the result, and use it to craft policy, we could affect a lot more than just the length of the national trouser legs. It turns out that when it comes to life outcomes, height matters a good deal — probably, in most professions, more than algebra or chemistry.

Sure, great height has its drawbacks — grow too tall and you sacrifice any chance of becoming a gymnast or a jockey. There’s also a slightly higher risk of cancer and blood clots when you get older.

But height also confers some pretty serious advantages. Taller people earn more and are more likely to hold high-status jobs — 58 percent of American chief executives are over 6 feet tall, though only 14 percent of the male population hits that mark.

Tall people are also perceived as more attractive by potential dating partners and score higher on various measures of happiness. And if academic achievement is what you’re interested in, it’s worth noting that tall people also score higher on achievement tests, even as children.

If we could train teachers to be more effective at increasing student heights, we’d erase a lot of other inequities too.

The only problem is that this is completely and obviously ludicrous.

If you’ve been mentally shouting as much while reading to here, you’re right: This result sounds crazy because it is crazy. Even if it looks like “high value” teachers affect student height, it’s clearly one of those specious correlations with which the world abounds.

And the paper’s authors know that. The point of “Teacher Effects on Student Achievement and Height: A Cautionary Tale” isn’t to propose looking for teachers who can make their students grow. The paper is critiquing the idea that teacher quality can be measured by looking at their students’ test scores.

As economist Arnold Kling said of the paper: “The effect of teachers on height is almost surely spurious. So the effect of teachers on achievement may also be spurious. … It provides support for the Null Hypothesis.” The “null hypothesis” being social-science jargon for the possibility that the plausible-sounding intervention you’re studying doesn’t actually do anything.

There has been plenty of research into “teacher value-added” in recent years, much of it suggesting that teacher quality can make an extraordinary difference in students’ lives — that high-quality teachers not only make children learn more but also help them (eventually) avoid teen pregnancy, graduate from college and earn more.

A team led by Stanford economist Raj Chetty famously estimated that replacing a teacher in the bottom 5 percent with one of average quality could mean the students in that classroom collectively earning an extra $1.4 million over their lifetimes. In response, many school districts have implemented measures of teacher value-added, which are used to make decisions about compensation and retention.

Now, the authors of the paper are quarreling more with the crude metrics used by school systems than with Chetty’s data. After all, it’s unlikely to be literally true that teacher quality doesn’t matter at all for student achievement — if you put a horse in front of a calculus class, the kids would presumably never learn to take a second derivative.

Schools don’t do that, however; they use human teachers who have some familiarity with the subject. And beyond that threshold, variations in teacher quality might matter less than variations in the natural ability or socioeconomic resources of the students, or random events such as illnesses and family crises. Researchers and program officers do try to control for those things, but the controls are unlikely to be perfect.

So at the very least, when exciting education results are in the news, keep the null hypothesis in mind. Maybe the education holy grail, the intervention that gives all kids the same chance no matter where they started out, has been discovered. But there’s always a chance somebody’s chasing a big fat null down a rabbit hole into a nonsense world where teachers can grow your body as well as your mind.

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