Primes and Probability

At the suggestion of a colleague, I recently started reading Charles Wheelan’s Naked Statistics: Stripping the Dread from the Data. So far, it’s a fun, demystifying sort of book, the kind I hope my students will enjoy (watch out Lafayette Economics, I’m coming, and I will make you read). It rests on the twin ideas that statistics can be fun and statistics are incredibly useful to explain, to tell stories.

The book was high in my mind this morning when I read this deliciously accessible Slate piece by Wisconsin professor Jordan Ellenberg about an advance in prime numbers by a University of New Hampshire mathematician. Economists like to make lots of bad jokes about how they are failed physicists, who are in turn failed mathematicians, so while it interests me, I wasn’t expecting to really understand the discovery when someone riffed on twitter about primes.

What’s so wonderful about this really intense mathematical discovery, at least according to the mathematician author of this piece, is that it’s really about statistics, which I can totally get my head around. The theory goes that primes come in infinitely many ‘twin pairs,’ like 3 and 5 or 17 and 19, and the intuition lies in that we can think about primes as random numbers.

And a lot of twin primes is exactly what number theorists expect to find no matter how big the numbers get—not because we think there’s a deep, miraculous structure hidden in the primes, but precisely because we don’t think so. We expect the primes to be tossed around at random like dirt.

Zhang didn’t quite prove the twin pairs theorem, but he made an important step towards proving it, it seems, and understanding probability and statistics is key to getting there.

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What’s in more than 99%?

Contrary to what it may seem from the title, I am not going to enter the OWS fray here. Nor am I going to offer a rant on income inequality or corporate profits. There are plenty of people in the twitterverse and blogosphere to give you that. Rather, I am going to toss my hat in the ring of the birth control debate. But again, I’m not really interested in joining the name-calling that has dominated much of this debate. This debate has been so full of vitriol and terrible words and I have no intention of adding to it. I won’t link to them; I won’t even say their names. I am curious, however, about some of the statistics they’ve been using.

When this debate was–for that short period–primarily about Catholics, many news outlets were quoting that 98% of all Catholic women had used contraception in at some point. It rang a little false for me, but the underscoring point seemed consistent with my experience growing up Catholic. American Catholics, as I knew them, were fairly progressive and dedicated to social justice, easing burdens on the poor, and bringing healthy, wanted babies into the world.

You can call me naive or blind, but this is what I knew and saw in my suburban Denver church and even in my mother’s very Irish family back in Ohio.

When the debate shifted to the Blunt amendment and moral exemptions, people started quoting a new statistic that more than 99% of all women, not just Catholics, had used contraception at some point.

This just seemed too high. And the more I thought about it, the more unlikely the Catholic stat seemed as well. So, I went looking, and asked for help on twitter, and eventually came across this Guttmacher report summarizing a Vital Health Statistics paper on contraception use in America.

It’s a fascinating read, you know, if you’re interested in that stuff, and does appear to be the source for the >99% stat. Only, it doesn’t really say what I think many have suggested it does. Methods of contraception include vasectomy, withdrawal, and natural family planning, among others. While these are all clearly ways of attempting to control one’s fertility–which is partially how the debate has been and I think should be framed–they are not that closely related to birth control pills or IUDs or even condom use, as I think the >99% statistic suggests.

It’s important to say that more than 99% of all women who have ever had sex made some sort of conscious effort to control their fertility. But I think it’s disingenuous to suggest, using the same statistic, that all those women sought medical care to do the same. The point is that women should be given the information and tools to make their own decisions regarding their fertility and their bodies. Those decisions are between a woman and her doctor, and hopefully to some extent her partner.

And while it is true that more than 99% of women in America aged 15-44 who have had sex have used a form of contraception, they’re not all using the kind we’re debating about: hormonal or non-hormonal forms that require a doctor’s prescription. How we define and present numbers is important to the credibility of a cause.

**Update: Because @randomsubu asked (and was responsible for helping me find the Guttmacher report), I dug a little deeper into the original Vital Health Statistics report. In fact, 82.3% of women interviewed aged 15-44 who had ever had sex had used the Pill at some point in their lives. 93% had used condoms, more than 22% had tried Depo shots, 10% had tried the patch, and only 7.4% had an IUD (down from 18.4% 30 years ago–which is pretty interesting in and of itself).

Lies, damn lies and gendered statistics

A Gallup poll released today claims that both men and women prefer male bosses. Or at least that’s what the headline says. The actual story, in my opinion, is that about half of the population doesn’t care. Or they know enough to say that they don’t care, even if they do (ah, these social norms following me everywhere). According to the poll, a little more than half of those polled had a preference, and a little less than half did not. Of that half that had a preference, yes, more preferred a male boss, but that doesn’t mean that Americans prefer male bosses, as the first line of the story claims. It means that if they’re willing to state a preference, they prefer male bosses.

So, here’s a little story rewrite for you. “About half of Americans have no preference concerning the gender of their boss. Of those that do have a preference, 40% prefer female bosses. This is a huge gain over the first such poll that was taken in 1953 when only 5% of Americans stated a preference for female bosses. In the intervening six decades, preference for female bosses has increased more than four-fold.”

Yes, I’m being both terse and a little bit snarky, etc, etc, etc.