# How Many Women?

Campus sexual violence continues to be a topic of discussion, as it should be. I have a post going up on the other site about the kangaroo court system that calls itself campus justice.

But in the course of this discussion, a bunch of statistical BS has emerged. This centers on just how common sexual violence is on college campuses, with estimates ranging from the one-in-five stat that has been touted, in various forms, since the 1980’s, to a 0.2 percent rate touted in a recent op-ed.

Let’s tackle that last one first.

According to the FBI “[t]he rate of forcible rapes in 2012 was estimated at 52.9 per 100,000 female inhabitants.”

Assuming that all American women are uniformly at risk, this means the average American woman has a 0.0529 percent chance of being raped each year, or a 99.9471 percent chance of not being raped each year. That means the probability the average American woman is never raped over a 50-year period is 97.4 percent (0.999471 raised to the power 50). Over 4 years of college, it is 99.8 percent.

Thus the probability that an American woman is raped in her lifetime is 2.6 percent and in college 0.2 percent — 5 to 100 times less than the estimates broadcast by the media and public officials.

This estimate is way too low. It is based on taking one number and applying high school math to it. It misses the mark because it uses the wrong numbers and some poor assumptions.

First of all, the FBI’s stats are on documented forcible rape and does not account for under-reporting and does not includes sexual assault. The better comparison is the National Crime Victimization Survey, which estimates about 300,000 rapes or sexual assaults in 2013 for an incidence rate of 1.1 per thousand. But even that number needs some correction because about 2/3 of sexual violence is visited upon women between the ages of 12 and 30 and about a third among college-age women. The NCVS rate indicates about a 10% lifetime risk or about 3% college-age risk for American women. This is lower than the 1-in-5 stat but much higher than 1-in-500.

(*The NCVS survey shows a jump in sexual violence in the 2000’s. That’s not because sexual violence surged; it’s because they changed their methodology, which increased their estimates by about 20%.)

So what about 1-in-5? I’ve talked about this before, but it’s worth going over again: the one-in-five stat is almost certainly a wild overestimate:

The statistic comes from a 2007 Campus Sexual Assault study conducted by the National Institute of Justice, a division of the Justice Department. The researchers made clear that the study consisted of students from just two universities, but some politicians ignored that for their talking point, choosing instead to apply the small sample across all U.S. college campuses.

The CSA study was actually an online survey that took 15 minutes to complete, and the 5,446 undergraduate women who participated were provided a \$10 Amazon gift card. Men participated too, but their answers weren’t included in the one-in-five statistic.

If 5,446 sounds like a high number, it’s not — the researchers acknowledged that it was actually a low response rate.

But a lot of those responses have to do with how the questions were worded. For example, the CSA study asked women whether they had sexual contact with someone while they were “unable to provide consent or stop what was happening because you were passed out, drugged, drunk, incapacitated or asleep?”

The survey also asked the same question “about events that you think (but are not certain) happened.”

That’s open to a lot of interpretation, as exemplified by a 2010 survey conducted by the U.S. Centers for Disease Control and Prevention, which found similar results.

I’ve talked about the CDC study before and its deep flaws. Schow points out that the victimization rate they are claiming is way more than the National Crime Victimization Survey (NCVS), the FBI and the Rape, Abuse and Incest National Network (RAINN) estimates. All three of those agencies use much more rigorous data collection methods. NCVS does interviews and asks the question straight up: have you been raped or sexually assaulted? I would trust the research methods of these agencies, who have been doing this for decades, over a web-survey of two colleges.

Another survey recently emerged from MIT which claimed 1-in-6 women are sexually assaulted. But only does this suffer from the same flaws as the CSA study (a web survey with voluntary participation), it’s not even claiming what it claims:

When it comes to experiences of sexual assault since starting at MIT:

• 1 in 20 female undergraduates, 1 in 100 female graduate students, and zero male students reported being the victim of forced sexual penetration
• 3 percent of female undergraduates, 1 percent of male undergraduates, and 1 percent of female grad students reported being forced to perform oral sex
• 15 percent of female undergraduates, 4 percent of male undergraduates, 4 percent of female graduate students, and 1 percent of male graduate students reported having experienced “unwanted sexual touching or kissing”
• All of these experiences are lumped together under the school’s definition of sexual assault.

When students were asked to define their own experiences, 10 percent of female undergraduates, 2 percent of male undergraduates, three percent of female graduate students, and 1 percent of male graduate students said they had been sexually assaulted since coming to MIT. One percent of female graduate students, one percent of male undergraduates, and 5 percent of female undergraduates said they had been raped.

Note that even with a biased study, the result is 1-in-10, not 1-in-5 or 1-in-6.

OK, so web surveys are a bad way to do this. What is a good way? Mark Perry points out that the one-in-five stat is inconsistent with another number claimed by advocates of new policies: a reporting rate of 12%. If you assume a reporting rate near that and use the actual number of reported assaults on major campuses, you get a rate of around 3%.

Hmmm.

Further research is consistent with this rate. For example, here, we see that UT Austin has 21 reported incidents of sexual violence. That’s one in a thousand enrolled women. Texas A&M reported nine, one in three thousand women. Houston reported 11, one in 2000 women. If we are to believe the 1-in-5 stat, that’s a reporting rate of half a percent. A reporting rate of 10%, which is what most people accept, would mean … a 3-5% risk for five years of enrollment.

So … Mark Perry finds 3%. Texas schools show 3-5%. NCVS and RAINN stats indicate 2-5%. Basically, any time we use actual numbers based on objectives surveys, we find the number of women who are in danger of sexual violence during their time on campus is 1-in-20, not 1-in-5.

One other reason to disbelieve the 1-in-5 stat. Sexual violence in our society is down — way down. According to the Bureau of Justice Statistics, rape has fallen from 2.5 per 1000 to 0.5 per thousand, an 80% decline. The FBI’s data show a decline from 40 to about 25 per hundred thousand, a 40% decline (they don’t account for reporting rate, which is likely to have risen). RAINN estimates that the rate has fallen 50% in just the last twenty years. That means 10 million fewer sexual assaults.

Yet, for some reason, sexual assault rates on campus have not fallen, at least according to the favored research. They were claiming 1-in-5 in the 80’s and they are claiming 1-in-5 now. The sexual violence rate on campus might fall a little more slowly than the overall society because campus populations aren’t aging the way the general population is and sexual violence victims are mostly under 30. But it defies belief that the huge dramatic drops in violence and sexual violence everywhere in the world would somehow not be reflected on college campuses.

Interestingly, the decline in sexual violence does appear if you polish the wax fruit a bit. The seminal Koss study of the 1980’s claimed that one-in-four women were assaulted or raped on college campuses. As Christina Hoff Summer and Maggie McNeill pointed out, the actual rate was something like 8%. A current rate of 3-5% would indicate that sexual violence on campus has dropped in proportion to that of sexual violence in the broader society.

It goes without saying, of course that 3-5% of women experiencing sexual violence during their time at college is 3-5% too many. As institutions of enlightenment (supposedly), our college campuses should be safer than the rest of society. I support efforts to clamp down on campus sexual violence, although not in the form that it is currently taking, which I will address on the other site.

But the 1-in-5 stat isn’t reality. It’s a poll-test number. It’s a number picked to be large enough to be scary but not so large as to be unbelievable. It is being used to advance an agenda that I believe will not really address the problem of sexual violence.

Numbers means things. As I’ve argued before, if one in five women on college campuses are being sexually assaulted, this suggests a much more radical course of action than one-in-twenty. It would suggest that we should shut down every college in the country since they are the most dangerous places for women in the entire United States. But 1-in-20 suggests that an overhaul of campus judiciary systems, better support for victims and expulsion of serial predators would do a lot to help.

In other words, let’s keep on with the policies that have dropped sexual violence 50-80% in the last few decades.