Mathematical Malpractice Watch: Rape Statistics

The Akin controversy has brought a lot of ugliness to light. I’ll push aside the broader political issues, which I’ve discussed on the other blog. Instead, I want to focus on a particular piece of nonsense from one of the more influential pro-Life figures, who has tried to argue that rape pregnancies are very rare.

You would think this would be straight forward. You could, for example, find rape victims and ask them if they got pregnant. And indeed, a study estimated that about 5% of rapes end in pregnancy and 32,000 fetuses are conceived in rape every year. You could also ask women getting abortions if they were raped. And indeed, Guttmacher did this and produced a lower estimate of about 10,000 or so. There is no real incentive, at this point, for women to lie about how they got pregnant. Or there are just as many reasons for them lie either way since many women are tragically ashamed of having been raped. But there is no a priori reason to suspect that either number is greatly inflated.

(The Guttmacher number seems a little better since the numbers in the former study would indicate about 640,000 rapes a year or three times what the FBI and NCVS conclude, even including the under-reporting factor. The difference is likely that Guttmacher is recent and Holmes was published in 1996, shortly after crime rates peaked. Rape rates have plunged in the last 16 years and are down about 85% over the last 30.)

But plain facts aren’t enough for some people, so John Wilke, “M. D.” has come up with a bizarre rape equivalent of the Drake equation to try to figure out how many rape babies are conceived every year and come up with a vanishingly small number.

It’s fairly easy to tear apart.

Of the 200,000 women who were forcibly raped, one-third were either too old or too young to get pregnant. That leaves 133,000 at risk for pregnancy.

I can’t find good numbers on this, but I suspect he has already over-estimate the pruning factor. Rape rates peak at young ages. It’s not unheard of for old women to be raped, but it’s relatively rare. Women in their late teens are four times as likely as the general population to be raped for a variety of reasons. Let’s be generous and cut the number to 180,000. This age business is going to be a recurring theme, by the way.

A woman is capable of being fertilized only 3 days (perhaps 5) out of a 30-day month. Multiply our figure of 133,000 by three tenths. Three days out of 30 is one out of ten, divide 133 by ten and we have 13,300 women remaining. If we use five days out of 30 it is one out of six. Divide one hundred and thirty three thousand by six and we have 22,166 remaining.

Wrong. This is just plain wrong. First of all, sperm can live in the reproductive tract for up to a week, as many women who have used the rhythm method have found out. Moreover, there is some evidence that women are more likely to be raped when they are near ovulation. There is good evidence that men can sense ovulation and are more likely to be sexually interested in women around that time. If a woman is more likely to be targeted at certain points in her cycle, this kind of simplistic analysis is badly wrong. But let’s just ballpark at as one fertile week in three non-menstruating weeks. We’re now down to 60,000 in reality.

One-fourth of all women in the United States of childbearing age have been sterilized, so the remaining three-fourths come out to 10,000 (or 15,000).

Problem: it’s rare for young women to get sterilized. This is far more common in women who are technically of child-bearing age but have decided to stop having kids or had health issues — i.e., women in their 30’s and 40’s. Where does the rape rate peak again? Right — in the younger women who are the least likely to be sterilized. So let’s just keep the number at 60,000 for the moment. I’ll roll this into a General Bullshit Factor later on.

Only half of assailants penetrate her body and/or deposit sperm in her vagina, so let’s cut the remaining figures in half. This gives us numbers of 5,000 (or 7,500).

This statistics is from a 1977 study. Why does someone use a (at the time) 22-year-old study? Because modern studies probably don’t give him the answer he wants. Not having access to the data, I can’t really estimate how badly he botches this but it’s worth noting that attempted rapes are not included in the 200,000 figure but probably are included in the 50% (the title of the article is about sexual dysfunction which is, again, less likely in the younger males who commit most rapes). Let’s be generous and bring the number down to 50,000.

Fifteen percent of men are sterile, that drops that figure to 4,250 (or 6,375). Fifteen percent of non-surgically sterilized women are naturally sterile. That reduces the number to 3,600 (or 5,400).

Here we get a clever manipulation. Infertility affects about 10% of couples, combining both male and female factors. What he does here is increase the rates by 5% and then multiply them against each other. This seemingly small manipulation prunes the number of rape pregnancies by 30% instead of 10%. Moreover, there is an age factor again. Rape victims and perpetrators are massively more likely to be young, when infertility rates are low. But let’s be generous and lop that number down to 45,000.

Another fifteen percent are on the pill and/or already pregnant. That reduces the number to 3,070 (or 4,600).

I should note that because rape is, by definition, unplanned, rape victims are less likely to be on birth control and probably less likely to be pregnant. But let’s throw this into the General Bullshit Factor and bring things down to 40,000.

Now factor in the fact that it takes 5-10 months for the average couple to achieve a pregnancy. Use the smaller figure of 5 months to be conservative and divide the avove figures by 5. The number drops to 600 (or 920).

This is the thing that provoked the post. There are two massive problems with step. First, we have … once again … the age factor. My wife and I have been trying to get pregnant for three and a half years. Even with medical help, we haven’t gotten a baby. For young people — again the people most likely to be victims and perpetrators — the fertility rate is MUCH higher. 85-90% of 20-year old women will be pregnant after a year of trying against 5% of women age 45.

Moreover, that pregnancy rate includes many of the other factors he is already counting like male sterility and (later on) miscarriage. In other words, he’s correcting his numbers twice for the same problems. So, let’s take out the sterility factor, put back in the odds-of-getting-pregnant-from-unprotected sex factor. Let’s call that 20,000.

In an average population, the miscarriage rate is about 15 percent. In this case we have incredible emotional trauma. Her body is upset. Even if she conceives, the miscarriage rate will be higher than in a more normal pregnancy. If 20 percent of raped women miscarry, the figure drops to 450 (or 740).

There is little evidence that stress increases the rate of miscarriage. There have been indications in the literature but nothing conclusive. In any case: (a) the rate of miscarriage is more like 50%; (b) do I need to even say it? Miscarriage rates vary with age, and; (c) we already included miscarriage in the “it takes five months to get pregnant” correction. So we’ll leave our number at 20,000.

We’re now slightly higher than number Guttmacher estimated, slightly lower than what Holmes estimated. I would say that’s pretty good considering all the bullshit we had to wade through. We could have, of course, just gone to the, you know, actual research. But I wanted to go through this point by point to show how the statistics have been manipulated by someone who clearly had the final answer in mind at the beginning. It’s a perfect illustration of Mathematical Malpractice: deliberately manipulating numbers in ways that sounds plausible but are, in fact, complete bullshit. Moreover, because he multiplies the numbers, that makes each bullshit factor much more powerful. It’s a very simple rule:

Bullshit + Bullshit = Double Bullshit

Bullshit x Bullshit = Unbelievable Bullshit

That’s how you underestimate the number of rape pregnancies by a factor of 100.

Oh, there’s this:

Finally, factor in what is certainly one of the most important reasons why a rape victim rarely gets pregnant, and that’s physical trauma. Every woman is aware that stress and emotional factors can alter her menstrual cycle. To get and stay pregnant a woman’s body must produce a very sophisticated mix of hormones. Hormone production is controlled by a part of the brain that is easily influenced by emotions. There’s no greater emotional trauma that can be experienced by a woman than an assault rape. This can radically upset her possibility of ovulation, fertilization, implantation and even nurturing of a pregnancy. So what further percentage reduction in pregnancy will this cause? No one knows, but this factor certainly cuts this last figure by at least 50 percent and probably more. If we use the 50 percent figure, we have a final figure of 225 (or 370) women pregnant each year. These numbers closely match the 200 that have been documented in clinical studies.

“No one knows” so we’ll just throw in a 50% factor. In fact, we do know. Women got pregnant during the Holocaust. Women have gotten pregnant during periods of mass starvation. Women have gotten pregnant from invading armies while their homes were burned down and their families were slaughtered. Women get pregnant from rape. If it were that easy to not get pregnant, we wouldn’t need an abortion industry. We wouldn’t need birth control. All you’d have to do is have a post-coital look at the federal budget projections and you would be good. Oh, and the “documented studies”? They indicate 10-30,000.

(Bizarrely, the CLR has doubled down on this, going with a different but equally garbage methodology to show that the pregnancy rate is lower in raped women. Their argument? We should ignore the 16-year-old study of 4000 women that claims 5% of rape victims get pregnant and instead go with a 30-year-old study of 700 women that says only 2% do. The mind would boggle if it weren’t already completely blown.)

Even if you are an intelligent design believer, you have to acknowledge that humans are designed to reproduce. It’s what we do. And we can reproduce under amazing stress and trial. Want proof?

Just ask the 10-30,000 women who got pregnant from a rape last year.

Update: It occurred to me in the car this morning that there’s another way to show how bogus Wilke’s numbers are. Almost all of his corrections apply, to varying degrees, to the population of women as a whole. If we take out the rape-specific factors, Wilke’s method would estimate the pregnancy rate for the female population as a whole to be less than 1%. And that’s not accounting for women who have planned for consensual sex and are using appropriate birth control.

In reality, about 10% of women of reproductive age will get pregnant in any year and about 5% will give birth. That ratio is lower for younger women (about 3%, according to Holmes). A good test of a method for measuring an unknown quantity is if it can give you an known quantity. Wilke’s “method” can’t.

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