CDC: MRA claims that “40% of rapists are women” are based on bad math and misuse of our data

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Feminists often complain, with considerable justification, that Men’s Rights Activists try to turn every conversation about women’s issues into a game of “what about the men?” You’re talking about female rape victims — well, what about the male rape victims?

The trouble with this strategy, from the point of view of the Men’s Rights Activists anyway, is that this little “gotcha” is much less of a “gotcha” then they’d like it to be.

In the case of rape, for example, feminists are well aware that men are raped as well: the “Don’t Be That Guy” ad campaign, which sent so many MRAs into hysterics, focused on male victims as well as female ones. The emergency room rape advocate organization that a friend of mine volunteers for provides advocacy for victims regardless of gender.

So many MRAs have started playing another game: trying to twist the conversation around in order to cast women as the villains. Rape is a bit tough for them here, since the overwhelming majority of rapists are male. So MRAs talk about the alleged epidemic of female false accusers instead. Or they change the topic entirely and make dead baby jokes (see my post yesterday).

Recently, MRAs have tried a new strategy, seizing on data from The National Intimate Partner and Sexual Violence Survey, a massive study conducted in 2010 under the aegis of the Centers for Disease Control, to claim that “40% of rapists are women.”

This is a claim repeated by numerous MRAs on numerous websites; see, for example, this post by A Voice for Men’s Typhonblue on the blog GendErratic. Here’s the same claim made into an “infographic” for the Men’s Rights subreddit.

Trouble is, this claim is flat-out false, based on an incorrect understanding of the NISVS data. But you don’t have to take my word for it: the NISVS researchers themselves say the MRA “interpretation” of their data is based on bad math. It’s not just a question of different definitions of rape: the MRA claims are untenable even if you include men who were “made to penetrate” women as victims of rape (as the MRAs do) rather than as victims of “sexual violence other than rape” (as the NISVS does).

I wrote to the NISVS for clarification of this matter recently, and got back a detailed analysis, straight from the horse’s mouth, of where the MRA arguments went wrong. This is long, and a bit technical, but it’s also pretty definitive, so it’s worth quoting in detail. (I’ve bolded some of the text below for emphasis, and broken some of the larger walls of text into shorter paragraphs.)

It appears that the math used to derive an estimated percentage of female rapists … is flawed. First, we will summarize the assertion and what we perceive to be the basis for the assertion.

According to the web links, the “40% of rapists were women” was derived from these two steps:

1) Combining the estimated number of female rape victims with the estimated number of being-made-to-penetrate male victims in the 12 months prior to the survey to conclude that about 50% of the rape or being-made-to-penetrate victims were males;

2) Multiplying the estimated percentage (79%) of male being-made-to-penetrate victims who reported having had female perpetrators in these victims’ lifetime with the 50% obtained in step 1 to claim that 40% of perpetrators of rape or being-made-to-penetrate were women.

None of these calculations should be used nor can these conclusions be correctly drawn from these calculations.

First the researchers clarify the issue of definition:

To explain, in NISVS we define rape as “any completed or attempted unwanted vaginal (for women), oral, or anal penetration through the use of physical force (such as being pinned or held down, or by the use of violence) or threats to physically harm and includes times when the victim was drunk, high, drugged, or passed out and unable to consent.”

We defined sexual violence other than rape to include being made to penetrate someone else, sexual coercion, unwanted sexual contact, and non-contact unwanted sexual experiences. Made to penetrate is defined as including “times when the victim was made to, or there was an attempt to make them, sexually penetrate someone without the victim’s consent because the victim was physically forced (such as being pinned or held down, or by the use of violence) or threatened with physical harm, or when the victim was drunk, high, drugged, or passed out and unable to consent.”

The difference between “rape” and “being made to penetrate” is that in the definition of rape the victim is penetrated; “made to penetrate” by definition refers to cases where the victim penetrated someone else.

While there are multiple definitions of rape and sexual violence used in the field, CDC, with the help of experts in the field, has developed these specific definitions of rape and other forms of sexual violence (such as made to penetrate, sexual coercion, unwanted sexual contact, and non-contact unwanted sexual experiences). We use these definitions to help guide our analytical decisions.

Now the researchers get into the details of the math:

Regarding the specific assertion in question, several aspects of mistreatments of the data and the published estimates occurred in the above derivation:

A. While the percentage of female rape victims and the percentage of male being-made-to-penetrate victims were inferred from the past 12-month estimates by combining two forms of violence, the percentage of perpetrator by sex was taken from reported estimates for males for lifetime (a misuse of the percentage of male victims who reported only female perpetrators in their lifetime being made to penetrate victimization). This mismatch of timeframes is incorrect because the past 12-month victimization cannot be stretched to equate with lifetime victimization. In fact, Table 2.1 and 2.2 of the NISVS 2010 Summary Report clearly report that lifetime rape victimization of females (estimated at 21,840,000) is about 4 times the number of lifetime being made-to-penetrate of males (estimated at 5,451,000).

B. An arithmetic confusion appears when multiplying the two percentages together to conclude that the product is a percentage of all the “rapists”, an undefined perpetrator population. Multiplying the percentage of male victims (as derived in step 1) above) to the percentage of male victims who had female perpetrators cannot give a percentage of perpetrators mathematically because to get a percentage of female rape perpetrators, one must have the total rape perpetrators (the denominator), and the number of female perpetrators of this specific violence (the numerator). Here, neither the numerator nor the denominator was available.

C. Data collected and analyzed for the NISVS 2010 have a “one-to-multiple” structure (where the “one” refers to one victim and the “multiple” refers to multiple perpetrators). While not collected, it is conceivable that any perpetrator could have multiple victims. These multiplicities hinder any attempt to get a percentage of perpetrators such as the one described in steps 1) and 2), and nullify the reverse calculation for obtaining a percent of perpetrators.

For example, consider an example in which a girl has eight red apples while a boy has two green apples. Here, 50% of the children are boys and another 50% are girls. It is not valid to multiply 50% (boy) with 100% (boy’s green apples) to conclude that “50% of all the apples combined are green”. It is clear that only 20% of all the apples are green (two out of 10 apples) when one combines the red and green apples together. Part of the mistake in the deriving of the “50%” stems from a negligence to take into account the inherent multiplicity: a child can have multiple apples (just as a victim can have multiple perpetrators).

D. As the study population is U.S. adults in non-institutional settings, the sample was designed to be representative of the study population, not the perpetrator population (therefore no sampling or weighting is done for the undefined universe of perpetrators). Hence, while the data can be analyzed to make statistical inferences about the victimization of U.S. adults residing in non-institutional settings, the NISVS data are incapable of lending support to any national estimates of the perpetrator population, let alone estimates of perpetrators of a specific form of violence (say, rape or being-made-to-penetrate).

E. Combining the estimated past 12-month female rape victims with the estimated past 12-month being-made-to-penetrate male victims cannot give an accurate number of all victims who were either raped or being-made-to-penetrate, even if this combination is consistent with CDC’s definition.

Besides a disagreement with the definitions of the various forms of violence given in the NISVS 2010 Summary Report, this approach of combining the 12-month estimated number of female rape victims with the 12-month estimated number of male victims misses victims in the cells where reliable estimates were not reported due to small cell counts failing to meet statistical reliability criteria. For any combined form of violence, the correct analytical approach for obtaining a national estimate is to start at the raw data level of analysis, if such a creation of a combined construct is established.

So you’re going to need to go back to the drawing board, MRAs.

What is especially distressing here is that the NISVS data could have been the starting point for a serious discussion of male victims of sexual assault by women, which is a real and often overlooked issue. Unfortunately, MRAs have once again poisoned the well by misusing data in an attempt to exaggerate the purported villainy of women and score cheap rhetorical points.

NOTE: A regular in the AgainstMensRights subreddit approached the NISVS researchers with this same question some months back. Unfortunately, the statement they got back from the NISVS contained an incorrect number. The statement I’m quoting here corrects this number and adds more context.

I can provide contact info for the NISVS representative who got back to me on this to any serious (non-troll) person who requests it.

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Posted on October 29, 2013, in all about the menz, antifeminism, evil women, misogyny, MRA, playing the victim, rape, rape culture, reddit, sexual assault, TyphonBlue and tagged , , , , , , , , . Bookmark the permalink. 507 Comments.

  1. ” (Using ‘working’ figures derived from what is already available helps us to choose the best approach and the ‘best place to look’ to find more accurate figures. We use a Bayesian approach to derive these, as this gives us a figure telling us how correct we are in thinking that the ‘working’ figure is correct (turtles all the way down :) ). I don’t think such an approach is possible in this case though)”

    I was going to claim LessWrongitis, but ze actually seems fairly well versed, I may actually reply.

    Well, I’ll certainly explain here. Adiabat is seeking an explain action why the lifetime data on perpetrator gender cannot be applied to the 12 month data. The answer to which is actually right in the initial question of why there’s such a discrepancy between the lifetime and 12 month data — with a handful of potential reasons so far, it’s impossible to answer that why. And without knowing why there’s such a difference between lifetime and 12 month data for the raw counts of victims, there’s no way to know if whatever is behind that is also affecting the variable of perpetrator gender. That is, without answering the first question (wtf is up with the counts), we can’t reliably guess at what the 12 month data would show for the genders of the rapists.

    I haven’t done an ice cream example yet have I? I’m slacking, stats without ice cream examples *shakes head*

    Example time, and yes, there will be ice cream. So, if we know that over the course of their lifetimes, 30% of women and 15% of men favor chocolate ice cream, but over the last 12 months 30% of men have favored chocolate while the women haven’t changed preferences and we know that over the course of their lifetime, 75% of men like their ice cream with sprinkles (or jimmies, or whatever you call them), can we say that over the last 12 months 22%~ favor chocolate ice cream with sprinkles? (30%*75%). Well no, because first we need to know why chocolate ice cream is so much more popular lately. Either that or survey how may men like sprinkles.

    In any case, you certainly can’t do “well twice as many men like chocolate, so twice as many men like sprinkles”, since, um, 150% of men? That sounds weird, did half of men grow a second head and it likes sprinkles?

    (Note, strawberry, chocolate syrup, no sprinkles :) )

    And adiabat, if you stop by, my genderqueer self uses gender neutral pronouns — ze / zir, not he / him. Thanks!

    …I want ice cream now >.<

  2. @n im sorry i don’t know what an outlier is and how its applied here.

    An outlier is something that stands outside of the average data. Usually it’s a result of extraordinary circumstances. For instance, if you were measuring the exam results of a group of students in order to determine the effectiveness of a particular curriculum, then the results of the best and worst students of that group will probably be outliers. You can’t take a 90% score from the very best student to argue that the curriculum is excellent, nor can you take 40% from the worst to argue that it’s useless, so you either set them aside as special cases rather than representative values, or make sure to count them in with the larger data set, but never use them on their own, since they’re misleading.

  3. An outlier is something that stands

    farther

    outside of the average data

    than makes statistical sense.
    Blerf. Late night word brain. Faily faily. :\

  4. Confession: I read that as resnet the first time, cuz that’s what Pitt calls, well, basically all the other student positions in the IT department, because they do *drum roll* networking stuff in the residence halls (and then there’s a handful of students in the IT office, and idk if my position in software licensing is still a student job, they were trying to get Pitt to okay it as a FT job)

    Outliers…Athwyren is mostly correct, but it depends just how far from the average that 90% and 40% are. It’s a smidge complex, but basically you find the median, and then the median of the top and bottom halves, do some math, and end up with two numbers, one being the low end of the normal distribution! the other being the high end. Anything outside that range is an outlier. So if you have 25 students and the scores go from 40% to 90%, but they are all 2~ points apart, those aren’t outliers. Otoh, if most of those students got 60-70%, and nearly all of them 50-80%, then yeah, 40% and 90% will probably be outliers.

    Sometimes you can just eyeball it though, like if one student on that managed to score 10% and everyone else got 40%+? Outlier.

  5. re outliers: This is why many people who get into CalTech, or MIT, etc. don’t fare well. They spent their lives before being ‘whiz-kids” who, by virtue of talent/good fortune, were well outside the norm in their schools, and didn’t have to work terribly hard.

    When they get to Carnegie-Mellon they discover they 1: aren’t the smartest person in the room, and 2: they have to work to keep up.

    Neither of these is bad (being average in a pool of the incredibly talented means… one is incredibly talented), but either one can be a real shock; both together is sometimes overwhelming.

  6. That kinda sounds fun…I never liked being able to not show up to courses that cost an arm and a leg. Then again, I was usually about the third smartest person in the room (‘crept English, cuz tracking and I can’t spell so lowest track and these people need to be read to, SAVE ME!)

  7. I was also always perfectly happy playing second chair violin, so not being first just doesn’t bother me any. Not being challenged does (for which you are a breath of fresh air btw)

  8. i am growing very frustrated … i saw yet another critique of this article, and ended up finding these two; blackforestgatomon.tumblr.com/post/65809912868/mra-male-rape-statistics-are-wrong, schaka.tumblr.com/post/65820948304/mra-male-rape-statistics-are-wrong
    i cnt believe the conclusion of the first post, 80% of rapists of men are women?! drastically bigger number than previously calculated! and schaka’s rates of both female and male victims in 12-mo. numbers seem inconsistent? i could be seeing this wrong?
    @athywren, argenti thank you i will read up more on the outlier notes later, but i think i have been wasting all your time in my vain endeavor to understand all this, especially when you all seem to be going through troubling events (i didn’t realize how much of a community this site is…) for now i need to rest my head. im really not suited for math

  9. before i forget to ask tomorrow - in adibat’s comment, why do they think lifetime figures are outliers though? and in schaka’s post this stuck out. “The 50% in the last 12 months is referring to men making up 50% of rape victims. Clearly not by their definition, but by the definition of most sane human beings.” does this mean they didn’t combine the two categories of rape and mtp?

  10. why do they think lifetime figures are outliers though

    Because that’s the only way to get the argument they want to make to make any sort of sense. You’re crediting them with far more honesty than they deserve.

  11. The CDC didn’t combine those categories, no. So combining them men made up 50%~ of rape victims in those 12 months…which is why they insist on discounting the lifetime data, where the rate is lower.

    “80% of rapists of men are women?!”

    That one is more or less true. Iirc it was 79%~ of men who had been made to penetrate had been forced to do so by a woman (now, I’m fairly sure there was a stat in there for men who were penetrated and that was largely by other men, but they’ll ignore that, it isn’t convenient right now)

  12. 93.3% of the 1.4% male respondents who reported having been raped by penetration reported a male perpetrator.

    For lifetime figures every 5th rape victim is a man and slightly less than every 5th rape victim is a man raped by a woman (1/5.25). For the last 12 months numbers every second (non-incarcerated) rape victim is a man.

  13. tried dissecting an article on my own! i doubt it worked. http://www.bbc.co.uk/news/magazine-24713110
    1. i understand the sample size issue that didn’t include other nations, but why did ‘a quarter’ terminology bother the author less than ’1 in 4′? do they not mean the same thing?
    2. athywren, argenti when they didn’t include numbers from recently conflcted areas those would be outliers, correct? because they didn’t best represent the average?
    3. the last issue they talked about in the article confused me the most. i know that since rape victims alone already have such a hard time coming out about their experiences, certainly people who knowingly commited rape would be even harder to draw out, so that was why they worded the question that way. but would its ambiguity affect the nature of the answers? i also saw a video of someone raising questions about rape studies in the united states; could this be the same thing?
    and i want to thank everyone so far who have been very patient with my lack of knowledge. its hard but i feel very motivated to study harder because of your assistance.

  14. @argenti, just curious, the ‘inconvenient’ stat of majority of male victims raped by men is also of a lifetime figure?

  15. Yes, the 12 month number was too small to be statistically reliable. And I’ll review your link in a bit, I need coffee to process Teh Maths :)

  16. Oh and don’t worry about asking questions, I’m happy to answer stats questions. I spent ages offering to teach MRAs how not to kill math, with no takers, so people who actually want to learn? Ask away!

  17. 1) I’m assuming you’re referring to these quotes -

    “‘Nearly a quarter of men interviewed reported perpetrating rape against a woman or girl.’”

    “”One in four men across Asia admit to having committed rape.” This statistic was widely reported around the world, following the publication of a UN study. Could that possibly be the case?”

    The issue isn’t 1 in 4 versus 25%, it’s “in Asia” versus “of men interviewed”. So you’re riht that the sample size is the issue — it just isn’t representative enough to say it applies to all of Asia, just the interviewed men.

    2) Yes. Areas experiencing civil conflict or war almost always have higher rape rates than though in a (relative) peacetime.

    3) The issue isn’t about whether they’d admit to it, the issue is that the women may’ve “consented” because they also felt that having sex was their wifely duty. That is, it may reflect oppressive gender roles better than rapists. In the US, Canada, UK, etc, that would be called rape now, but in the US, until a few decades ago, you couldn’t rape your wife — you were legally entitled to sex from her whenever you wanted. If that’s the case in the areas studied, that question doesn’t tease out men who coerced her from men who simply went along with the gender roles they’d been raised wih. The latter is still wrong, but reflects on gender roles, not rape, and that question conflates the two.

    I’d need to see the video on the US studies to comment on that though, sorry.

    Also, could you capitalize at least the beginning of your sentences? It’d make it a bit easier to follow what you’re asking :)

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