Posted by Eugene Volokh:
Research on False Rape Reports:

   I've been doing some reading on the debate about the incidence of
   false rape reports. I've looked at a lot of studies on this, and hope
   to blog some more about it later (short summary: estimates range from
   under 2% to 40+%, though I have no opinion about which is right). But
   in the meantime, I thought I'd mention one observation that may be
   helpful for thinking about other debates as well.

   Many people who believe that false rape reports are a tiny fraction of
   all rape reports argue that very few women would make such false
   reports. The common line is that women don't lie about rape, which
   must really mean that very few women lie about rape.

   But even if this is true -- and I strongly suspect that it is -- this
   is entirely consistent with the possibility that a substantial
   fraction of rape reports are false. Let's say, for instance, that only
   2% of all women age 16-19 would ever lie about rape; and that any
   particular year, only 2% of that tiny fraction actually do falsely
   report a rape to the police. So 98% of all women (including relatively
   young and not very mature women) would never lie about rape, and even
   of those who might under the right circumstances, most never will. (I
   use the 16-to-19 age group because the risk of rape is highest there;
   the same analysis could apply, though, to other age groups.)

   There are, however, about 8 million women in the 16-to-19 age group in
   the U.S., and 2% x 2% x 8 million = 3200 false rape reports per year.
   The [1]National Crime Victimization Survey (2002 data, see table 3)
   reports that 2.7 out of 1000 people age 16 to 19, which means 5.4 out
   of 1000 women age 16 to 19, are raped each year. This is an estimate
   based on a survey, not on police reports, and it may well be low (the
   actual rate may be higher); but in any event, we know that the rate of
   rapes reported to the police is roughly half that estimated to the
   NCVS (compare the [2]Uniform Crime Reports data, and remember that the
   UCR data aggregates rapes and attempted rapes, while the NCVS breaks
   them out). This means that roughly 2.7 out of 1000 women age 16 to 19
   report an actual rape each year, for a total of 2.7/1000 x 8 million =
   21,600 true rape reports per year.

   Under this model, then, 13% of all rape reports to the police would be
   false (in the 16-to-19 age group), even though only 2% of all women in
   that age group would ever make a false rape report, and only 2% of
   those actually make a false rape report each year. Ninety-eight
   percent of all women may be completely truthful on this subject, and
   yet we may still have a substantial false rape report rate.

   This, of course, is just a model, based on numbers picked out of thin
   air. Maybe, for instance, the fraction of women who'd ever make a
   false rape report is much lower than 2%, or maybe it's higher. We
   can't know for sure.

   But the model does illustrate that it's perfectly possible to believe
   that (1) only a tiny fraction of women would ever lie about being
   raped, (2) a huge fraction of rapes are unreported (quite possibly
   even more than 50%, so that rape may be a highly underreported crime
   by many women, as well as overreported by a few), and yet (3) a
   substantial fraction of rape reports to the police are false.

   Some people who worry about false rape reports may in fact believe
   that women are psychologically wired to lie about such things; I'm
   certainly not one, but historically that has been the view of some, to
   which others have understandably reacted with hostility. That may be
   why some people take the opposite view: Instead of "women often lie,
   so the false rape report is very high," they say "women very rarely
   lie, so the false rape report is very low." But that doesn't follow.
   False rape reports, however rare they may be as a fraction of all
   women might still be substantial as a fraction of all rape reports.

References

   1. http://www.ojp.usdoj.gov/bjs/pub/pdf/cvus02.pdf
   2. http://www.fbi.gov/ucr/cius_02/pdf/02crime2.pdf

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