Rape statistics: a case study in public flim-flam
<p>A commenter on a recent thread claimed &#8220;the lifetime risk of rape for a woman [in the U.S.] is one in six&#8230;Almost everyone who deals with the issue considers that wildly too low to be realistic. But one in six is indisputable.&#8221;</p>
<p>No incidence of rape above zero is acceptable to me.  I teach women pistol self-defense at no charge.  You may correctly infer my motives from the fact that the first time a female student of mine shoots a good tight center-of-mass group,  my normal mode of expressing approval is to say &#8220;That&#8217;s one dead rapist!&#8221;</p>
<p>Accordingly, I found this claim so disturbing that I decided to research it.  What I found appears to be a classic case of unreliable statistics being oversimplified through rumor, hysteria, the telephone effect, and self-serving inflation.</p>
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<p>Where not cited, numbers are from the <a href="http://en.wikipedia.org/wiki/Rape_statistics#United_States">Wikipedia page on rape statistics</a>.</p>
<p>I found the first layer of flimflam almost immediately.  The public source of the 1 in 6 number is probably the Colorado Coalition Against Sexual Assault, which actually said 1 of 6 U.S. women has experienced an attempted or  completed rape.  </p>
<p>The inclusion of &#8220;attempted&#8221; rape is a clue that games were played to inflate the significance of this statistic by people using or passing it along. There are actually two levels of distortion here: one in which the categories of attempted and completed rapes are merged, and a second which trades on the listener&#8217;s tendency to equate &#8220;rape&#8221; with &#8220;forcible rape&#8221;.</p>
<p>In 2005, there were according to the USDOJ 191,670 reports of &#8220;rape or sexual assault&#8221; in the U.S.  This is a larger category than rape or even rape plus  attempts, but I&#8217;ll go with it for a first approximation most generous to CCASA.</p>
<p>In evaluating numbers derived from this  the USDOJ figure, note that The Rape, Abuse &#038; Incest National Network defines sexual assault as &#8220;unwanted sexual contact that stops short of rape or attempted rape. This includes sexual touching and fondling&#8221;.  I note that it can also include statutory rape, a notoriously elastic category which can include consensual sex between minors of similar ages.</p>
<p>The U.S. Bureau of Justice Statistics (1999) estimated that 91% of rape victims are female and 9% are male.  Thus, I estimate from the USDOJ statistic that there were 174,419 reports of incidents against women in 2005.</p>
<p>The U.S. Department of the Census gives the U.S. population in 2005 as  296,410,404. According to the CIA World Factbook the M/F ratio in the U.S is 0.97 male/female, so women comprised 157097514 people in that population.</p>
<p>In 2005, then, we can approximate a woman&#8217;s risk of being the victim of  a reported rape or sexual assault as 0.0012.  Now, how does this convert to a lifetime risk?</p>
<p>I have included women at all ages in the population used to calculate the raw incidence, so I&#8217;ll simply multiply by the average female lifespan of 78 years.  The thing to note is that if we picked an age range to restrict to  the result we want would not change, as it would shrink the multiplier and the  baseline population in the same way.  So we get a lifetime incidence rate of 0.0936, or 9.3%.  This is a rate of 1 in 11.</p>
<p>I found a web page on forcible rape rates from the <a href="http: //www.allcountries.org/uscensus/336_forcible_rape_number_and_rate.html">2000 U.S. census</a> that implies an incidence of forcible rape in 1982 (the latest year they list) of 66.2 per 100K females, implying a forcible rape figure per annum risk 0.0006.  This implies a lifetime incidence of 0.0468, implying a lifetime rate of about 1 in 23.</p>
<p>According to the National Crime Victimization Survey, the most recently available rape victimization rate is 0.4 per 1000 people.  Applying the  0.91 percentage of female rape victims corrects this to 0.364 per 1000, implying a lifetime incidence of 3.64 and a rate of 1 in 27 (note &#8211; I previously bobbled this and got a 1 in 29 rate.). </p>
<p>But what about underreporting&#8230;and, for that matter, overreporting? The National Crime Victimization Survey (NCVS) said only 39% of rapes and sexual assaults were reported to officials.  But one 1994 study in the U.S. found overeporting of 41%. A vociferous critic of that study estimated overreporting at 5.9%, and a study in Great Britain found a false-allegation rate of 8%.  </p>
<p>The methodology of studies on underreporting and overreporting of rape is notoriously dispute-prone. For a first approximation I will combine assumptions 39% underreporting and 5.9% overreporting to reach an estimate of the the ratio between reported and actual crimes. There are reasons to suspect this is quite generous to rape alarmists, but I&#8217;ll do it anyway in order to generate the largest reasonable incidence numbers.</p>
<p>(r + r*0.61) &#8211; r*0.59 = r*1.00 + r*0.61 &#8211; r*0.059 = r * 1.551</p>
<p>How does this change our figures?  From the DOJ statistics we reach a lifetime incidence of 14.41% and rate of 1 in 7.  From the census data on forcible rapes, a lifetime incidence of 0.0725 and a lifetime rate of 1 in 14.  From the NCVS, a lifetime incidence of 0.564 and a lifetime rate of 1 in 18.</p>
<p>None of these figures are compatible with &#8220;1 in 6 women will be raped&#8221;, and those least corrupted by definitional flimflam are the least compatible. </p>
<p>UPDATE:  I am revising the end of this post, because I am persuaded that one of my formulas  was in error.  I will preserve the original ending in a comment.</p>
