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A recent survey in the UK claims that about 10% of women have been raped but that most do not report the incident even to friends. In the words of one news report:

One in 10 women has been raped, and more than a third subjected to sexual assault, according to a major survey, which also highlights just how frightened women are of not being believed. More than 80 per cent of the 1,600 respondents said they did not report their assault to the police, while 29 per cent said they told nobody – not even a friend or family member – of their ordeal.

Wikipedia's summary suggests similar numbers in the USA and some other countries but there is a huge discrepancy between officially recorded numbers and the numbers reported in anonymous surveys. The gap between officially recorded rape and what the surveys suggest is partially a result of statistical misunderstandings (official figures tend to report incidence (rapes per year) whereas surveys report lifetime prevalence (number of people who have ever been raped at any time in their life)). But, even taking the statistical confusions into account the reported numbers are much smaller than the numbers implied from anonymous surveys.

So, given the size of the gap between official numbers and the survey results, which is right?Are these recent estimates that one in ten women have experienced rape credible?

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    @Sklivvz: Exactly. Note that Wikipedia also talks about attempted rape, but I still don't see how this gets us to 10% or more (except for the worst possible countries). My guess is that estimates of unreported cases play a big role here. – Hendrik Vogt Mar 14 '12 at 17:01
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    @Sklivvz In the wikipedia page section on the usa there is the following quote "1 of 6 US women has experienced a completed or attempted rape" (sorry, can't link from this computer). I should have made the distinction between recorded official numbers and reported survey numbers clearer. – matt_black Mar 14 '12 at 17:09
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    One has to be careful about what definition of "rape" is used when making these kinds of assertions. Some of the larger numbers use a very inclusive definitions., as compared to the official crime statistics which are relatively exclusive in the way they define the term. Perhaps posters should be explicit. – dmckee Mar 19 '12 at 0:38
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    What sort of evidence would you find convincing, in either direction? We could quote from official numbers, but that wouldn't help. We could quote from surveys, but that wouldn't help. I don't believe there is any "gold standard test", so I don't know what evidence could be offered here. – Oddthinking Mar 19 '12 at 0:43
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    @Oddthinking I'd like to see some discussion of the methods used for all the numbers, official and survey. If it turns out that the surveys use robust definitions of rape and are conducted on representative samples in a statistically reliable way, then I'd be more inclined to trust the results. Same for official stats. For something as important as rape, I'd like to know the numbers were not deliberately exaggerated by poor statistical choices. – matt_black Mar 19 '12 at 12:54
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The 10% quoted in the British survey is not credible because of how the survey was conducted, but reliable numbers might be as high as 4%

The original survey that prompted the Question was conducted by UK campaigning website Mumsnet as part of their Rape Awareness Campaign. Unfortunately their good intentions are undone by bad survey design and some statistical illiteracy in how they quote their results.

The situation is analysed here and here by UK fact checkers Straight Statistics. The first problem is that the survey was not a properly conducted random sample but a self selecting voluntary survey. This is always a major source of bias but a good way to back up campaigns when you are less than choosy about the statistical rules. As Straight Statistics says:

The Mumsnet survey is part of a campaign called We Believe You. I certainly don’t disbelieve Mumsnet’s respondents, as it’s unlikely they are making it up. But I don’t believe that any self-selected survey of this sort provides a basis for reaching any conclusion at all.

But they also showed some illiteracy when adding up their numbers. In the second comment in Straight Statistics the problems is explained like this:

I overlooked the very strange way in which the survey was reported by Mumsnet. The PDF of the survey results on the Mumsnet website shows one question that read as follows:

mumsnet results table from Straight statistics

Mumsnet reported this as 10 per cent reporting having been raped and 35 per cent sexually assaulted. But this ignores the third answer, those who have suffered both rape and sexual assault. Taking this into account, the true figure should be that 27 per cent have been raped and 52 per cent sexually assaulted, with only 38 per cent experiencing neither. Even worse than Mumsnet claimed! The figures make it even more unlikely that the responses represent a true representation of women’s experiences, but the survey was widely reported, using the headline figures in the Mumsnet press release.

So they underreported the answer but didn't give a convincing account of their statistical skills.

To put this in perspective Straight Statistics quote the results of a more reliable source:

The best data we have, from the British Crime Survey (BCS), suggests this is an overestimate. The latest bulletin on Homicides, Firearm Offences and Intimate Violence, published in January, indicates (Table 3.01) that 3.7 per cent of women report having been raped since the age of 16 (4.5 per cent if attempted rape is included), and 18.6 per cent report having experienced any form of sexual assault – around half the proportions reported by Mumsnet.

The BCS figures come from a properly-chosen sample of more than 6,000 women. The Mumsnet results come from “write-in” responses on its website from 1,609 women.

To me the much more reliable BCS results are still disturbingly high and the mumsnet survey just muddied the waters by exaggerating by bad survey design. Newspapers mostly swallowed the numbers with little critique or reference to previous, better, work. On topics as important as this they should have done a better job.

  • It occurred to me just after I wrote this that a similar analysis of the USA surveys would be good. I'll leave that to others to provide a chance for someone else to post the accepted answer. – matt_black Mar 27 '12 at 19:59
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    Not to sound insensitive, but I feel that the definition of "sexually assaulted" varies by culture. In many workplaces (at least in America, I can't speak for others), sexual assault could be as simple as brushing against someone. I find these sources and conclusion to be credible, and a good point of reference, but the skeptic in me feels there may be a very finite vision for the definition of "sexually assaulted" that could potentially pollute to waters for those who have an ACTUAL assault. My conclusion comes from the "Any form" part of the blocked text. – Anoplexian - Reinstate Monica Apr 29 '16 at 17:02
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For a brief summary of the relative merits of victim surveys and official crime statistics (in this case related to Australian data) you might like to check out this website:

enter image description here

http://www.aifs.gov.au/acssa/statistics.html

It contains links to relevant stats and information about research methodology, sampling etc.

Obviously not all 'surveys' (and therefore all stats) are equally reliable or scientific, however I assume that you will be able to find US and UK sources (check out government statistics bodies and government criminology bodies) that are as sound and scientific as those conducted on behalf of the Australian government at the above link.

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    Note: This infographic talks about sexual assault, which is a broader crime than rape. – Oddthinking Mar 1 '15 at 22:19

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