[Disclaimer: This post contains speculation based on wild guesses and back-of-the-envelope calculations, and therefore shouldn’t be taken too seriously.]
Last month, there was some discussion in the blogosphere about the alleged Star Trek-pedophile connection. According to an article in the L. A. Times (no longer available online), detectives in the Toronto sex crimes unit had noticed that “All but one of the [over 100] offenders they have arrested in the last four years was a hard-core Trekkie.”
So, what does this tell us about Star Trek fans? Jokes aside, most commentators have emphasized what it doesn’t tell us. Even if all pedophiles were Trek fans, we could not logically conclude that all Trek fans are pedophiles. Said the article’s original author, “It is important to note that they are not saying that every Star Trek fan is a pedophile -- just that it was a surprisingly common element among those they had arrested.”
But that’s needlessly all-or-nothing thinking. We can’t say anything with certainty about Trek fans’ sexual tendencies, but we can make judgments of probability. The question is this: Given that someone is a hard-core Trek fan, what is the probability that he is a pedophile?
We can address this question through an application of Bayes’ Rule. We also need some other statistics: the percentage of the whole population who are pedophiles, and the percentage of the non-pedophiles who are Trek fans. These are both rather difficult to estimate.
I couldn’t find an estimate of what fraction of the public is pedophile; no one wants to commit to a figure. But based on the number of men surveyed who say they were sexually abused in their youth (about 16%) and the average number of victims per sexual abuser (about 100 victims each, according to a website I can’t find anymore), we can guess that about 0.08% of people are sexual abusers of male children. Doing the same with numbers for female victims (27% of women sexually abused in youth, 20 victims per abuser), about 0.675% of people are sexual abusers of female children. Assuming the two groups don’t overlap, we can figure 0.755% of people is a sexual abuser of children. Allowing for some overlap, I’ll round down to 0.5%, or one person in 200. I will call these people “pedophiles.” [UPDATE: I realized later that I've assumed an impossible amount of overlap, so the pedophile-percentage should be larger. That would result in an even bigger estimate of the probability a Trek fan is a pedophile.] (Lots of assumptions are built into these calculations, so take them with a grain of salt.)
So what about the fraction of the non-pedophiles who are Trek fans? This one’s even more difficult to estimate. We can approximate it with the fraction of general public who are Trek fans (since pedophiles are so rare). As many as 50% of Americans claim to be Trek fans – but we’re not interested in just run-of-the-mill fans; we need the kind of fans who would have Trek paraphernalia in their homes for detectives to discover. I’m going to make a wild stab and say 1%. That’s probably too high. But assuming a large number here will give us a conservative estimate of the probability that a Trek fan is a pedophile.
Now for the calculations. Say we have a population of 100,000 people. Of those people, 99,500 are normal and 500 pedophiles. Since 1% of the normals are Trek fans, we have 995 normal Trek fans. Since 99% of pedophiles are Trek fans (according to the Toronto detectives), we have 495 pedophile Trek fans. So the fraction of all Trek fans who are pedophiles is 495 / [495 + 9950] = 0.332. That is, almost a third of hard-core Trek fans are pedophiles!
Now, just to be clear, there’s still a 67% chance your Trekker neighbor is perfectly normal (in the sense of not molesting kids). On the other hand, 33% is 66 times larger than the chance a non-Trekker is a pedophile. If it makes you feel any better, keep in mind that we’re only taking about hard-core Trekkers here.
My calculations are highly sensitive to the assumptions, particularly the percent of the general public who are pedophiles. If you’d like to redo the calculations using your own assumptions, here’s the formula:
ac / [ac + (1 - a)b]where a = fraction of general public who are pedophiles; b = fraction of the non-pedophile public who are Trek fans; and c = fraction of pedophiles who are Trek fans. My calculations assumed a = 0.005, b = 0.01, and c = 0.99.
I welcome corrections to my calculations, since I’d rather not be suspicious of my Trek-loving friends.
5 comments:
I don't see on what basis you're estimating the percentage of non-pedophiles who are Trekkies. Since people's pedophile-identity is relatively private, it seems that you would be in a much better position to estimate the percentage of all people (or all adult males) who are Trekkies. This would also simplify the calculation, since if there are q Trekkies and p pedophiles out of every 100,000 people, and (almost) all pedophiles are Trekkies, then the proportion of Trekkies who are pedophiles is (almost) p/q.
That number of Trekkies, q, is still difficult to estimate, largely because the articles are so vague about what level of Star Trek fanhood is necessary to qualify as a Trekkie. They give a few anecdotes of hard-core fans with weird Trekkie paraphrenalia, but there are some suggestions that milder types of fanhood (e.g. owning at least one Star Trek video) qualify. Combined with Z's objection about the non-random sampling procedure, this suggests that your precision is highly misleading and your result is likely an overestimate of the percentage of Trekkies who are pedophiles. So you can have some more faith in your Trek-loving friends, and don't put too much stock in the Trekophile connection until they come out with some more carefully collected data.
Z -- Your first point (about non-random sting operations) is very well taken, and is one of many reasons my calculations here shouldn't be taken too seriously. On the other hand, your second point (about socially-maladjusted people) strengthens the case for a Trek-ped connection. Indeed, that's probably the causal explanation behind the correlation.
Blar -- Actually, I *did* estimate the percentage of non-pedophiles who are Trekkies by using the percentage of the population as a whole. As I said in the post, "We can approximate it with the fraction of general public who are Trek fans (since pedophiles are so rare)." You are right, of course, that it would be silly to reach strong conclusions without better data -- hence the disclaimer at the top of the post. However, the formula provided at the bottom allows you to pick whatever assumptions you want.
Lee -- It was quasi-debunked. The detectives admitted that 99% figure was probably an exaggeration, but they stuck by the claim that a surprisingly large number of their perps were Trek fans. Follow the links at the top of the post for more. If you want to see what happens estimates lower than 99%, just plug them in the formula at the bottom.
Glen, if Trekkies are almost as rare as pedophiles and the overlap between the two groups is large, then you cannot estimate the fraction of non-pedophiles who are Trekkies with the fraction of general public who are Trekkies. IF 1% of non-pedophiles are Trekkies, you get that about 1/3 of Trekkies are pedophiles. But with 1% of the general public Trekkies, that fraction increases by 50%, all the way up to 1/2.
You could estimate the fraction of the general public who are Trek fans, calculate the percent of non-pedophiles who are Trek fans (instead of approximating it poorly), and then apply Bayes' rule, but the answer would simplify to the formula I suggested earlier, c(p/q), where c is as you defined it and p & q are as I defined them.
Blar -- Okay, I see your point now. You're right. So I wonder what fraction of the non-pedophile public are Trek fans? That's the number I need. Of course, I totally made up the 1% figure for Trek fans in the general public, so I can just as easily make the same unfounded assumption for the non-pedophile public.
As I said from the beginning, none of this was meant to be taken too seriously. But if there's anything serious to be gotten from it, it's that Bayes' Rule supplants the all-or-nothing logic of (A --> B) =/=> (B --> A).
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