[statistics for the people, and of the people]

I just can’t seem to escape sexual assault. For the span of six months I analysed the Stollznow/Radford case, then finished an examination of Carol Tavris’ talk at TAM2014, so the topic never wandered far from my mind. I’ve bounced my thoughts off other people, sometimes finding support, other times running into confusion or rejection. It’s the latter case that most fascinates me, so I hope you don’t mind if I write my way through the confusion.

The most persistent objection I’ve received goes something like this: I cannot take population statistics and apply them to a specific person. That’s over-generalizing, and I cannot possibly get to a firm conclusion by doing it.

It makes sense on some level. Human beings are wildly different, and can be extremely unpredictable because of that. The field of psychology is scattered with the remains of attempts to bring order to the chaos. However, I’ve had to struggle greatly to reach even that poor level of intellectual empathy, as the argument runs contrary to our every moment of existence. This may be a classic example of talking to fish about water; our unrelenting leaps from the population to the individual seem rare and strange when consciously considered, because these leaps are almost never conscious.

Don’t believe me? Here’s a familiar example.

P1. That object looks like a chair.
P2. Based on prior experience, objects that look like chairs can support my weight.
C1. Therefore, that object can support my weight.

Yep, the Problem of Induction is a classic example of applying the general to the specific. I may have sat on hundreds of chairs in my lifetime, without incident, but that does not prove the next chair I sit on will remain firm. I can even point to instances where a chair did collapse… and yet, if there’s any hesitation when I sit down, it’s because I’m worried about whether something’s stuck to the seat. The worry of the chair collapsing never enters my mind.

Once you’ve had the water pointed out to you, it appears everywhere. Indeed, you cannot do any action without jumping from population to specific.

P1. A brick could spontaneously fly at my head.
P2. Based on prior experience, no brick has ever spontaneously flown at my head.
C1. Therefore, no brick will spontaneously fly at my head.

P1. I’m typing symbols on a page.
P2. Based on prior experience, other people have been able to decode those symbols.
C1. Therefore, other people will decode those symbols.

P1. I want to raise my arm.
P2. Based on prior experience, triggering a specific set of nerve impulses will raise my arm.
C1. Therefore, I trigger those nerve impulses and assume it’ll raise my arm.

“Action” includes the acts of science, too.

P1. I take a measurement with a specific device and a specific calibration.
P2. Based on prior experience, measurements with that device and calibration were reliable.
C1. Therefore, this measurement will be reliable.

Philosophers may view the Problem of Induction as a canyon of infinite width, but it’s a millimetre crack in our day-to-day lives. Not all instances are legitimate, though. Here’s a subtle failure:

P1. This vaccine contains mercury.
P2. Based on prior experience, mercury is a toxic substance with strong neurological effects.
C1. Therefore, this vaccine is a toxic substance with strong neurological effects.

Sure, your past experience may have included horror stories of what happens after chronic exposure to high levels of mercury… but unbeknownst to you, it also included chronic exposure to very low levels of mercury compounds, of varying toxicity, which had no effect on you or anyone else. There’s a stealth premise here: this argument asserts that dosage is irrelevant, something that’s not true but easy to overlook. It’s not hard to come up with similarly flawed examples that are either more subtle (“Therefore, I will not die today”) or less (“Therefore, all black people are dangerous thugs”).

Hmm, maybe this type of argument is unsound when applied to people? Let’s see:

P1. This is a living person.
P2. Based on prior experience, living persons have beating hearts.
C1. Therefore, this living person has a beating heart.

Was that a bit cheap? I’ll try again:

P1. This is a person living in Canada.
P2. Based on prior experience, people living in Canada speak English.
C1. Therefore, this person will speak English.

Now I’m skating onto thin ice. According to StatCan, only 85% of Canadians can speak English, so this is only correct most of the time. Let’s improve on that:

P1. This is a person living in Canada.
P2. Based on prior experience, about 85% of people living in Canada speak English.
C1. Therefore, there’s an 85% chance this person will speak English.

Much better. In fact, it’s much better than anything I’ve presented so far, as it was gathered by professionals in controlled conditions, an immense improvement over my ad-hoc, poorly-recorded personal experience. It also quantifies and puts implicit error bars around what it is arguing. Don’t see how? Consider this version instead:

P1. This is a person living in Canada.
P2. Based on prior experience, about 84.965% of people living in Canada speak English.
C1. Therefore, there’s an 84.965% chance this person will speak English.

The numeric precision sets the implicit error bounds; “about 85%” translates into “from 84.5 to 85.5%.”

Having said all that, it wouldn’t take much effort to track down a remote village in Quebec where few people could talk to me, and the places where I hang out are well above 85% English-speaking. But notice that both are a sub-population of Canada, while the above talks only of Canada as a whole. It’s a solid argument over the domain it covers, but adding more details can change that.

Ready for the next step? It’s a bit scary.

P1. This is a man.
P2. Based on prior experience, between 6 and 62% of men have raped or attempted it.
C1. Therefore, the chance of that man having raped or attempted rape is between 6 and 62%.

Hopefully you can see this is nothing but probability theory at work. The error bars are pretty huge there, but as with the language statistic we can add more details.

P1. This is a male student at a mid-sized, urban commuter university in the United States with a diverse student body.
P2. Based on prior experience, about 6% of such students have raped or attempted it.
C1. Therefore, the odds of that male student having raped or attempted rape is about 6%.

We can do much better, though, by continuing to pile on the evidence we have and watching how the probabilities shift around. Interestingly, we don’t even need to be that precise with our numbers; if there’s sufficient evidence, they’ll converge on an answer. One flip of a coin tells you almost nothing about how fair the process is, while a thousand flips taken together tells you quite a lot (and it isn’t pretty). Even if the numbers don’t come to a solid conclusion, that still might be OK; you wouldn’t do much if there was a 30% chance your ice cream cone started melting before you could lick it, but you would take immediate action if there was a 30% chance of a meteor hitting your house. Fuzzy answers can still justify action, if the consequences are harsh enough and outweigh the cost of getting it wrong.

So why not see what answers we can draw from a sexual assault case? Well, maybe because discussing sexual assault is a great way to get sued, especially when the accused in question is rumoured to be very litigious.

So instead, let’s discuss birds…

[HJH 2015-07-19: Changed a link to point to the correct spot.]