Two weeks ago I cited two well-known statistics to you. Well, at least they’re well-known to me. The first was:
1 in 5 women will be the victim of some sort of sexual assault.
The second one, from my 19 years of teaching, was:
5% of the students cause 95% of the problems.
I also said that the first statistic did not necessarily imply that 20% of all sexual encounters between women and men involved some sort of assault.
Today is where I show you how that works, by looking at 20 women and 200 dates.
Now before I start out, let me just say that the information I present here is not going to be done to the same rigorous standards that it would be if it were done by a certain statistician I know, but it should be enough to make my point.
We’re going to start off with a set of 20 women, labled F1 through F20, and have them each go out with 10 men over the course of a number of years, thus giving us a total of 200 dates. The 10 men each woman goes out with may or may not be from the same set, since people move around a lot. This means that there could be as many as 200 different men involved or there could be some overlap. It really doesn’t matter.
What does matter is that 5% of the up to 200 different guys are assholes who don’t know the meaning of the word “no”, and that they will cause problems for four of the 20 women. With 200 dates, that means that a chart of the women and dates would look like the one below:
So while 20% of the women have dealt with some form of sexual assault on a date, 96% of the dates…and possibly guys…are just fine.
Now let’s take a look at what the statistic isn’t saying, but could easily be misunderstood to mean. It most definitely is not saying that 20% of all dates go horribly wrong. If that were true, then the chart would look like this one:
Now, notice that even though one fifth of all dates here ended up with some sort of assault, the assaults weren’t evenly distributed. F1 only had one date that resulted in an assault, and F17 got off scot free. On the other hand, F20 was a very unlucky woman.
So now that we know what it is and what it isn’t, we’re faced with two possibly conflicting sets of statistics: The first says that 20% of all women will have to deal with an incident of sexual assault. The second says that 96% of all dates are just fine.
If you’re a woman, which set of stats should you let guide your life?
As a person who knows that flying is statistically the safest way to fly, but whose favorite airline is Amtrak, and hasn't flown since 1987, I don’t really have an answer to that.