Slandering with Statistics

One thing that I keep getting mail about is various folks misusing statistics. There are a lot of examples of this, from young earth creationists, to the intelligent design bozos that I've spent too much time on, to various racist assholes, to HIV/AIDS denialists.

A link to a comment from another blog posted by a racist asshole trying to argue that the accuser in the Duke Rape case is probably lying is an example of a kind of misuse of statistics that I haven't talked about yet, so I thought it was worth taking a moment to look at it.

So here's what the asshole had to say:

Unfortunately, statistically a black women is significantly more likely to make a false accusation of rape than to have been raped by a white man. According to the National Crime Victimization Survey ( http://www.ojp.usdoj.gov/bjs/pub/pdf/cvus/current/cv0342.pdf ), less than .0004% of black rape victims were raped by whites. (The NCVS reports the percentage as 0% because there were less than 10 reported cases. I assumed 9 cases, to come up with an actual percentage) Even with the most conservative figure of 2% of rape allegations being false, this means in the case of the Duke Rape Case, the victim is 5000 times more likely to have made a false accucation than to have actually been raped.

Before I hit the real point, I'll point out that there's a really dumb math error in there: it's not "0.0004%"; it's "0.04%". Yeah, sure, we're still talking about small numbers, but two orders of magnitude is nothing to sneeze at, and it shows either how little concern the writer has for the facts; or it's a deliberate attempt to dishonestly skew the numbers by adding a percent sign.

But what's really important are the errors in how he uses statistics. He's making two major errors. One is a sampling error in producing a meaningful statistic; and one is an error in how you can apply a statistical result.

Statistics are a way of analyzing large quantities of data to understand patterns and trends, and they're very useful for that. But you have to understand what a statistic means and how it was gathered in order to know when it can be applied. In general, statistics are useful when they are generated from a large enough pool of correctly sampled data; statistics can be meaningfully applied to data in the aggregate (applying broad statistical trends to individual cases is rarely enlightening).

Now, in the above quoted gunk, the writer admits that the size of the sample from which he is extrapolating is vanishingly small in the data. You cannot generate anything meaningful from such a small sample: that "0.04%" number is basically just made up - it has no validity, no statistical meaning.

That's not the only sampling error that he makes. Even if there were enough data in the survey that he cited to draw some conclusion, you have to recognize the properties of the data that you're working with - the nature of the sample, and what, if any, data skew you would expect to see.

Whites raping blacks is something with a long history in America. We know that historically, it was extremely common. We also know that there is a significant social factor to this kind of crime: the usual dynamic of it is a poor black woman raped by a comparatively wealthy white man. In this dynamic, the victim is, at best, going to be socially stigmatized by coming forward. (For example, do you think that the black woman who had Jesse Helms' illegitimate daughter could have come forward and said he raped her? Do you think that the poor black "servant" in Helms childhood home actually wanted to have sex with him?) What this means is that because of the social environment, crimes like white-on-black rape are very likely to be under-reported.

This is a property of the sampling of the data. It's based on reported crimes; and we know that rape is a chronically under-reported crime, and that there are good reasons to suspect that the under-reporting is especially pronounced in the cases of black victims with white perps. So when we use that data, we need to recognize the sampling bias in it - and consider that when we use the data to draw conclusions.

You cannot use crime report statistics without recognizing the biases that are a natural part of the reporting process that generates those statistics. We know that the data are very likely to be flawed when it comes to this subject; to then use a microscopic subset of the flawed data and try to apply it to an individual case to purportedly say something meaningful - that's just nonsense.

But that's exactly what our little racist buddy does: he creates a meaningless number from a meaninglessly small sample of data with a known bias, and tries to combine it with other statistics to come up with a number that he can use in an argument.

Then he tries to apply the statistic that he generated. One of the very important properties of statistics is that they talk about populations, not individuals. The average american family has often been cited as having something around 2.7 children. You can't use that statistic to say that a particular family probably has two and two-thirds children.

But again - that's exactly what he does: he creates a nonsense statistic, and then applies it to a specific individual to argue that we should believe that she is lying.