Mathematical Malpractice: Spree Killings Again

This analysis, which claims that the US has more school spree killings than 36 nations combined, is getting a lot of play. It shouldn’t. It is extremely bad mathematical malpractice.

The basic reason it is mathematical malpractice is the same reason the Mother Jones study was: it is difficult to analyze extremely rare events. When you narrow your investigation to events that happen maybe once a decade and are compiled haphazardly, you are simply going to be dominated by small number statistics and selection bias. You can therefore use those numbers to say, basically, anything you want.

Let’s break down just how bad the numbers are being twisted here.

1) The sample ends in 2009. That excludes the recent spate of knife attacks in Chinese schools that have left 21 dead. If you did this analysis a week ago, you would have had to drop China from the right column.

2) The sample excludes acts of terror or war. But if Islamists shoot up a school because they don’t want girls to read, are those kids any less dead? If a drone strike misses its targets and kills a classroom, are those kids less dead? Why must we exclude the Beslan attack that left 186 kids dead?

3) The sample excludes single homicides, which amount to 302 deaths in the United States over the time involved and God knows how many in other countries. So you are literally excluding 90% of the problem and focusing just on a tiny subset of killings.

4) Comparing us to 36 other countries is ridiculous when some of those countries are places like Bosnia-Herzegovina (population 4 million). We have more population, period, then 30 of the countries on that list combined. Also included in that list of countries are England, Scotland and Northern Ireland, which are, technically speaking, not countries.

5) The problem of small number statistics can be best illustrated by playing with the data a bit. If I include the knife attacks and move China into the left column, suddenly China has more violent deaths than 30 other countries. If I move Germany onto the left side, suddenly they have more spree killings than a bunch of other countries. If I define the sample in the 1990’s, suddenly Australia dominates the statistics. You simple can not draw conclusions from samples that are that sensitive to single events.

6) Combining points 4 and 5, if you look at spree killing rates rather than the deliberate mathematical malpractice of comparing absolute numbers, the situation is very different. In 2009, the Winnenden shooting killed 15. Scaled up to the population of the United States, that would be the equivalent of 60 people dead, more than the worst year the United States has ever had. In 1996, 35 people were kill in Port Arthur, Australia. Scaled up to the US population, that would almost equal 500 dead. It is an event that is seared into the memories of Australians. My point is not that these countries are worse than we are. My point is that these are rare and horrible events and you can manipulate the numbers to prove anything you want.

7) The biggest thing missing here is a sense of time. Is the rate of school killings going up or down? The answer, of course, is down. Check out chart one at Ezra Klein’s blog that shows that the rate of assault death has fallen by over half since 1970. Check out the NCES page I link above which shows a significant decline in on-campus homicides, from 40/year in the 90’s to 30/year in the 00’s. That decline is a hundred more kids running in the sunshine. The NCES data, based on a complete sample of over 600 incidents, is useful. This …. isn’t.

I’m not trying to downplay the horror that unfolded on Friday. However, I don’t think any debate can proceed unless we have a good grasp of the problem we are trying to solve. Far too many children are murdered in school in this country — that was as true on Thursday as it is today. But to be useful, the debate needs to be on honest terms. Committing mathematical malpractrice by deceptively comparing the United States to 36 other countries as though there something to be learned from that is not an honest debate and is likely to produce a panicky and ill-considered response.

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