A while back, I picked up an old introduction to statistics book from the 1950s, just out of interest to see how things were done before computers, and I rememb

A while back, I picked up an old introduction to statistics book from the 1950s, just out of interest to see how things were done before computers, and I remember that near the beginning, there was a cautionary tale. It started out with a simple bimodal distribution and explained that it was the results of some student tests. The reason it was bimodal was simply that it was the results from two different classes, the "smart" class and the "others". And talked about how this is a classic way to spot that you are dealing with two populations. Then it related the tale of First World War marksmen. It turns out that when they were training their sharpshooters, the results, when plotted, had a bimodal distribution where they were expecting a normal one. They took this to mean that there were such things as "natural shots": men with a natural ability for shooting. If they could identify early which ones were the natural shots, they could concentrate their training much more effectively. But it didn't work. After they separated the groups, it turns out that not only did the "natural" group also have a bimodal distribution, but they actually didn't perform any better than the "bad shots". To cut a long story short, they discovered that the bimodal distribution was actually an artifact of the scoring system they were using. When they recalculated the data with a different scoring system, they had a regular normal distribution. It's a simple story with a simple moral: you can't interpret your results if you don't understand your data. Maybe I'm wrong though; it's been a while since I did stats and I've driven most of it from my memory. :-) Oh, and it's not at all sad that I buy second-hand statistics books for fun reading. It's just not.