Statistical Laws, Then and Now

Or was nature creating such distributions after all [referring to Gaussian distributions]? Did phenomena really fit Quetelet's curves? For a great many years, any empirical distribution that came up in a hump was Gaussian because that was all it could be. That was all it could be because of the story of little independent causes, which had, for a while, created another synthetic a priori truth. No one devised routine tests of goodness of fit, because the question did not arise. The first tests were not proposed for another 30 years, and then by German writers like Lexis who were altogether sceptical of what they called Queteletismus, and indeed of the very idea of statistical law. Porter has admirably reported Lexis's struggle with tests of dispersion. Lexis was not explicitly testing the hypothesis that distributions are Gaussian, but he did conclude, in effect, that about the only thing that was distributed in that way was the distribution of births - a happily binomial type of event.

- Ian Hacking, from The Taming of Chance, p. 113

Apparently there was a time when educated people saw Gaussian (aka 'normal') distributions everywhere. As Hacking points out, it's hard to blame the scientists of the 1800s: they just didn't know better. They didn't have goodness of fit tests, and certainly didn't know about relative distribution methods. Besides that, they didn't have a whole lot of parametric distributions to choose from, and knew nothing of non-parametric models.

But now, some 200 years later, we have a similar phenomenon going on in the field of complex systems. People see power laws everywhere. Sometimes there's a generative model that makes a good story. But a lot of the time researchers fit a line through a log-log plot and call it a day.

Of course, pointing this flaw out isn't anything new. It's just funny how, two centuries later, people continue to see simple truths in complex things.