The Distribution of Library Book Circulation Is Not a Power Law | Hacker News Reader

The Distribution of Library Book Circulation Is Not a Power Law

cscs.umich.edu

30 pointschrismealy6 comments

Many, many things aren't a power law, but are widely reported to be due to sloppy statistics and a deep misunderstanding of regression on log-transformed data.

The problem is this: people frequently log-transform empirical counts of things (like library book circulation) and then fit a line to the distribution. Since the line generally fits very well, with very high (but ultimately meaningless) R-squared values, they rush off to write a paper.

I could cite at least a dozen very "important" papers that gush over power law relationships in this or that. Instead, I'll let Cosma Shalizi's excellent blog post on the topic do the talking and citing: http://cscs.umich.edu/~crshalizi/weblog/491.html

It's an excellent read for anyone reaching for a log-transform.

EDIT: I didn't realize that Cosma was the author of the linked piece. The other blog post by him I link here is also highly recommended.

Everything is linear if plotted log-log with a fat magic marker.

It's not just that -- if the tail of the distribution doesn't seem to fit, you can just call it a "power-law with a cutoff", "exponential tail", "multiple scaling regimes", "piecewise linear" or some other cruft. Physicists, particularly, are egregious abusers of this. Like Agent Mulder, they want to believe.

I like Cosma's (the author of this piece) point on another of his blog-posts on this topic of whether you've found a power law distribution[1]:

Ask yourself whether you really care. Maybe you don't. A lot of the time, we think, all that's genuine important is that the tail is heavy, and it doesn't really matter whether it decays linearly in the log of the variable (power law) or quadratically (log-normal) or something else.

But I don't know why I would expect the distribution of library books to be a power law: physical books are inherently limited in how many people can hold them. And the number of books at my school library that are permanently checked out always is rather high. There's a strict upper bound on the max-circulation of a book, so you don't get those super-high values for a few books required to make a power law work. Besides, do you care that it is log-normal and not power? I think the lesson is stop calling things "power law" when you mean "fat-tailed".

Fat-tailed is a good enough description in most use-cases anyway.

-- [1] http://cscs.umich.edu/~crshalizi/weblog/491.html

Note that you've got a cutoff because a library book can only circulate to one patron at a time (and libraries will rarely buy 10+ copies of a bestseller)

You very well may have a power law in the range before that, but all systems that show power laws practically have finite size and other cutoffs.

95% of academic work on power laws is bunk. Ask your average professor or graduate student whose name is on a power law paper what a "statistical estimator" is and you'll get a blank look.

"Zipf, Power-laws, and Pareto - a ranking tutorial"

http://www.hpl.hp.com/research/idl/papers/ranking/ranking.ht...

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