Power laws and log-log plots II.

Back again to power laws. After some more googling, I found an even more important piece of blogging by Cosma Shalizi: Speaking Truth to Power About Weblogs, or, How Not to Draw a Straight Line. The title says it all: just don’t play with power law distributions by fitting straight lines to log-log plots, because chances are that you will get a reasonably looking line and R squared will be relatively large, but that still does not mean that there is a power law distribution. Shalizi is complaining about papers in statistical physics and complexity theory that do such things — well, he should see what is going on in sedimentary geology, where somebody invented the ‘segmented power-law distributions’ and now everybody who is measuring bed thicknesses is fitting not one, but two or even more straight lines to log-log plots of cumulative distributions. It’s utter nonsense, even more so than with a single straight line, but it looks very sophisticated and regular, and people keep doing these plots and all kinds of fancy interpretations based on them (earthquakes, self-organizing criticality, confinement, erosion, etc.). If it plots as a straight line – fine, it’s a power law, we explained everything. If it does not plot as a straight line — well, just fit two straight lines and talk about two populations, and how the original power-law distribution has been modified by erosion, confinement, etc. – and we explained everything again. I know I am also guilty of some of this in my thesis, but at least I have never done the segmented power law plots.

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