Be Careful with Power Laws

This article, published in Science magazine, urges researchers to be careful when saying their data can be approximated by a power law. There are two reasons why they should be cautious.

The first is that power laws are falsely claimed a lot. As we‘ve seen in class, a quick way to check a power law is to graph the log-log plot of the data. If there is a linear relationship on this plot, it may be true that there is a power-law. But a graph check is qualitative, so it shouldn’t be the only test used. Unfortunately, the article implies that a lot of scientists believe a linear plot suffices when determining whether data follows a power law. In reality, a nonlinear plot is good for ruling out the power law, but a linear plot by itself cannot confirm the presence of one. Researchers need to run a quantitative test.

But even if a power law is found quantitatively, researchers should still be cautious. When claiming a power law, they need to propose a story or mechanism that causes it. Without that, saying that data follows a power law is unremarkable. A power law can occur by chance, as a product of data taken from multiple distributions.

Luckily for us, the link distribution discussed in the book and in class is an example of data that passes both tests. The authors of the book show us the log-log plot, which appears linear, but also tell us that the exponent on k is slightly larger than 2. This finding fits with the idea that for a true power law, the exponent should be between 2 and 3. The authors also provide a story that could generate finding, the rich-get-richer model.

One thought on “Be Careful with Power Laws”

  1. That is an insightful observation about the probability of falsely claiming a power-law effect in data. I would of said that my understanding of the linear-relationship within log-log graphs is sufficient for identifying the existence of a power law effect; however, now I am much more cautious of the denominator K’s exponent being slightly higher than 2, between 2-3. Very cool. I wonder if this problem has occurred in any prevalent studies, that maybe they needed to reexamine their results because of a power-law assumption?

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