In this post we’re going to take a journey into the world of power-law distributions. Power laws pop up again and again in my research. But I

Power-Law Distributions in Graphical Form

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2021-05-20 15:35:05

In this post we’re going to take a journey into the world of power-law distributions. Power laws pop up again and again in my research. But I’ve never taken the time to discuss what makes them so weird. This post will be a little ‘power-law primer’ that I’ll reference in future blog posts.

Let’s start by defining the word distribution. A ‘distribution’ refers to how data is spread out. I’ll use human height as an example. Suppose we have data on the heights of many different individuals. Within this data, we can analyze the frequency of different heights. This frequency quantifies the ‘distribution’ of human height.

Histograms are the main way we visualize distributions. Histograms plot frequency against size. To make a histogram, we divide the data into a series of ‘bins’. For height, this might be 5cm intervals (i.e. 160-165cm, 165-170cm, etc.). Then we count the frequency of the data within each bin, and plot the result. The shape of the histogram allows us to visualize the distribution of height.

The figure below shows histograms of male and female height in a sample of Americans. (OK, technically these plots are ‘frequency polygons’, but the distinction is not important here).