Chapter 8. Visualizing Distributions: Empirical Cumulative Distribution Functions and Q-Q Plots

In Chapter 7, I described how we can visualize distributions with histograms or density plots. Both of these approaches are intuitive and visually appealing. However, as discussed in that chapter, they both share the limitation that the resulting figure depends to a substantial degree on parameters the user has to choose, such as the bin width for histograms and the bandwidth for density plots. As a result, both have to be considered as an interpretation of the data rather than a direct visualization of the data itself.

As an alternative to using histograms or density plots, we could simply show all the data points individually, as a point cloud. However, this approach becomes unwieldy for very large datasets, and in any case there is value in aggregate methods that highlight properties of the distribution rather than the individual data points. To solve this problem, statisticians have invented empirical cumulative distribution functions (ECDFs) and quantile-quantile (q-q) plots. These types of visualizations require no arbitrary parameter choices, and they show all of the data at once. Unfortunately, they are a little less intuitive than a histogram or a density plot is, and I don’t see them used frequently outside of highly technical publications. They are quite popular among statisticians, though, and I think anybody interested in data visualization should be familiar with these ...

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