# A critique of slopegraphs

I’ve recently posted a pre-print of an article, A critique of slopegraphs, on SSRN. In the paper I provide a critique of the use of slopegraphs and present alternative graphics to use in their place, using the slopegraph displayed on the cover of Albert Cairo’s The Functional Art as motivation – below is my rendering of that slopegraph.

Initially I wanted to write a blog post about the topic – but I decided to give all of the examples and full discussion I wanted it would be far too long. So I ended up writing a (not so short) paper. Below is the abstract, and I will try to summarize it in a few quick points (but obviously I encourage you to read the full paper!)

Slopegraphs are a popular form of graphic depicting change along two independent axes by means of a connecting line. The critique here lists several reasons why interpreting the slopes may be misleading and suggests alternative plots depending on the goals of the visualization. Guidelines as to appropriate situations to use slopegraphs are discussed.

So the three main points I want to make are:

• The slope is not the main value of interest in a slopegraph. The slope is itself an arbitrary function of how far away the axes are placed from one another.
• Slopegraphs are poor for judging correlation and seeing a functional relationship between the two values. Scatterplots or just graphing the change directly are often better choices.
• Slopegraphs are difficult to judge when the variance between axes changes (which produce either diverging or converging slopes) and when the relationship is negative (which produces many crossings in the slopes).

I’ve catalogued a collection of articles, examples and other critiques of slopegraphs at this location. Much of what I say is redundant with critiques of slopegraphs already posted in other blogs on the internet.

I’m pretty sure my criminal justice colleagues will not be interested in the content of the paper, so I may need to cold email someone to review it for me before I send it off. So if you have comments or a critique of the paper I would love to hear it!

1. #### Jon K Peck

/  March 19, 2014

One other, perhaps obvious, point is that parallel coordinate plots in general become pretty useless with large or even medium size datasets – probably much more quickly than scatterplots degrade where techniques like hexbinning extend the usable range.

Jon Peck (no “h”) aka Kim Senior Software Engineer, IBM peck@us.ibm.com phone: 720-342-5621

• #### apwheele

/  March 19, 2014

Yes I agree Jon. Most of the example slopegraphs in popular media I collected don’t have very many points (in general news-viz tend to be pretty insipid in terms of complexity they portray). The 51 points in the example Cairo graph is one of the largest.

I have seen examples of PCP being binned or smoothed, e.g. (Wegman, 1990), although I’m unfamiliar with any implementation in modern software. Very judicious use of alpha blending helps some with the overplotting in that case.