Exploring Univariate Combo Charts
Take a look at this very interesting chart recently published by TechCrunch:
The left axis used by the bar chart visualizes guest stays. The right axis used by the line chart visualizes the year-over-year growth rate of guest stays. In other words, this is a combo chart visualizing a single variable across two separate axes: left for the absolute values of the variable, and right for the growth rates of the same variable.
Now take a look at this K chart:
It is also a combo chart visualizing a single variable across two separate axes: left for the absolute values of the variable, and right for the rolling sums of the same variable.
I call both charts Univariate Combo Charts, because they visualize a single variable (univariate) across two separate axes. In most cases, the left axis is used for absolute values of the variable, while the right axis is used for a derivative computation on the variable.
Now, the deep relation between these two charts does not stop there. The first one, which I call a Growth Chart (until someone gives me its official name), visualizes a growth rate, which is computed by making subtractions. For its part, the K chart visualizes a rolling sum, which is computed by making additions. In other words, these two charts are close siblings.
And if you were to go from a discrete horizontal axis to a continuous one, you could create variants of these visualizations in the continuous domain, with the former visualizing a derivation, and the latter visualizing an integral (that's for the maths lovers among us).
Interestingly, such univariate combo charts are not limited to bar charts. In fact, they can be created from any chart visualizing extensive variables (variables that can be summed). According to Principia Pictura, this would not work so well for line charts, but it would be perfect for area charts. Or to be more precise, an equivalent to the growth chart could be produced from a line chart, because subtractions are available, but a similar equivalent of the K chart should not be produced from a line chart, but can be produced from an area chart.
Similarly, univariate combo charts could be produced using operators other than simple additions and subtractions. In fact, there is a virtually-unlimited number of statistical operations that could be applied in order to create more and more sophisticated visualizations. Not all of them would be useful, but some certainly are, and we will take advantage of our weekly series of data visualization articles to explore some of them.
Credits
Many thanks to Paul M. for his help understanding all this...
Vanity References
If you're into arithmetic, you might enjoy these two (totally unrelated) articles:
- The Missing Operation (easy read)
- Hyperlogarithmic Arithmetic (not so easy read)