Displaying convoluted indices

I reviewed another batch of projects from Ray Vella's class at NYU. The following piece by Carlos Lasso made an impression on me. There are no pyrotechnics but he made one decision that added a lot of clarity to the graphic.

The underlying dataset gauges the income disparity of regions within nine countries. The richest and the poorest regions are selected for each country. Two time points are shown. Altogether, there are 9x2x2 = 36 numbers.

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Let's take a deeper look at these numbers. Notice they are not in dollars, or any kind of currency, despite being about incomes. The numbers are index values, relative to 100. What does the reference level of 100 represent?

The value of 100 crosses every bar of the chart so that 100 has meaning in each country and each year. In fact, there are 18 definitions of 100 in this chart with 36 numbers, one for each country-year pair. The average national income is set to 100 for each country in each year. This is a highly convoluted indexing strategy.

The following chart is a re-visualization of the bottom part of Carlos' infographic.

I shifted the scale of the horizontal axis. The value of zero does not hold special meaning in Carlos' chart. I subtracted 100 from the relative regional income indices, thus all regions with income above the average have positive values while those below the national average have negative values. (There are other challenges with the ratio scale, which I'll skip over in this post. The minimum value is -100 while the maximum value can be very large.)

The rescaling is not really the point of this post. To see what Carlos did, we have to look at the example shown in class. The graphic which the students were asked to improve has the following structure:

This one-column structure places four bars beside each country, grouped by year. Carlos pulled the year dimension out, and showed the same dataset in two columns.

This small change makes a great difference in ease of comprehension. Carlos' version unpacks the two key types of comparisons one might want to make: trend within a given country (horizontal comparison) and contrast between countries in a given year (vertical comparison).

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I always try to avoid convoluted indexing. The cost of using such indices is the big how-to-read-this box.