Fixing the visual versus fixing the story
A startling chart about income inequality, with interpretative difficulties

An unsuccessful adaptation of a classic

Found this chart in Hemispheres magazine on board a United flight:


A quick self-sufficiency test reveals the biggest shortcoming of this visual presentation.


What would you guess is the difference in areas between the two white-ish sectors (pointing at 9 o'clock and 2 o'clock)? The actual numbers are 18.3% and 12.5%. So roughly, if one takes the 2-o'clock sector (right), halve it and add it back to itself, one should obtain the area of the 9-o'clock sector (left). Clearly, the piece on the left is much too big.

The following chart shows the index of exaggeration increasing with the value of the data. (For example, the highest value of 18.3% is about 9 times the lowest value of 2.3% but the the ratio of the areas depicted is ~500 times.)


The distortion is larger than usual because the designer encodes the data twice, once in the angle of the sector, and again in the radius. Both those quantities contribute to the area of a circle.

Readers must look at the data in order to read this chart properly, therefore the visual elements are not self-sufficient. Further, if readers chose to perceive the relative sizes of the sectors, they would have misread the data massively.


The designer was probably inspired by the Nightingale rose diagram (link to Wikipedia):


In the original, Nightingale does not encode data into the angles. The circle is divided evenly into 12 pieces to display the 12 months of the year (She might have taken into account 28-31 days; it's hard to tell by inspection). The data is encoded once along the radial axes.

Another difference between the two charts is the ordering of the data. In Nightingale's version, the order is logically determined by the passing of time. In the Hemispheres chart, the order is chosen based on taste. A more natural order would be by the proportion of employment but I think the resulting chart would look like a snail's shell, or worse. I must say a more balanced "rose diagram" looks nicer but it forces my eyes to jump around to answer a simple question such as which are the top three employment sectors in San Francisco.


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Soren Messner-Zidell

I'm really struggling to find practical value in these 'polar diagrams'. Even Nightingale's are really cool, but seem really difficult to comprehend. They are basically a more exciting radar chart, correct? I've noticed a lot of infographic designers are using these, and every time i see them the data is wildly distorted. Is there really ever a time when a polar diagram is appropriate? I'd love an example. Thanks!


Soren: Someone asked this same question at a seminar I gave recently. While the Nightingale chart is a classic, I don't use it. As statisticians, we like people to know that the celebrity Nightingale was a statistician, and female too.


Yes, it's a classic.

A Model-T is a classic too. But we don't build cars that way anymore, and for good reasons. :)

Meta Brown

I spotted this chart on my way to lead one of my Storytelling for Data Analyst workshops, and gave it to a student to evaluate during one of the exercises. To my surprise, the student didn't even notice the chart. His comments were all about the text.

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