My talk on Friday
Light entertainment: multiculturalism

From fellow readers

Have been getting a lot of reader suggestions lately. Thanks to all of you! Some of these, for various reasons, I won't be able to write full posts on. But they are still worth looking at.

Boardingpasswallet Julien D. invites us to interact with a different community, graphic designers -- that's graphics as in fine arts, not statistical charts. This is a great post concerning how they would re-design boarding passes. This is akin to Ed Tufte's effort to re-design bus schedules.

While there is no statistics involved in these designs, the virtues of clean, simple, direct communication of data to people still apply. Pretty is also desirable.


I first saw this infographics of U.S. tax brackets on Felix Salmon's twitter feed (he found this "pretty".) Now, it landed in my inbox via Troy O. My reaction to Felix was "pretty but pointless". Sunset through a smoky lens? Impressionist painting? Scatter plot? Density plot? This one is crying out for your comments.



Julien D., same person as above, also pointed us to an animation of the re-birth of European air routes after the volcanic ash scare.  (Vimeo link)


For this sort of exercise, my main interest lies in admiring the behind-the-scenes effort to collect the data, clean and process the data, code the graphics and animation. I'm not sure the animation tells us anything we don't know by reading the news.


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I disagree that the taxation graphic is pointless. It does not obviously misrepresent the data and whilst it may be difficult to read specific data points from it gives an interesting and concise overview of US taxation system over the century. There are clear discontinuities corresponding with historical events; war, depression, the Reagan years.

That said, the chart is not "glancable", it requires the reader to engage with it (and it assumes some knowledge on their part), I think it rewards this effort.

If it's lacking anything I think it's in adding context to the data, perhaps a plot of how GDP or income distribution changed over the same time or marking key events which precipitated changes in taxation policy...


I actually ran into the former graphic on a forum a few days ago. Here's an edited version of what I posted about then:

It is only a useful image if people already know what the numbers mean; otherwise, it is far too confusing an image. In particular the color scheme sucks. It's hard to use a gradient when it has to go from 0 to 90 interpolated across a (usually) 256 value scale yet all values have to be meaningful/distinguishable. This is made worse by it being non-obvious how percentages translate into actually useful information. For example:

Going from 15% tax to 25% is paying over 60% more tax. Going from 70% to 90% is paying only 30% more tax. However, look at how similarly shaded 15% and 25% are as compared to 70% and 90%.

On the other hand, going from 15% tax to 25% tax means having almost 90% of what you did before the change. Going from 70% tax to 90% tax means having about a third of what you did before the change.

Any time you have that kind of math involved, it's near impossible to just grasp intuitively what it actually means (consider miles per gallon vs. gallons per mile). This is made a lot worse by the color scheme and the fact that this is just marginal tax rates - that is, not total percent of income or total dollars. Even if you know what the graph 'means' - understanding what the three values represent - that doesn't necessarily imply you know how tax brackets work.

So this chart is OK, if people already know what it's trying to say and are just looking for a pretty visual summary. But if the viewer doesn't understand why '90% tax' doesn't mean 'takes home a dime on the dollar' they're going to come away with the wrong impression."

I recently wrote an article about chart design for a graphic design audience. I'll send in a link to it once it's published!

Tom West

My main gripe about the tax graphic is the colour range is too narrow... a red-purple-blue would highlight the differences far more.
That said, because our eyes are fairly good at picking up differences between colours, you can pick up exactly where step changes occured. Also, because it's denoted in real dollars, you can see the switch from having bands that remain constant in real rather than absolute terms.
I like it.

Kymberly Helton

Another problem with the tax graph (which I have also seen posted various places over the past week) is that it doesn't account for the changes in income distribution or inflation. For example, in 1960 the top marginal rates kicked in at just above $1M/year in income, but how many people made that much money in 1960? And compared with the number of people who qualify for today's top marginal rate? Or those who would qualify for 1960's top rate if it was still in effect? You can't compare anything in real terms using this chart.

It's a lovely representation of the history of the income tax code, but apart from that it's pretty much useless.


I'm trying to create a chart showing similar information -- income tax rates since the Regan administration. I'd love some suggestions.

I would definitely change the color scale and would probably add presidential administrations to the date range.

I don't have much of a statistical or mathematical background. Is a logarithmic scale appropriate here?

By the way, I've learned a lot from comments on this site.

Jon Peltier

The income tax bracket chart looked like nothing more than an inkjet cartridge gone awry.


The tax graphic is brilliant! As some have said, it's takes some time to get oriented and you might be able to improve the color scale and legend... but once you've figured out how to read it, it has an astonishing level of data density and clarity.

The best way to see why is to try to show the same data in a different way. I've seen people try this with a series of line charts (one for each bucket of income levels) and, in addition to being just an approximation of the original data set, it turns into quite a mess.

For what it's worth, I think that complaints about charts should explain either (a) why the data is not worth visualizing; or (b) how the data could be visualized better, as a baseline.

For instance, commenter eronarn addresses (a), while Tom West addresses (b). I'm not sure I agree with erornarn, but I respect the thoughtful analysis and it definitely advances the argument. Tom West's also could be argued (hm, does the midpoint of the color scale set an artificial baseline, and is that worth the better level of detail?) but it's a very interesting debate. To me, these are excellent examples of chart criticism in action.

What is not useful is a comment like Jon Peltier's... maybe it's a joke, but it's painfully close to hearing someone say about a Jackson Pollock, "my 6-year-old could do that".


I quite like the US tax graphic now I've studied it at full size: the thumbnail here doesn't do it justice. It's a combination of the familiar (I knew about the 90% top tax bracket in Eisenhower's day) and the new (I didn't know about the 0% bottom tax bracket under Carter).

I don't think they did themselves any favors with the subtle colors of the graphic, or the small thin text. The percentage labels could have been fatter and bolder, and the colors could have spanned a slightly greater hue range. But I'm grateful they didn't go with the "scientist's rainbow", which is the more usual error of an inappropriately large hue range, unsupported by any range of value or saturation. So, a respectable mark from me, but a note in the margin to say "could do better".

To Troy I'd say: you could try addressing Kymberly Helton's objection with a scale using percentile of tax payers in each year. But it might take a lot of work, and where you'd get the data from, I don't know. Alternatively, yes, try a log scale. It would sort of mimic the income distribution, it's not illegitimate, and it might help clarify the graph. It could go either way really.


Thanks, Derek. I'm still experimenting with the presentation.

In case anyone else wants to take a crack at it, here's the data:


I think the tax graphic is beautiful. You can immediately see the high top tax rates in the halcyon years of the greatest economic equality, shining like a sunbeam in a glade.

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