Implied comparisons in visualization

One blog I follow is WTF Visualizations and all these examples I’ve acquired from there. I think they demonstrate a common thread of people failing to fully consider what comparisons are implied by their chart.

What I mean is, suppose you have a series of numbers, like 8, 10, 20, and you represent that as a 4cm bar, 5cm bar, and 10 cm bar. You’ve translated the raw numbers into a measurement, in this case the length of the bars. You can’t lose sight of the fact that doing this implies you can visually compare the magnitude of 8, 10, and 20. If they aren’t numbers that can or should be compared, maybe there is no value in presenting them visually. And there is also sometimes an implied comparison to what could be the maximum number.

First up is this one showing, which demonstrates it especially because Francis Gagnon tried out an alternate method of displaying the data. The original is on the left, his modification is on the right:

So this is an example of what I’m looking at, because the biggest change he makes is he changes the scale so the implied maximum is 100%. Whatever the maximum of your graph is, there’s an implied comparison to that maximum. There are many cases where you can’t help but choose the maximum of your graph arbitrarily, but in this case, since the numbers are percentages, 100% is a non-arbitrary choice.

He later tried one more redesign, where he set the implied maximum at 50% instead of 100%. Because it’s a percentage, I can see how you could think of 100% as the obvious maximum. But 50% makes a lot of sense in this context, since 50% would be the point where you have equal numbers of male and female CEOs.

He also re-oriented the bar chart. You may miss it at first glance, but the one chart uses data from Fortune 500 companies and the other uses data from “durable goods manufacturing” so directly comparing the two might not make sense.

The point I made about implied comparisons applies here, as well:

In something like this, the use of graphics just becomes meaningless decoration. Ask yourself what are we supposed to be comparing? Are we supposed to compare the three numbers? But they are all on different scales; the 6 billion curve is not 6 times the length of the 1 billion curve, and the 2 million curve isn’t 1/500th the length. And comparing “number of videos added everyday” to “unique visitors every month” to “hours of videos” doesn’t seem very useful. Are we supposed to compare to their implied maximums? The maximums seem chosen arbitrarily; would 7 billion be the absolute maximum number of hours people could watch in a month? According to these stats the number of internet users in 2012 was about 2.4 billion. It seems to me that would be a non-arbitrary maximum you could apply to “unique visitors” but instead that curve uses an implied maximum of about 1.8 billion. So yes, these curves don’t appear to do serve any purpose other than decoration.

Next up, this one is sort of a radial graph:

I’ll leave aside the issues of 1) the “spikes” are scaled in both width and length, so it’s ambiguous whether you’re supposed to compare area or length or what, and 2) the spiky ends don’t have any semantic meaning and would further make such comparisons imprecise. Because what’s the point of a precise comparison when there’s really no point to the comparison in the first place? The numbers on the radial shapes are a ranking. When you’re ranking something, you’ve essentially removed the actual measured values.

If they had retained some measured value, such as the number of posts mentioning Pope Francis, the election, and so on, then you could visualize whether Pope Francis beat the election by a small fraction or more than double, or what. By reducing it to just ranking, without any magnitude to compare, essentially this visualization is only telling us which number come first.

And last, I’m kind of repeating the earlier Youtube thing:

But at least comparing the top reverse speed and top forward speed sort of makes sense. They are both speeds, both measured in MPH, but then they ruin that by having the two displays using different scales. The implied maximum forward speed is 10.4 MPH, but the implied maximum reverse speed is 8.5 MPH. (Determined by using selection tools and the Photoshop histogram to compare areas.)

So again, they’re treating visualization as just decoration. I suppose I don’t hate decoration as an end in itself, but trying to use the aesthetics of visualization without any consideration to what it means is somewhat analogous to getting Chinese characters tattooed on you without considering that for many people this is an actual language and not just pretty pictures.