New Video: Linear vs. Quadratic Change

Linear vs. Quadratic Change Thumbnail

Scaling objects to represent a value is a key part of visualization, but it’s not without its pitfalls. Especially when it comes to fancy infographic bar charts, it can easily distort the value’s appearance. Why that is, and where else this can happen, isn’t always obvious. In my new video, I show how it happens and how to do it right – and how this issue inspired ISOTYPE.

This is essentially the video version of a blog post I wrote on linear vs. quadratic change some 12 yers ago. Cole Nussbaumer Knaflic reminded me of it in a Clubhouse conversation (remember Clubhouse?) a month or so ago. So I decided to turn this into a little video.

There’s also the infographic you see in the thumbnail, which made the rounds last year and I recently thought of it again. My concern is less with the icons and the color scheme, and more with the exaggeration of the differences. I explain how this happens, why it’s a problem with pictorial bar charts in particular, and where else it can happen. And it isn’t always in the most obvious places, not everybody immediately understands that the area of a circle wedge grows with the square of the radius, for example. Anyway, more on all that in the video.

This video takes a different approach than my previous ones in that it’s all motion graphics, no more me talking into the camera. That’s obviously a ton of work, and I’m not sure if it’s the way to go for all my videos, but it has been an interesting experiment and I’ve learned a lot in making this – and I’m very curious to see what people think and how well this video does.

Below is the teaser, watch the full video (in all its 6:08 glory) over on YouTube!

As always, let me know what you think! This is a different approach than my other videos, does it work?


One response to “New Video: Linear vs. Quadratic Change”

  1. Helwig Hauser Avatar
    Helwig Hauser

    Dear Robert, thank you for this video!

    I’m glad to see that you point your finger at this topic and, as you, also I find myself irritated when seeing charts that depict a linear data relationsship as a quadratic area relationsship. It’s pretty clear that this is wrong. But what’s right?

    After some exchange with others, I find this question much harder to answer, actually. Li et al.’s work from 2010 [1], for ex., suggests that the truth is somewhere in the middle.

    If you’d consider the following three sequences: — which one, would you say, corresponds, perceptually, to a linear data sequence?

    Do you know of other studies that attempted to actually derive the right mapping?

    I’d expect that it easily may depend on the aspect ratio of the scaled area, as well.

    [1] J. Li, J.-B. Martens, J. J. van Wijk: A model of symbol size discrimination in scatterplots; Proc. of CHI 2010, pp. 2553–2562