Tuesday, March 17, 2020

Linear or non-linear scales? Why not both?

The coverage of coronavirus has rekindled the debate about whether most readers understand non-linear scales. In How Charts Lie I have a cute fictional example of when this type of scale is necessary: imagine that you own four gerbils, two males and two females.

The four gerbils mate and each couple gives birth to four little ones (eight little gerbils in total.) For the sake of argument, let's imagine that the parents die shortly after giving birth. The gerbils keep reproducing at this constant rate, so each generation is double the size of the previous one.

If you plot this exponential growth on an arithmetic Y scale, the line remains very close to the 0 baseline for ~25 generations. Therefore, it'd be impossible to estimate the rate at which you need to increase the amount of food to purchase for your adorable critters:

However, if you use a non-linear scale, the exponential growth of gerbil population becomes clearer. By the 32nd generation there'll be more gerbils in your backyard than people in the world:

When doing graphics about pandemics, we do need non-linear scales because contagion is also non-linear: if you are infected, you likely won't infect just another person, but two, three, or more every n days. That's why community mitigation strategies such as staying at home and washing your hands are so important.

But it's true that most of us have a hard time wrapping our heads around non-linear scales. What to do? Well, we can explain them. As I've said in recent talks, the impulse of too many editors when they think that readers won't understand a visualization is to avoid that visualization. That's self-defeating and wrong. If you never use a type of graphic or scale, how are your readers ever going to learn how to read it?

Another solution is to take advantage of interaction. Showing data on a linear scale is also valuable; it's not just more dramatic than a non-linear scale, but it gives readers an additional view of the data. Why not letting people switch between a linear and a non-linear scale? That's exactly what Spain's El PaĆ­s did in this visualization.

Our World in Data's coronavirus page has a similar feature, although it's harder to see where to click on to switch between scales.