How Charts Lie by Alberto Cairo

Author:Alberto Cairo
Language: eng
Format: epub
Publisher: W. W. Norton & Company
Published: 2019-09-12T16:00:00+00:00

When it comes to designing a chart, which values are better, nominal (nonadjusted) or real (adjusted)? It depends. Sometimes, adjusted values matter much more. Comparing box offices or any other kind of price, cost, or salary over time doesn’t make sense if you don’t adjust your figures, as we’ve just seen. To understand a nominator, you need to pay attention to the denominator, particularly if you make comparisons between groups that have different denominators.

Imagine that I give you two slices from one pizza and I give another person three slices from a different pizza. Am I being mean to you? It depends on how many slices each of the pizzas is divided into:

Not taking denominators into account can have grave consequences. Here’s a bar graph inspired by fictional data provided by Judea Pearl in his The Book of Why: The New Science of Cause and Effect:

Pearl’s fictional data reflects numbers thrown around during heated debates in the 19th century, when the smallpox vaccine became widespread, between those in favor of universal inoculation and those opposed. The latter were worried because the vaccine caused reactions in some children and those reactions sometimes led to deaths.

As alarming as it looks (“More children died because of the vaccine!”), the chart I designed isn’t enough to help you make a decision about whether to vaccinate your own children. For it to tell the truth, I need it to display much more data, including the denominators. This flow and bubble chart can make us smarter at reasoning about this case:

Let’s verbalize what the chart reveals: 99% of children out of my fictional population of 1 million took the vaccine. The probability of having a reaction is roughly 1% (that’s 9,900 out of 1 million). The probability of dying if you have a reaction is also 1% (99 out of 9,900). But the probability of dying because of the vaccine is just 0.01% (99 out of 990,000 who were inoculated).

On the other hand, if you don’t take the vaccine, there’s a 2% probability of getting smallpox (200 out of 10,000). And if you do get the disease, there’s a 20% chance that you’ll die (40 out of 200). The reason why my first chart shows that many more children died because of a reaction to the vaccine than because of smallpox itself is simply that the population that took the vaccine (990,000) is enormously larger than the population of children who didn’t (10,000), a fact that I should have disclosed.

I agree that 99 versus 40 still looks like a huge difference, but try to reason with a hypothetical. Imagine that no children were inoculated against smallpox. We know that 2% will get the disease. That’s 20,000 children out of a population of 1 million. Of those, 20% will die: 4,000 in total. Here’s my updated chart:

The 139 there is the result of adding the 40 kids who weren’t vaccinated and died of smallpox and the 99 who were vaccinated and died after a reaction to the vaccine.

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