How to Lie with Statistics -- COVID Edition

Neil Irwin at NYT:

Did you hear about the booming air travel industry? It’s up 123 percent in just the last month!

Technically, that’s an accurate number. Over the seven days ended Sunday, an average of 212,580 people went through U.S. airport security checkpoints, up from 95,161 in the week ended April 17.

But of course, that is all wrong if you know anything about the underlying reality of the air travel industry. This time a year ago, 2.4 million people a day went through those same checkpoints. By any reasonable measure, these remain disastrous times for air traffic. It’s just that the shutdown in March and early April made even the slight recovery that has taken place seem like an enormous surge in percentage terms.

Get ready for the same effect to apply to all sorts of numbers — most notably with economic data. These swings are artifacts of the arithmetic of percentage change. But if you aren’t attuned to the yo-yo effect that we are likely to see in crucial data in the coming months, you could get a misleading impression of where the United States stands.

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When something falls by 10 percent and then rises by 10 percent, it might seem as if it ends up back where it started. But that’s not how the math works.

A 10 percent drop from 100 to 90, followed by a 10 percent gain, would return it only to 99. With bigger swings, those effects become more striking. A 40 percent drop followed by a 40 percent gain would result in a quantity 16 percent below the starting point.

At even greater extremes, you end up with bonkers numbers like those in the air traffic example, in which a 96 percent drop followed by a 123 percent gain leaves you with a number that is still 91 percent below normal.