Testing Numbers vs. Case Numbers

Trump asserted that more testing leads to more cases. Not necessarily. Let's think this through.

If cases were distributed randomly, and tests were done randomly, then there should be no relation between the two, right?

If cases cause some infected people to feel ill (and note that it need not be all of them), and feeling ill motivates getting a test, then yes you'd expect to see a positive relationship.

On the other hand, if cases is what encourages people to get tested, and the capacity is there ... perhaps you end up testing a lot of people who weren't likely to be infected in the first place. In this case you'd expect to see a negative relationship.

Here's the thing: Trump's story (shared by many) is about looking at just two variables, but the stories I outlined above have extra variables.

Not sure about that? Look closely. The phrases "... feeling ill motivates getting a test ..." and "... cases is what encourages people to get tested ..." imply extra variables(s). That implies that both Trump and the smart people at the COVID Tracking Project who produced this graph are oversimplifying and are probably subject to omitted variables bias:

The Trump argument is probably best exemplified by Louisiana and Georgia: differences in rates of tests and rates of positives. But for the most part, the rest of the chart shoots down the Trump logic. Now it doesn't show his logic directly, since it does not have a number or rate per 100K for cases along the horizontal axis. In fact, Trump's story will check out if we were to regraph this to show cases rather than rates, and just the states to the right of the dashed line.

But even so it would miss the most important part of the story told here. Look at the scale on the left. Arizona, for example, is testing roughly 200 out of every 100,000 people every day. That's less than 1%. What's going on with the other 99%? Trump is right: if we tested all those other people the number of cases would go up. But that's infantile: what we really need to know is by how much.

As always, drawing attention to Utah, and ... we look pretty crappy right now. We're just not testing that many people, and we get a lot of positives amongst those we do.