Thread, on why a general lack of understanding of Bayes Theorem, in a low baserate situstion—which #COVIDー19 is—will get people killed.

We are getting tests soon to see if someone has antibodies. But highly accurate “you do!” STILL MEANS YOU LIKELY DON’T. https://twitter.com/taaltree/status/1248467731545911296

So the risks are clear. People take test with “90-some percent accuracy!” Test says “you have antibodies!” So ppl stop social distancing.

But pct who ACTUALLY have antibodies are low. So small error rate on saying “you do” impacts large(r) pop, equals many false positives.

Here’s a simple ex.

A test says “you’re sick” when you’re not 2% of the time. Says “you’re sick” 100% of the time when you are.

100,000 ppl, w 1%, or 1,000, sick.

All 1,000 sick ppl get “sick.”
Of the 99,000 healthy, 2%, or 1,800, get “sick.”

So 1800/2800 = 64%, are WRONG.

Now obv, the test isn’t useless. Before hearing “sick,” a sick person thought there was a 1% chance they were sick. Now it’s a 36% chance. That’s useful!

But being told a test is 98% accurate does not lead us to think a “you’re sick” = 36% chance!