Sharing Zachary Binney’s Twitter thread on test sensitivity and specificity with kids

I saw a neat twitter thread from Zachary Binney last week:

The FDA has approved the first antibody test for COVID-19, from Cellex. It theoretically tells you if you've had it & are, as far as we know, immune for some time.

Sensitivity is 93.8%, specificity 95.6%. Sounds great, right?

Well, sort of. (1/6)

— Zachary Binney, PhD (@zbinney_NFLinj) April 2, 2020

The ideas in Binney’s thread are really important if you want to understand testing, so I thought I’d share them with the boys this morning. We started by looking at the thread and then going to Wikipedia to get a few definitions:

Now we went through a few specific examples. For all three we assumed the test was 95% accurate. In our first example we assumed that 5% of the population would have a disease. What is your chance of having the disease if you test positive?

Next we looked at what would happen if only 1% of the population has the disease (sorry the camera wasn’t showing the bottom of the white board here 😦 ):

Finally we looked at what would happen if 30% of the population had the disease:

The problem we are looking at here is a pretty famous one in probability and statistics. Binney’s twitter thread made for a great opportunity to show how the ideas aren’t just theory or problem set problems, too.