Why do we need statistics?

My husband asked me to explain an article in the New York Times today that absolutely mystified him.  This was a very odd request because my husband doesn’t usually ask me to explain much of anything to him! The opinion piece (https://www.nytimes.com/2020/05/13/opinion/antibody-test-accuracy.html?referringSource=articleShare), was not, in my mind, very well written and my proof for that was in my husband asking me to explain the statistics in it.

So what was giving him trouble?  This statement: “In a population whose infection rate is 5 percent, a test that is 90 percent accurate could deliver a false positive nearly 70 percent of the time.”

WHAT?????  That doesn’t make any sense! 

45 minutes later I finally got him to understand! Crazy, huh?

Let me explain…… 

Test 100 people for antibodies.  You should get 5 positives (the infection rate is 5 percent).  But, for every 10 people you get 1 positive (90% accurate), so for 100 people you have 10 positives.  You don’t know which of those 10 are TRUE positives and which are false positives, so your false positive rate is 1 - (5/10) or 50%.  That’s a pretty crazy high number. Flip a coin and you have 50% chance it will come up heads. So, with this test, if you test positive, you actually don’t have a clue if you are positive or not.

See how easy that was?

What’s it mean?  It means that 90% accurate is not accurate enough!  Let’s imagine that we have an antibody test that is 99% accurate….

Now test 100 people for antibodies.  You should get 5 positives.  But, for every 100 people you get 1 false positive plus the 5 positives.  Again, you don’t know which of those 6 are true positives, so your false positive rate is 1- ⅚ or 16%.  Still not great, but much better numbers!

How important is this to you?  It should be pretty important!  Our country is planning on using antibody tests to determine whether you or I can walk around and not worry about infecting other people.  If you have the antibodies to the COVID-19, you’ve been infected, you’ve recovered, and you won’t infect anyone else.  That’s the idea anyway.  But, as you can see here…..  it’s not that simple…...  if the test is not accurate and if the infection rate is low.  Your confidence in that test may be massively inflated and that means…. you may not have had the virus even if you test positive for the antibodies…. which means you may be at risk for catching the virus and you may be at risk of infecting others.

Bottom line - we need a more accurate antibody test.