Wednesday, May 13, 2020

Professors and Their Fallacies

Let me begin with a simple review of some basic statistics. Consider testing for the presence for an antibody, Ab. One either has it or not. A binary probability. A factual issue. Now we use some specific test. We know that tests are fallible. There are such measures as False Positives and False Negatives. Namely a False Positive is saying you have the Ab when you do not and a False Negative is saying you do not have it when you do have it.

How are these measures done? In most cases you take a sample of knowns, namely ones with Ab and ones without, use the test, and calculate the result. Fairly simple stuff.

Now along come some Professors, Business and Ethics types, don't know what bona fides they really have, and in the NY Times they state:

Here’s an example. If you took an antibody test that was 90 percent accurate, and it determined that you had coronavirus antibodies, how confident should you be that you actually have those antibodies? Most people say about 90 percent, with the average answer being above 50 percent. This makes sense. After all, 90 percent accuracy is pretty high.But the predictive value of an antibody test with 90 percent accuracy could be as low as 32 percent if the base rate of infection in the population is 5 percent. Put another way, there is an almost 70 percent probability in that case that the test will falsely indicate a person has antibodies.

Now I am really confused. In the 100 plus years of doing this test if I have measured an accuracy, namely 1-False Negative, and my sampling was high enough with the assay then 90% is 90%. I read the reference which is some sociological text but  if you have an instrument with a False Negative of 10% then it yields 90% accuracy. 

The biggest problem in this mess of a Pandemic is we have too many Professors and Scientists. It reminds me of the Vietnam War and McNamara's Boys, data and interpretation. Somewhere there will be found a Pentagon Papers Report, where is our new Ellsberg?