This webpage is for drawing a frequency box to apply Bayes's Rule visually a le Gigerenzer. It asks you to answer three questions, using the context of a medical test for whether someone is infected with a disease or not and the test gives the answer YES or NO.

There are two parts to the accuracy of the test: how often an infected person tests YES, Prob(Prob(YES|Infected), and how often a healthy person tests NO, Prob(NO|Healthy).

You may have to think for a minute to see why those can be wildly different numbers. Here's an example. Suppose we have a test which ALWAYS says YES. In that case you might say it is very accurate, because it always catches the infection: Prob(YES|Infected) = 1. Or you might say it is very inaccurate, because it always says, falsely, that someone who is healthy is infected: Prob(NO|Healthy) = 0.

Another way to think of test accuracy is in terms of the false negative rate, Prob(YES|Infected), and the false positive rate, Prob(YES|Healthy). Note that Prob(YES|Healthy) = 1 - Prob(NO|Healthy).

What we're interested in, though, is not those probabilities I've just been talking about, but Prob(Infected|YES), which answers the question, "How worried should I be if I take the test and it says I'm infected, but I know the test makes mistakes sometimes."

To answer this question, you need to give me three numbers as basic data, answering the questions below.













My server runs the code and a diagram will pop out on your screen after some time has passed. Your box diagram is saved on my server with the name indicated on the output page, as something like http://rasmusen.org/cgi-bin/bayesbox-box56732rasmusen1.png.

This was written by Eric Rasmusen, [email protected], on April 27, 2020 and last revised May 1, 2020. All code is free for anyone to use. This page is at http://www.rasmusen.org/cgi-bin/bayesbox.htm.

If you have a different Bayes's Rule problem, you can still use this webpage, but you will have to translate my language to your own context. This webpage takes the prior Prob(A) = Prob(Infected) and turns it into the posterior Prob(A|B) = Prob (Infected|Yes). So think "A= infected, B = YES", for your own application. If you want to change the text on the figure to match your application, you'll need to run the Python program yourself, which is pretty easy if you know Python, hard if you don't. Just choose the 3 input data nubmers and change the output labels in the input file http://www.rasmusen.org/cgi-bin/bayesbox.py.