BAYES' THEOREM CALCULATOR
(also available as a Mathematica cdf file)

This program considers a test for a disease . Use the sliders to input:

1. the prevalence of the disease, $Pr($Have the disease$)$
   i.e. how common the disease is in the general population.
   
   
2. The sensitivity of the test,  $Pr($Positive test $|$ Have the disease$)$
   i.e. how often the test correctly identifies people we know have the disease.
   
   
3. The specificity of the test, $Pr($Negative test $|$ Do not have the disease$)$
   i.e. how often the test correctly identifies people we know do not have the disease
   
   

The program will outputs are

• The true positive rate, $Pr($Have the  disease $|$ Positive test$)$
  i.e. the probability that someone with a positive test has the disease
  
• The true negative rate, $Pr($Do not have the  disease $|$ Negative test$)$
  i.e. the probability that someone with a positive test has the disease
  

For a rare disease, you will find that even with a very good test it is hard to accurately identify if someone has the disease.