Bayes’ Theorem Demonstration

Questions to be answered before the simulation are not yet implemented in this test version.


Begin by answering the questions, even if you have to guess. The first time you answer the questions you will not be told whether you are correct or not.


Once you have answered all the questions, answer them again using the simulation to help you. This time you will get feedback about each individual answer.


General Instructions


This demonstration lets you examine the effects of base rate, true positive rate, and false positive rate on the probability that a person diagnosed with disease X actually has the disease. The base rate is the proportion of people who have the disease. The true positive rate is the probability that a person with the disease will test positive. The false positive rate is the probability that someone who does not have the disease will test positive. The demonstration is based on 10,000 people being tested. A tree diagram showing the results and calculations based on Bayes’ theorem are shown. They should always agree.


You can change the initial values and then press the “Calculate” button.


Step By Step Instructions


1. Try the following parameters:
base rate: .80
true positive: .50
false positive: .50


Compare P(D|T) to P(D) to determine whether the test has any usefulness.


2. Try the following parameters:
base rate: .01
true positive: .99
false positive: .05


Notice that even though the test is very accurate, most of the people diagnosed testing positive do not have the disease.


3. Suppose a test of suicidal behavior has a hit rate of .85 and a false positive rate of 0.10. Further suppose that the rate of suicide attempts in a college were 0.05. If the test were given to all students in the college and those testing positive were hospitalized to prevent suicide, what proportion of those hospitalized would have attempted suicide.


4. Tryout various other combinations of the parameters and explore the results.


Summary


The base rate is a very important determinant of the probability that someone who is diagnosed with a disease actually has it. Screening programs of low-risk populations can lead to a high proportion of false diagnoses.