Previous | ToC Labs: Probability & Statistics. Part 1. Math Alive

Disease Testing Experiment

A certain percentage of the total population is infected with some particular disease. There exist tests to check whether someone is infected, and it is known how reliable these tests are. These reliabilities are given by two percentages:

  • If the test is administered to infected people, for what percentage does the test result confirm infection? (Reliability of positive tests)
  • If the test is administered to non-infected people, for what percentage does the test show they are indeed not infected? (Reliability of negative tests.)
Suppose you take the test. It comes back "positive," i.e. indicating that you are infected. Since the test is not 100% reliable, there is a chance that the test is mistaken, and that you are not infected at all. What is the probability that you are truly infected?

This lab lets you experiment with this question. You set the percentage of infected people in the total population and the reliabilities of the tests, the lab then computes the number of people who are infected or not, and the number within each of these groups who get a "positive" or a "negative" result.

If your test came out positive, then you are either in the "positive and infected" or "positive and not infected" groups. By looking at the sizes of these two groups, you can see how likely it is that you are infected.

Enter values in the top four white windows and click "Calculate." To try another set of data, click "Start Over." The applet doesn't work with decimal numbers as input. It also doesn't round off when the formula gives a non integer answer even though a "number of people" should always be an integer. If you want to make sure that you get integer answers for the number of people, input a multiple of 10,000 for total population.

Disease Testing Calculator

Previous | ToC Last Modified: August 2008