False positives

Suppose a person is chosen at random and is given a test for a disease. For example, imagine that this is a routine screening for a disease; the person may not have any symptoms. Suppose we know how effective the test is when it is given to a person who does have the disease (the probability the test is positive) and when given to a person who does not have the disease (the probability the test is negative). Furthemore, suppose we also know the percentage of the population that has the disease.

If a person tests postive, what is the probability that the person is ill?

The answer is to look at what percentage of positive tests are true positives.

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Dave Richeson, Created with GeoGebra