False Positive Test Result
A health clinic administers a test to determine if a patient has a certain disease. Assume the following is true: a) 2% of the overall population has the disease. b) If a person does have the disease, then the test has a 95% chance of correctly indicating that the person has it. c) If a person does not have the disease, then the test has a 10% chance of incorrectly indicating that the person has it resulting in a “false positive". If a patient tests positive, what is the probability that they actually have the disease?
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
Assume a large portion of the general population is being tested for the disease, say about 1,000. We know that 2% of the population, or 20 people are likely to have the disease while 980 don't. Of the 20, 95% or 19 persons will test positive. We also know that of the 980, 90% or 882 will test negative. The remaining 10% or 98 people test positive when they don't have the disease, "false positive." Therefore, the portion of persons tested that actually have the disease is 1 9 + 9 8 1 9 = 16%.