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Suppose you undergo a test for a nasty disease that affects one out of every 50,000 people. Your doctor assures you that the test is 98% accurate. It comes out positive. How likely is it that you have the disease?

Consider it this way. 50,000 people will fit in a typical major-league baseball stadium in the United States. The odds are that one person in the crowd has the disease. Now, administer the test, and tell everybody who has negative results to leave the stadium. The one afflicted will presumably stay, and so will everybody else with false positive readings. Since we are testing 50,000 people, and the test is only wrong one out of 50 times, a thousand people are going to get the wrong reading, and will be asked to stay. We've now got a thousand people in the stadium, and still only one has the disease, so your chance of having the disease is one in a thousand.

Our natural tendency, when combining evidence with what we already know, is to disregard what we already know and go with the evidence.

All contents of these pages Copyright 1997 by David H. Thornley.