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ROGER THORNHILL



Thursday, August 04, 2005

The base-rate fallacy

Suppose there is a horrible disease that afflicts one in 10,000 people. And suppose the test for the disease is 99.99% accurate (i.e., a .01% chance of a wrong result). You test positive. What is the likelihood that you have the disease?

It doesn’t look promising, does it? But wait . . .

If you take 10,000 people, one of them will have the disease and 9,999 will not. The person with the disease is 99.99% likely to test positive. Testing the other 9,999, you can expect .01% of the tests to give a wrong result. Multiplying 9,999 by .0001, you get .999, meaning, for all practical purposes, that one person of the 9,999 gets a false positive.

So for every two people who test positive, one result is a false positive. You have a 50% chance of having the disease.

This illustrates the base-rate fallacy, "the tendency to ignore or under use base-rate information (information that describes most people) and instead to be influenced by distinctive features of the case being judged."

3 Comments:

Anonymous Anonymous said...

ok freak, you need to teach college level math in a non-english speaking country as pay back for all the "quality" teaching assistants at WSU from Bangladesh.

August 05, 2005 1:51 PM  
Blogger MWR said...

I'm trying to find ways to interpret this as a compliment, but it's tough.

August 05, 2005 2:17 PM  
Blogger Chase said...

I am trying to find ways to understand what the F@#* "anonymous" said.

August 07, 2005 9:49 PM  

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