Say you have a new disease, called Super-AIDS. Only one in a million people gets Super-AIDS. You develop a test for Super-AIDS thats 99 percent accurate. I mean, 99 percent of the time, it gives the correct results - true if the subject is infected, and false if the subject is healthy. You give the test to a million people.
One in a million people have Super-AIDS. One in a hundred people will generate a "false positive" - the test will say he has Super-AIDS even though he doesnt. That's what "99 percent accurate" means: one percent wrong.
What's one percent of one million?
1,000,000/100=10,000
One in a million people has Super-AIDS. If you test a million random people, you'll probably find one case of real Super-AIDS. But your test wont identify one person as having Super-AIDS. It will identify ten thousand people as having it.
Your 99 percent accurate test will perform with 99.99 percent inaccuracy.
Thats the paradox of the false positive. When you try to find something really rare, your test's accuracy has to match to the rarity of the thing you're looking for. If you're trying to point at a pixel on your screen, a sharp pencil is a good pointer: the pencil tip is a lot more accurate than the pixels. That basically explains the paradox of the false positive.
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2 comments:
this is very interesting
i never knew that it was the exact opposite
no wonder so many have unexpected pregnancies AFTER taking the test
Corry Doctorrow used this in Little Brother. nice to read btw.
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