Suppose an illness that can affect 1% of the people. Also assume that there is a test for that illness, that gives the correct result 99% of the times.

If you take that test, and receive a POSITIVE result, should you worry much?

If you take it again, and once more get a POSITIVE, should you worry then?

How many consecutive POSITIVEs would you have to get in order to be sure that the chances of a wrong diagnostic are 1 in a million?

I'm afraid this statistical effect is very common in real life, yet it is not understood by our society. For example, there have been many documented suicides among university students who have received a false positive in a single HIV test. Now many labs run at least two independent tests before giving out a positive.

The chances of sentencing an innocent person in our courts are also "pulled" by this statisticall effect.

For the sake of arguing, let's assume the prosecution and judicial system is correct 99.99% of the time. This is ok for common crimes, but for uncommon crimes the ratio of convicted innocent to total number of convicted people starts going up dramatically. For example, let's suppose that 0.01% of the population has ever committed a murder. Then the chances of an innocent person being convicted are 50%!!!!.

Of course in real life these numbers might be different, but the same statistical effect that brings the number of false positives up is present in lot's of aspects of our life.

I wonder how many people are aware of this. No one seems to bring it up in any of the debates I've seen about the burden of proof or the death penalty. They will debate about the 99.99% number (how often the justice system is correct), but that's about it.

A less exciting example is the number of people with "false positive" lottery tickes that show up at the lottery office. The people who claim the common prizes ususally have a winning ticket, but in the case of the jackpot a good percentage of them make an honest mistake.

Posted by ajosin on 2005-02-28 14:46:13