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Direction, Not precision.

Most rational people know not to let a statistic make decisions for them. For example, 90% chance of rain tomorrow doesn’t actually mean that it is definitely going to rain. Adding class where 90% of students get an A doesn’t mean you should stop attending class and stop doing all homework. However, for some reason, many people feel that a probability that is calculated using formulas learned in school produces more definitive answers. For example, if I said that Bayes’ Theorem calculates a 90% chance that person X was the murderer, you’d probably be more inclined to believe he did the crime than it’s going to rain just because a forecaster was 90% sure of it. In fact, you’d probably be extremely convinced he was the killer, and be cautious if you were left in the same room with him.

However, according to an article in the Wall Street Paper, this is not an assumption you should make—the 90% statistic should not be enough evidence to convict a man. Information in such a complex scenario is always incomplete—even if the database is as convincing as a library of DNA. This incompleteness may only account for the “missing 10%”, but means so much more. In a court trial, whether the man on trial committed the murder has already been determined (he either did it, or didn’t) to be 0 or 1. The 90% has absolutely no influence on whether the man committed the murder—even if more recent evidence and Bayes’ Theorem determined that there was a 99.99% chance he is guilty.

Suppose, by some chance, the man is not the murderer, the “missing 10%” would then explain the difference between a 0 and 1 chance of him committing the crime… and also the difference between a 0 and 1 chance of him becoming convicted. Therefore, the 90% has a misleading amount of power in the courtroom. A number shouldn’t hold someone hostage. The statistic should provide a general direction in pointing to the unlikelihood of the crime having been committed by another man, not the definitive likelihood of the crime being committed by this one.

http://online.wsj.com/article/SB10001424052970204002304576628660692030584.html

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