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An example

Posted By: David Rockwell
Date: Saturday, 30 June 2012, at 3:01 a.m.

In Response To: Timothy (Matt Cohn-Geier)

Here's the problem that I see with the mathematics. Let's say that you put a case in front of me where someone correctly guessed X% of coin flips. I do my statistics and find that the odds against this happening were 1 in 10,000. I conclude that the guy must have been cheating with his guesses because that is so unlikely. Then I discover that 100,000 people took part in the experiment. And this guy had one of the best records. That's why he was chosen for evaluation. Now this looks entirely different. It was very likely that someone was going to get at least X% right. The flips may have been random. But, the person wasn't randomly selected for evaluation. He was selected because he did so well. This is why a statistician would collect subsequent data after the subject was selected.

This example was constructed as an extreme case to illustrate the technical point raised by the others who commented. As seen by MCG's illustration, there are times when common sense should trump scientific purity. I'll step aside and let others decide where to draw that line.

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