posted 12-04-2008 02:24 PM            

Which gets me thinking. The odds seem intuitively to be astronomical.

The problem is that those astronomical odds are not as astronomical as one may think. If hole-in-one-events are truly a feature of random chance alone, and nothing else, then, yes, the odds are astronomically small. If hole-in-one events are non-random, and are a result of identifiable causal factors, like golfing skill, familiarity with the course, etc., then the odds are not unfathomable.

Truly random events will generally produce a Poisson distribution, non-random events more often follow a normal distribution. Non-random events, as factors, (and I suppose random events) can be evaluated for their correlation to outcomes, and can be combined through regression models to work in combination to improve predictive accuracy. That's what insurance companies and actuaries do.

It's like the lightning striking the same guy twice problem. Yes, the odds are low, and lightning is presumed to strike randomly. But lightning does not strike completely randomly. It favors certain targets. That's why lightning rods work. Also, the probability of being struck by lightning is a lot less random, and presumed greater, for the guy who is more often outdoors during lightning storms.

Truly random events tend to assume a Poisson distribution shape, for which the mean is equivalent to the variance. Non-random data more often follow a normal distribution shape.

The practical question is: how can we use our understanding on Poisson distributions and normal distributions, and the differences between the occurrence of random and non-random events, to evaluate the significance of odd or unusual tracing features during a polygraph test.

r

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