Thursday, October 14, 2010

For Those Of You Who Thought

...that FLG's conversation about the hypothesis test for slope of regression line was funny, FLG learns of a new blog, Andrew Gelman's, from Jim Manzi over at American Scene, about statistics. FLG'll be adding it to the blogroll.

Here's something from the latest post:
Exercise 1(b) involves evaluating the normal pdf at a single point. But p(Y=y|mu,sigma) = 0 (and is not simply N(y|mu,sigma)), since the normal distribution is continuous. So it seems that part (b) of the exercise is inappropriate.

The solution does actually evaluate the probability as the value of the pdf at the single point, which is wrong. The probabilities should all be 0, so the answer to (b) is undefined.

For those of you unfamiliar with statistics, this probably becomes even funnier when spoken aloud.

For example, "Exercise 1(b) involves evaluating the normal pdf at a single point. But p(Y=y|mu,sigma) = 0 (and is not simply N(y|mu,sigma)), since the normal distribution is continuous. So it seems that part (b) of the exercise is inappropriate."

Becomes:
"Exercise 1(b) involves evaluating the normal probability density function at a single point. But the probability that Y equals y conditioned upon mu and sigma equals zero and is not simply the normal distribution of y conditioned upon mu and sigma, since the normal distribution is continuous. So it seems that part (b) of the exercise is inappropriate."

Or at least FLG think it becomes that. FLG doesn't really know anything about statistics, which is why this will be added to the blogroll.

1 comment:

Andrew Stevens said...

Our conversation in the comments of that post would have been a lot less convoluted if I could find my textbook. I know I went through a derivation once, but damned if I can remember it now. I'm pretty sure I got close with my last comment, except there really ought to be a square root of n in there. I'm sure it just cancels out somewhere with the other piece, but I'd be happier if I could confirm that.

 
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