# Re: the ways of child prodigies

From: Michael Vassar (michaelvassar@hotmail.com)
Date: Tue Nov 08 2005 - 15:17:30 MST

GPA is the sum of a modest number of correlated variables. That could be
approximately Gaussian or could not be depending on the number of variables,
the range of values they can take, and the strength of the correlation. For
instance, given a single grade, or given two possible values (not
implausible in many classes) and a .5 correlation between grades in
different classes, GPA would be uniformly distributed. I wonder what the
actual distributions are, but that's not a SL4 question. Using good H&B
examples could be SL4 relevant however, because it's important that people
learn normative reasoning and H&B properly. Regression, like entropy and
evolution is not (as many though surely not most posters here think) an
active force but rather a statistical tendency that arises from logic in
many different circumstances.

>>Finally, I'm uncomfortable with the diagnosticity example. Reversion to
>>the mean is a consequence of a non-uniform distribution of priors. With a
>>uniform distribution of priors, say, GPA 3.5-4.0, 3.0-3.5, 2.5-3, 2-2.5,
>><2 (I'm guessing that those are rough quintiles) the subjects predictions
>>should not revert, though their confidence intervals should broaden.
>
>Priors in this case should be approximately Gaussian, in which case
>reversion to the mean is appropriate.

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