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--- In equismetastock@xxxxxxxxxxxxxxx, superfragalist <no_reply@xxxx>
wrote:
> If the central limit theorm says that a sample size of 30 is
> statistically significant and my doctor concludes that based on having
> done the surgery 30 times, I only have a 2% chance of dying, I might
> feel somewhat reluctant to embrace the central limit theorm in regards
> to trusting it with my life. I may want to tell my doctor to call me
> when there's been 30,000 of these surgeries and give me my odds.
I beg to differ. The central limit theorem is "sorta kinda" related to
your claim but your "explanation" is highly misleading. The CTL
(Central Limit Theorem) 'says' that if you add a 'sufficient' number of
random variables together then the distribution of resulting composite
distribution converges to a Gaussian or normal distribution REGARDLESS
of what the distributions of the individual random variables are. There
are several caveats involved. An essential caveat is that the random
variables must be independent. It is commonly assumed that stock
returns are normally distributed BECAUSE of the CLT. Unfortunately,
there are VERY MANY commonly traded equities that categorically DO NOT
have Gaussian or normally distributed returns. Fortunately, (heh heh)
those cases produce highly mispriced option premiums BECAUSE the Black-
Scholes pricing model assumes (relying on the CLT) that returns are
Gaussian. Further, garden variety measures of central tendency
(averages) and/or data dispersion (standard deviation) only
have 'meaning' when applied to Gaussian data. Sure, folk use logarithms
to 'shoe-horn' stock data into something resembling a normal
distribution but they do that so they can "sorta kinda" apply stat
tools (Averages, Std. Devs. etc)where they have meaning. All of the
discussion concerning "Statistical Significance" when the time
structure of a series is thrown out the window is nonsense. Of course,
when your only tool is a hammer - all the world is a nail. Have fun but
be careful! Regards,
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