From: John Conover <john@email.johncon.com>
Subject: Re: Judgment, Evaluation, Feedback, etc. LO9962
Date: Sun, 15 Sep 1996 19:52:59 -0700
John Constantine writes:
> Replying to LO9928 --
>
> Eric Bohlman speaks eloquently regarding the damned bell curve
> requirements which can inflict such pain on an organization by
> necessitating that there be some "bad" among the "good". As mentioned in
> another post (Thomas Benjamin) I offered that there are usually few good
> metrics which would provide justification (quantifiable) for telling
> someone across the desk that they are "bad" in relation to "our
> standards", when the standards themselves are flawed in the first place.
>
Which "bell curve" are you referencing? Those that have a standard
deviation that adds linearly, (ie., Brownian fixed increment fractals,
which are very common,) or, maybe, one that adds root mean square,
(ie., Gaussian, or Normal, which, also, are very common)[1]?
There is an interpretational difference. Many statistical variations
have characteristic distributions that look like "bell curves,"
(differing only by the kurtosis of the tails of the curve.) The
interpretation of "good" and "bad," (whatever those two terms mean,)
is subjective, and not objective without clarifying the mechanism of
the underlying statistical process[2]. Without this clarification, any
interpretation is nothing but "contemporary numerology. [see same
reference.]"
Actually, there are infinitely many "bell curves," all of which must
be interpreted differently [see first reference]. Such simple
classifications as "good" and "bad" have little meaning in formal
statistics-which, if I am not mistaken, is the essence of your
posting.
Just a formal clarification.
John
[1] "Fractals, Chaos, Power Laws," Manfred Schroeder, W. H. Freeman
and Company New York, New York, 1991, ISBN 0-7167-2136-8, pp. 157.
[2] "Searching for Certainty," John L. Casti, William Morrow, New
York, New York, 1990, ISBN 0-688-08980-1, pp. 201.
BTW, just as a tutorial note, two dice at a crap table exhibit a
Normal, or Gaussian, distribution of the variance of numbers on the
dice, over many throws. The gambler's capital, (that is playing
craps,) exhibits a variance that is fractal in character. The variance
of the dice can not be optimized and exploited by a gambler. The
variance in the gambler's capital can. Billions have been lost on
schemes that attempt to optimize the "dice" on Wall Street, as opposed
to optimizing the wagering strategy of a portfolio. A very subtile
difference, indeed. Both variances have "bell curve" distributions.
Ask any programmed trader, or see reference 1, pp. 128.
--
John Conover, john@email.johncon.com, http://www.johncon.com/