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[Phys-L] Re: A Chi-square Failure



In his cryptic Phys-L post of 28 Nov 2005 22:55:18-0800 titled "A
Chi-square failure," Bernard Cleyet wrote (in its entirety!):

"<http://www.mcn.org/c/irapilgrim/men05.html> Any comments? bc, who
thanks Brian W."

A more informative version might read something like this:

Several decades ago Ira Pilgrim
<http://www.mcn.org/c/irapilgrim/irahome.html> published an article
"A Solution to the Too-good-to-be-true Paradox and Gregor Mendel"
[Pilgrim (1986)]. Pilgrim wrote, in part [bracketed by lines "PPPPPP
. . ."; see that article for the references]:

PPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
In 1936, R.A. Fisher(1) concluded, on the basis of a Chi-square
analysis, that Gregor Mendel
<http://www.mcn.org/c/irapilgrim/menhome.html> had falsified his
data. Because of my experience with experimental data, I believed,
empirically, that Fisher was wrong. The first step in refuting him
was to logically demonstrate that his method and conclusions might be
suspect. In 1984(3), I was able to show that Fisher's reasoning
contained a number of paradoxical elements, and that Mendel's honesty
or dishonesty could not be conclusively demonstrated using chi
square. Recently, Monaghan and Corcos(2) . . .[Note by Hake: I assume
that the date 1885 for this reference is a typo]. . . reviewed
Fisher's(1), Weiling's(5) and other's work. They concluded that:

"although the statistical procedure is undoubtedly correct, the
conclusion seems to us to be illogical. We have a series of
independent experiments, none of which show evidence of bias and
whose Chi-square values show no systematic trend. Yet the sum of
these individually unbiased experiments is judged as showing bias.
There seems to be no satisfactory solution to this problem at
present, at least not in the statistics."

The second step in refuting Fisher, is to show where he went wrong. I
have now solved that problem and can show why chi square is an
inappropriate tool for the detection of falsified data.
. . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . .
PPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP

Perhaps some Chi-square experts might like to comment.

See also Ira Pilgrim's interesting Science Page at
<http://www.mcn.org/c/irapilgrim/scihome.html>, especially his essay
on Darwin at <http://www.mcn.org/c/irapilgrim/sci61.html>.


Richard Hake, Emeritus Professor of Physics, Indiana University
President, Association for the Abolishment of Bare URL's (AABU)
24245 Hatteras Street, Woodland Hills, CA 91367
<rrhake@earthlink.net>
<http://www.physics.indiana.edu/~hake>
<http://www.physics.indiana.edu/~sdi>


REFERENCES
Pilgrim, I. 1986. "A Solution to the Too-good-to-be-true Paradox and
Gregor Mendel," Journal of Heredity 77:218-220, online at
<http://www.mcn.org/c/irapilgrim/men05.html>.
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