Re: Curious coincidence

[reeds@xxxxxxxxxxxxxxxxxxxx (Jim Reeds)]

On Jun 12, 10:26, Gabriel Landini wrote:

... 
> SD makes sense only if the distribution is normal... but coin tossing 
> is not a gaussian process.
> What is that calculation trying to explain?
> Please do not take this as an impertinent comment. I just don't 
> understand what is the relation.

Gabriel is wrong about only gaussian random variables having
standard deviations.  Formulae involving standard deviations
of binomial (coin-toss-count) random variables are found in
all statistics & probability books.

But I share Gabriel's confusion about what the calculation is
trying to explain.  I took the given 2 by 2 count data,
(8772, 9016;  8591, 8423) and worked out two chi-squared test
statistics for it.  One was based on the null hypothesis that
all 4 counts had the same expectation (8700.5), which seems to
be what Stolfi and Rene are excited about, and the other is
the null hype that rows & columns are independent, that is,
the cell expectations are 
8874.577438     8913.422562
8488.422562     8525.577438

The first test has "3 degrees of freedom" and the second has "1
degree of freedom".  The test statistic values are 22.2572 and
4.8399, respectively.  The first is wildly significant and the
second is only silightly so: the 4 counts are obviously unequal,
and seem to look inhomogeneous.     




-- 
Jim Reeds, AT&T Labs - Research
Shannon Laboratory, Room C229, Building 103
180 Park Avenue, Florham Park, NJ 07932-0971, USA

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