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Topic: lit/refs on bias of chi-sq. goodness of fit test due to fractional expected values
Replies: 6   Last Post: Sep 15, 2012 3:06 PM

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Richard Ulrich

Posts: 2,961
Registered: 12/13/04
Re: lit/refs on bias of chi-sq. goodness of fit test due to fractional expected values
Posted: Sep 7, 2012 9:28 PM
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On Wed, 5 Sep 2012 15:16:51 -0700 (PDT), Schorsch_MCMLX
<> wrote:

>When computing the chi-square test statistics for goodness of fit, almost always integral observed values are compared to fractional expected values. That means there will almost never be a fair chance for the test statistics to attain a value of zero. Thus, it will be biased towards larger values. Unfortunately, I cannot find any sources explicitly addressing this kind of bias. Does somebody know of references (printed or on the web) that are concerned with this bias? Can it simply be neglected in case the most frequently mentioned minimal recommendations on classes' frequencies etc. are fulfilled?
>Thanks for any hints... Schorsch

Any given small table has a limited *set* of p-values that
can be obtained by a particular, fixed procedure. I don't
think I would use the term "bias" for the absence, sometimes,
of computed values of 0, but there are certainly some
interesting issues that can be raised.

If you want "exact probabilities" to use the whole range,
so that you see p's all the way from 0 to 1,
you can employ an ad-hoc randomization of what is to be
reported. (So far as I know, no one has ever tried to
use this theoretical correction.)

The one place that I found a bunch of discussion was in these
"Journal of the Royal Statistical Society" references

Fishers vs 2x2 Pearson. ] Yates, et al. JRSS Series A (1984)
Shuster. JRSS Series A (1985) 148:317-327.
Upton. JRSS Series A (1992) 155:395-402.

In the 1984 article, Upton leant strongly against using Fishers' test.
In this article, he announces own conversion, crediting the arguments
of Barnard.

Rich Ulrich

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