"Radford Neal" <[EMAIL PROTECTED]> wrote in message
[EMAIL PROTECTED]">news:[EMAIL PROTECTED]...
> Contrary to some posts, I think situations with believable null
> hypotheses do exist. For instance, you might be interested in whether
> two genes are or are not on the same chromosome, and have linkage data
> to address this question. The quite believable null hypothesis would
> be that the genes are on different chromosomes, and therefore are
> completely unlinked.
I think that the point is not really whether there are true nulls (e.g.
unlinked genes), but whether the null can be expected to hold under the
conditions of your test statistic. In the case of your genes, one could use
a molecular biological protocol such as FISH and directly observe the
location of the genes on a chromosome, but there is not much statistics in
this. From an inference point of view, if one wanted to determine a lack of
linkage, then one must test whether the recombination fraction is equal to
0.5 (the segregation rate), as it should be under the true null hypothesis.
There are a number of reasons (segregation distortion, differential
viability effects of other linked loci on gametes and/or zygotes, occasional
translocations) why the statistic probably will not *exactly* equal the null
even when the biological null is true.
It is a combination of the lack of "all other things being equal" in real
physical systems and the fact that a specific statistic must be specified
that leads to the problem. I've heard some scientists call this a "problem
of too much power" -- they got a significant difference when they did not
--
Patrick Phillips
Biology Department
University of Oregon
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