analysis questions

Dmitri Zaykin zaykin at statgen.ncsu.edu
Thu Feb 6 18:44:30 EST 1997


smallm at PBS.DFO.CA wrote:
> CHIHW said the populations was in HWE with a probability of 0.96
> yet the Selander D value (probability of the observed hz = expected hz)
> was 0.

Was D equal to zero, or the probability of observing your data
under the hypothesis D=0 was zero?

It might be that you have allele names like "a" and "A", but your
version of CHIHW treats lower- and upper case the same. At some point
we got rid of that "feature". If this is the case, you can take an
updated version:

   ftp://brooks.statgen.ncsu.edu/pub/zaykin/chihw.exe

I will put it there this evening.

> Has anyone had populations out of equilibrium test out within equilibrium 
> with CHIHW?  I would appreciate any light people can shed on these puzzling 
> results.

CHIHW performs a test conditional on allele counts. Genotype arrays
are ranged by the magnitude of X2, D, and abs(D). If departure from
HWE is caused by inbreeding (or otherwise there is a single fixation
index for all heterozygote classes), then D and abs(D) will show
greater power. An alternative for X2 ranking is the inverse of
conditional probability. In that case the test is a Monte Carlo
multi-allelic form of Haldane's test. The difference in power between
conditional X2 and 1/Cond_Pr depends on the circumstances. An
important thing is that these tests are conditional. Suppose that we
are drawing samples of fixed sizes from the same population. Every
time the number of alleles of any type differs from some a priori
fixed number, we disregard that particular sample. Then we compute the
test statistic for all remaining samples. We expect that the
(conditional) statistic values will fall into the rejection region 5%
of the time or less (considering only these remaining samples). Under
such (not necessarily valid) arrangement the Haldane's test based on
the cumulative conditional probability should be superior over other
conditional tests.

Unconditional exact test for HW disequilibrium is computationally
hard, but possible.

Dmitri



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