heterogeneity (RxC) tests power

Ivan Zimogorov ivan at manifesto.nihonkai.jp
Wed Nov 6 21:01:31 EST 1996

joe at evolution.genetics.washington.edu (Joe Felsenstein) wrote:
> In article <6352FR831.6FBV101996 at manifesto.Nihonkai.jp>,
> Ivan Zimogorov <ivan at manifesto.nihonkai.jp> wrote:
> >Well I came up with a novel way to test heterogeneity of gene frequencies
> >between samples of haploid individuals from several populations (sounds
> >like Karl Pearson, so what? :-)). The question is how to compare other
> >methods (like X^2, Fisher's exact, conditional X^2 etc) with it. I
> >simulated genetic drift by the coalescence process, then sampled from
> >diverged populations, repeated that process many times to get empirical
> >powers for the different degrees of divergence.. Therefore, under the
> >neutral scenario I have an idea how things behave.
> As you seem to be aware, heterogeneity chi-squares are testing whether
> the gene frequencies are different at all, and that difference could be 
> due to genetic drift.

Yes, but I look for the difference in power, and this could be different 
depending on what caused population divergence. Like, when one tests for
H-W disequilibrium due to a non-random mating, she's better off just by
doing a homozygosity test [H0: Hom(obs)=Hom(exp)]. But goodness of fit X2
will perform better in other situations (e.g. when there is no overall
trend in excess/deficit of heterozygotes).

Ivan Zimogorov

P.S. Thanks for the clarification regarding selection and 
non-equilibrium populations.

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