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Luis A. Afonso
Posts:
4,518
From:
LIsbon (Portugal)
Registered:
2/16/05


Of course NOT Mr. Whitlock . . .
Posted:
Aug 30, 2012 2:25 AM


M. C. Whitlock, Combining probability from independent tests: the weighted Zmethod is superior to Fisher´s approach J. Evol. Biol. 18 (2005)13681375, European Society for Evolutionary Biology.
Reporting . . . Fisher´s method, however, does have one significant in this context. It treats large and small Pvalues asymmetrically. It is easiest to see this problem with an example (see Rice 1990). Imagine there were two studies on a topic that we would like to combine. One of these studies rejected the null hypotheses with P=0.001 while the other did not with P=0.999. Clearly, on average there is no consistent effect in these two studies, yet by Fisher´s method the Pvalue is P=0.008.
Rice W. R. (1990) A consensus combined Pvalue test and a familywide significant of components tests. Biometrics 46 303308.
My Objection
My analysis focuses exclusively the text above. In particular the Rice/Stouffer´s method does not concern me here. Given that F = 2*(log .001 + log .999) = 13.8175 and Prob. Chi2(4) >13.28 = 0.990 I got Rice is thinking at a twocomponent experiment. Then it is easily shown by simulation that a Pamplitude of two random numbers larger than 0.998 is very unlike: prob.= 4/million approx. So the Null Hypotheses shared by both is completely unacceptable (see text ). It results that Rice´s argument against Fisher´s way falls on earth . . . Of course if the number of components gets large then is more and more likely they reach large amplitudes. A crucial point: the Pvalues follows a uniform Distribution only if we hit *the bulls eye*, the proposed/tentative parameter´s value to test is exactly equal to the Population one. As long I got Whitlock had performed his task following this direction: finding backwards the population pvalues by simulation data resampling and drawing conclusions about.
Luis A. Afonso



