Re: Multiple comparison correction using p values alone

Of course Jerry is referring to problems with independence when he
asserts P(AB) is not P(A)*P(B), in general. I think much of my problem
with this thread is my faulty dealing with long-run concepts in
frequentist statistics. If I were to couch my question in terms of
probabilities, not p values, there would be less kerfuffle.

I'm working with the problem of multiple conclusions of monophyly in a
phylogenetic tree, retrodicting single historical events, so simple
probabilities seem appropriate. Ignoring for the moment problems with
correlation and sufficient statistics, if we have a molecularly based
tree that splits a long-uncontested taxonomic group into two groups
(lineages), and the person publishing the tree asserts Bayesian
posterior probabilities of 0.95 for each of two lineages of the split,
that means that the SET of two lineages being monophyletic (coherent,
not splitting themselves) has a probability (the product) of only 0.90
of being correct. For two lineages to be correct at the same time
(using molecular data which is probablistic, not descriptive), the
lineages must each average 0.957, nu?

The reason I ask this question on a statistics news group is to get
opinions uncontaminated by years of ignoring multiple comparison
problems in evolutionary phylogenetic study.

Richard

In general, P(AB) is not P(A)*P(B).

Jerry, what if we are given two independent p-values, say from two
different studies on separate groups of subjects. Study 1 tests the
hypothesis that some quantity say "Chemical X" is different than zero
in the population and using a t-test on their sample data finds that
the hypothesis may be rejected at p=0.02. Study 2 conducts a similar
test but finds p=0.10. May we conclude that the joint probability of
zero Chemical X in the popuation = (.02)(.10) = .05?

It seems Zander may reach that conclusion based on the theorem you
provided.

.

Relevant Pages

  • Re: Multiple comparison correction using p values alone
    ... asserts Pis not P*P, ... probabilities, not p values, there would be less kerfuffle. ... correlation and sufficient statistics, if we have a molecularly based ... posterior probabilities of 0.95 for each of two lineages of the split, ...
    (sci.stat.consult)
  • Re: Small Markov models problem
    ... Ross Clement (Email address invalid - do not use) wrote: ... is calculated with an independence assumption between two variables ... degrees of dependence between the two variables, ... probabilities leaves the extra step of having to fix-up the marginal ...
    (sci.stat.math)
  • Re: calculating P(X>=Y)
    ... Mark said: ... If you don't assume independence, then you have to resort to brute ... force summation of the probabilities where X and Y satisfy X>=Y. ... The uniform is a special case where you can get a simple ...
    (sci.stat.math)
  • Re: calculating P(X>=Y)
    ... independence. ... force summation of the probabilities where X and Y satisfy X>=Y. ... The uniform is a special case where you can get a simple ... Well done Afonso. ...
    (sci.stat.math)