On Thu, 5 Feb 2009, Albyn Jones wrote:
The computation 2*sum(dbinom(c(10:25),25,0.061)) does not correspond
to any reasonable definition of p-value. For a symmetric
distribution, it is fine to use 2 times the tail area of one tail.
For an asymetric distribution, this is silly.
"Silly" is much too strong. There is a perfectly good reason to compare
2*sum(dbinom(c(10:25),25,0.061)) to a two-sided test threshold.
The argument is that what we are really doing in usual two-sided location tests
is two one-sided tests at alpha/2 rather than one two-sided test at alpha. The
null hypothesis is being compared to two different alternatives (better or
worse vs same) and the decisions about the future would be different depending
on which tail we ended up using.
This argument says that we we should compare a one-sided tail area such as
sum(dbinom(c(10:25),25,0.061)) to alpha/2; equivalently that we should compare
2*sum(dbinom(c(10:25),25,0.061)) to alpha [or to informal standards for
strength of evidence or whatever you typically do with p-values]. I'm not
saying that this is the only sensible way to handle and interpret p-values in
two-sided tests, but I really don't think it can be dismissed as 'silly'.
-thomas
Thomas Lumley Assoc. Professor, Biostatistics
tlum...@u.washington.edu University of Washington, Seattle
PS: Daniel Dennett has described as an occupational hazard for philosophers the tendency to go from "I can't imagine X" to "No one can imagine
X" to "X is inconceivable". The transition from "I can't imagine how X would be used" to "X is useless" is somewhat
similar, as is the Extreme Bayesian transition from "X wasn't derived by a formal consideration of posterior expected loss" to "X can't be
derived by a formal consideration of posterior expected loss" to "X is incoherent". Why, yes, I am grumpy about a reviewer. How did you guess?
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