Date: Dec 11, 2012 12:44 AM
Author: Ray Koopman
Subject: Re: Response to your last re Q and p

On Dec 10, 5:11 pm, djh <halitsk...@att.net> wrote:
> You wrote:
>
> ?But forget S-W and all the others in the list I gave. You want to be
> sensitive to what Stephens (1974) calls "alternative A", so you should
> use Q = -2*sum{ln p}. Refer Q to the chi-square distribution with df =
> 2*(the # of p's). This is a one-tailed test: the p-value for Q is the
> area in the upper tail of the chi-square distribution. For the p's
> that you sent, (Q, p) = (174.954, .00731) for e*u and (254.377,
> .870e-9) for u^2.?
>
> OK, will do. I?ll compute these before I finish the ?4-ups?.
> (However, I?d still like to eventually finish the 4-ups as well
> because for subset=S, method=N, fold=a1, set=1, the plot for u*e not
> only hit me right between the eyes, but did so strongly I was almost
> knocked out.)
>
> But one question.
>
> For getting p?s back from the t-distribution via the GNU/GSL functions
> accessible from PERL, we wound up doing this:
>
> one-tailed p = 1 - ( gsl_cdf_tdist_P( t, df )


Didn't we go into this once before? It seems familiar,
but I can't find the old posts. Anyhow, I suspect that

gsl_cdf_tdist_Q( t, df )

will get you the same thing, without having to subtract from 1,
the rule being that _P gets the lower tail and _Q gets the upper.
Also, shouldn't you be using abs( t ) ?

>
> where gsl_cdf_tdist_P is described here:
>
> http://www.gnu.org/software/gsl/manual/html_node/The-t_002ddistributi...
>
> So from what you just wrote re referring Q to the chi-sqaure
> distribution, I assume that I should do this:
>
> one-tailed p = 1 - ( gsl_cdf_chisq_Q( Q, df )


You want the upper tail, so don't subtract from 1.
Try it! Be an experimentalist, not a theoretician!

>
> where Q and df are computed as you specified and gsl_cdf_chisq_Q is
> described here:
>
> http://www.gnu.org/software/gsl/manual/html_node/The-Chi_002dsquared-...
>
> If you disagree, please let me know.
>
> Thanks very much, as always.