Date: Dec 10, 2012 5:21 PM
Author: Ray Koopman
Subject: Re: 1) Just u*e and u^2(!!); 2) IOTs vs “proper”<br>	 tests

On Dec 10, 7:23 am, djh <halitsk...@att.net> wrote:
> I.
>
> You wrote:
>
> ?Hence there is no point in testing the coefficients of e and u in the
> regression of c on (e,u,e*u,u^2).?
>
> Thanks! Not only will it cut work load in half, but also allow me to
> put the C,N and S,N results for u*e and u^2 | fold,set on one page in
> what printers used to call a ?4-up? in the old-days. (See, for
> example, the 4-up for a1_1 I?ve sent offline.)
>
> In turn, such 4-ups will not only mean less PDF?s for you to look at,
> but may also reveal possible relations between u*e and u^2 that would
> otherwise not even be apparent. (I have many questions about such
> relationships between u*e and u^2, but will hold off until all the 4-
> ups are done.)
>
> II.
>
> You wrote:
>
> ?When the IOT test is not clear, there are many ways to do a proper
> test of the hypothesis that the p-values come from a Uniform[0,1]
> distribution ...?
>
> I?m going to wait till all 18 4-ups are completed for fold x method,
> and if some really interesting but IOT-undecidable cases arise within
> the 18, I will do the S-W?s using the PERL implementation described
> here:
>
> http://search.cpan.org/~mwendl/Statistics-Normality-0.01/lib/Statisti...
>
> That way (heh-heh-heh), I won?t even have to UNDERSTAND the S-W as
> described here:
>
> http://www.itl.nist.gov/div898/handbook/prc/section2/prc213.htm
>
> (Although seriously, I am interested in learning exactly how the ?a?
> constants in the S-W numerator are ?generated from [...] means,
> variances, and covariances [...].
>
> III.
>
> Here?s a dumber-than-usual question about S-W, if you have a moment.
>
> I used the Stata version of S-W back in 2005 to test the original
> dicodon over-representation data for normality BEFORE t-testing them.
> (I didn?t t-test anything that wasn?t normal.)


Such pre-testing for normality is usually not a good idea.

>
> And what I thought S-W was doing was seeing how well the data
> conformed to the familiar Gaussian or bell curve.
>
> But now we?re talking about S-W measuring departure from a uniform
> [0,1] distribution (i.e. the ?random backdrop? in the plots you?ve
> taught me how to construct.
>
> Is testing for fit to a Gaussian curve and testing for departure from
> a uniform [0.1] distribution the same thing?


For the record, no. 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.

>
> If you have time, could you clarify here? I realize it?s elementary,
> but when you explain something, I tend to understand it more or less
> immediately (as opposed to explanations by the "usual suspects".)