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".)