Date: Dec 15, 2012 6:44 PM Author: Ray Koopman Subject: Re: Effect of multiplying SE by sqrt(N), as per your post of 12/14 at 10:34pm On Dec 14, 10:33 pm, djh <halitsk...@att.net> wrote:

> I have sent offline a PDF of the plots of AuqSE for N_1_a1_S and

> N_2_a1_s AFTER multiplying AuqSE by sqrt of its associated N. (This

> is the case we?ve been discussing in our last couple of posts as

> possibly indicating a putative ?SET? effect (set 1 vs set 2) on

> distribution of AuqSE over L.) Also, as you suggested in your last

> post, I?ve done these new plots as true scatter plots without

> connecting lines.

>

> Next to the N_1_a1_S and N_2_a1_S plots in the PDF, I have placed the

> R_1_a1_S and R_2_a1_s plots for comparison, and also the N_1_a1_C and

> N_2_a1_C plots. All four of these additional plots were also computed

> with the sqrt(N) multiplier.

>

> After looking at the PDF, please let me know at your earliest

> convenience whether you agree with the following:

>

> i) the switch from N_1 to N_2 STILL tightens the a1_S AuqSE

> distribution at higher values of L, even after multiplication of SE by

> sqrt(N) (so the effect is presumably NOT a sample-size artifact.)

>

> ii) the switch from R_1 to R_2 does NOT tighten the a1_S AuqSE

> distribtion at higher vslues of L;

>

> iii) the switch from N_1 to N_2 does NOT tighten the a1_C AugSE

> distribution at higher values of L.

>

> If you do agree with (i-iii), then I have to start again and, as

> above, present you with all N_1_S v N_2_S plots side-side-by-side with

> the corresponding R_1_S and R_2_S plots and the corresponding N_1_C vs

> N_2_C plots. (Any other choice of presentation would make it

> necessasry to shuffle too many sheets of paper (or windows) to see the

> presence/absence of the critical effect.) In addition, I have to

> regenerate the same n-tuples of plots with N_1 replaced by N_3 and R1

> replaced by R3 throughout.

>

> BUT, as per your instruction to work downwards from the most complex

> regression, I will start with the plots for AubqeSE and AubquSE (the

> SE?s of the average slopes for the regression of c on (e,u,u*e,u^2).

I agree with i,ii,iii. But I would do the SEP plots before doing the

AubqeSE & AubquSE plots. SEP is a structural parameter, but AubqeSE

& AubquSE depend on both SEP and the bivariate distribution of e & u

in your sample.

>

> I don?t know how to thank you beyond my usual expressions of gratitude

> ? we MAY have reached ?critical mass? here with respect to data that

> not only legitimize our linear regressions as generators of predictors

> for our logistic regressions, but also support a very SIMPLE

> evolutionary hypothesis regarding the role of the S subsets of our

> three nonrandom dicodon sets in the evolution of protein messages and

> the structures arising therefrom.

>

> Finally, I will be talking to Arthur Lesk this week-end about a1

> hemoglobin structure, so ?for the record?, please note the change in

> the distribution of AuqSe at N_1_a1_S and N_2_a1_S somewhere between

> 60 < =L <= 80. If my memory of hemoglobin structure is still intact,

> it is no accident we?re seeing a change in the distribution of AuqSE

> within this length interval.