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 <> 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.