Date: Dec 15, 2012 1:33 AM
Author: Halitsky
Subject: Effect of multiplying SE by sqrt(N), as per your post of 12/14 at 10:34pm

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 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.