Date: Dec 5, 2012 3:00 AM
Author: Halitsky
Subject: I'm VERY glad you'll know how to answer this "perms and combs"<br> question !

The following table is derived in the obvious way from the rankings of
"m" in CI plots of the regressions of two of our average slopes
against all available singleton lengths (Average slope ?Aube? is for
the e coefficient of the regression c on (u,e,u*e) and average slope
Aubqe is for the e coefficient in the regression c on (e,u,u*e,u^2).


a1 a3 b1 b47 c1 c2
C S C S c S c S C S C S "Het"

N1 Aube H H L L H H H H L L L L 0
Aubqe H H L L H H H H L L L L 0

N2 Aube L L L H H H H H L L H L 2
Aubqe L H L H H L H H L L H L 4

N3 Aube L L H H L L H H H H L L 0
Aubqe L L H H L L H H H H L L 0

R1 Aube H L H H H L H L L L L H 4
Aubqe H L H H H H H L L L L H 3

R2 Aube L L L H L H L L H H H H 2
Aubqe L L L H H H L L H H L H 2

R3 Aube L H L H L L H H H H L L 2
Aubqe L H L H L L H H H H L L 2


For example, the N1 Aube row was derived from this set of values:

Fold
Method
Set
Subset Aube

c1_N_1_C -0.000013
a3_N_1_C 0.000002
a3_N_1_S 0.000174
c1_N_1_S 0.000222
c2_N_1_C 0.000543
c2_N_1_S 0.000581
a1_N_1_S 0.000598
b47_N_1_C 0.000639
b47_N_1_S 0.001017
b1_N_1_S 0.001754
a1_N_1_C 0.001913
b1_N_1_C 0.002033

in which:

a) both a1 values are among the highest 6
b) both a3 values are among the lowest 6
c) both b1 values are among the highest 6
d) both b47 values are among the highest 6
e) both c1 values are among the lowest 6
f) both c2 values are among the lowest 6

So here?s the question:

What is the probability of ?het = 0?, as in the case of the N1 Aube
and Aubqe rows and the N3 Aube and Aubqe rows. That is, what is the
probability that every one of the six folds will have the same value
(H or L) for both S and C?

The reason why this question is so important is that the above data
paradigm is kind of the ?inverse? of the one we saw for average slope
Auq, where ?het = 6 for N1 and 5 for N2. And in that sense, the
scientifically interesting thing about Aube and Aubqe is that the
solution to the mystery of their behavior lies in the Sherlock Holmes
story whose plot turns on the fact that the dog DIDN?T bark:

http://en.wikipedia.org/wiki/Silver_Blaze