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