Statistical puzzle j8X001
James L-W
LYONSW at UCONNVM.UCONN.EDU
Wed Jun 15 10:05:57 EST 1994
I've got a real problem, and I hope to tap into the community
brain power. Credit goes where credit is due:
Supposed I have a 5 X 5 grid of squares, each square 25 cm long. They
are numbered at random (1-25), and I drop a canister of pick-up sticks
at random over the grid. I then count the number of times any two
squares share a stick TO THE EXCLUSION OF A THIRD. I start a matrix:
STICK
SQUARE PAIR 1 2 3 4 5 6 7 8 9 10 11 12 13 14...
#1,#2
#1,#3
#1,#4
#1,#5
#2,#3
The entries are the value which I will call RELATIVE APPARENT PROXIMITY,
taking uniquely shared sticks as a proxy for distance. If this value
is summed for all sticks, the value is SIGMA RAP for each taxon pair.
I then send these pairwise scores to a colleague with the challenge to
recreate the correct arrangement of the squares.
My question is: if three squares share a stick, is the value RELATIVE
APPARENT SYNAPOMORPHY for squares i and j independent of the RAP
value for i and k and j and k *to my collegue*?
HELP!
James
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