Andy Long
This note is based on the technical appendix on page 35 of
[1]. It assumes that there are n regions on a map, and
that some regions are colored white and some black. Let be the
``connection matrix'' for which
if the
and
regions are joined, and
otherwise (Queen's contiguity).
Let
if the
area is black, and
if it is white.
Then
where
Assume that BW is asymptotically normally distributed for large enough n. The
first two moments of BW then approximate E(BW) and . Those
moments may be evaluated under two different assumptions:
In the first case,
and
in the second,
and
where A is the total number of joins on the map, and is the total
number of areas joined to the
area. Thus
while
and
Finally,
may be treated as a standard normal score (N(0,1)), and tested for significance.