Geoscience Reference
In-Depth Information
Poisson distribution is dei ned by only one parameter (Section 3.4), the
number of degrees of freedom is ʦ=6-(1+1)=4. h e measured ˇ
2
of
chi2 = sum((n_obs - n_exp).^2 ./n_exp)
chi2 =
3.7615
is well below the critical ˇ
2
, which is
chi2inv(0.95,6-1-1)
ans =
9.4877
We therefore cannot reject the null hypothesis and conclude that our data
follow a Poisson distribution and the point distribution is random.
Test for Clustering
Point distributions in geosciences are ot en clustered. We use a
nearest-
neighbor criterion
to test a spatial distribution for clustering. Davis (2002)
has published an excellent summary of the nearest-neighbor analysis,
summarizing the work of a number of other authors. Swan and Sandilands
(1996) presented a simplii ed description of this analysis. h e test for
clustering computes the distances
d
i
separating all possible pairs of nearest
points in the i eld. h e
observed mean nearest-neighbor distance
is
where
n
is the total number of points or objects in the i eld. h e arithmetic
mean of all distances between possible pairs is related to the area covered
by the map. h is relationship is expressed by the
expected mean nearest-
neighbor distance
, which is
where
A
is the area covered by the map. Small values for this ratio then
suggest signii cant clustering, whereas large values indicate regularity or
uniformity. h e test uses a
Z
statistic (Section 3.5), which is