Geoscience Reference
In-Depth Information
7.9 Statistics of Point Distributions
h is section is about the statistical distribution of objects within an area,
which may help explain the relationship between these objects and
properties of the area. For instance, the spatial concentration of hand-axes in
an archaeological site may suggest that a larger population of hominins lived
in that part of the area, the clustered occurrence of fossils may document
environmental conditions that were favorable to those particular organisms,
the alignment of volcanoes may ot en help in mapping tectonic structures
concealed beneath the surface.
Various methods for the statistical analysis of point distributions are
introduced below. We i rst consider a test for a uniform spatial distribution
of objects, followed by a test for a random spatial distribution and i nally, a
simple test for a clustered distributions of objects.
Test for Uniform Distribution
In order to illustrate the test for a uniform distribution we i rst need to
compute some synthetic data. h e function
rand
computes uniformly-
distributed pseudo-random numbers drawn from a uniform distribution
within the interval [0,1]. We compute
xy
data using
rand
and multiply the
data by ten to obtain data within the interval [0,10].
clear
rng(0)
data = 10 * rand(100,2);
We can use the ˇ
2
-test introduced in Section 3.8 to test the hypothesis that
the data have a uniform distribution. h e
xy
data are now organized into 25
classes that are square subareas with dimensions of 2-by-2. h is dei nition
of the classes ignores the rule of thumb that the number of classes should be
close to the square root of the number of observations (see Section 3.3). Our
choice of classes, however, does not result in any empty classes, which should
be avoided when applying the ˇ
2
-test. Furthermore, 25 classes produce
integer values for the expected number of observations that are easier to
work with. We display the data as blue circles in a plot of
y
versus
x
. h e
rectangular areas are outlined with red lines (Fig. 7.10).
plot(data(:,1),data(:,2),'o')
hold on
x = 0:10; y = ones(size(x));
for i = 1:4, plot(x,2*i*y,'r-'), end
for i = 1:4, plot(2*i*y,x,'r-'), end
