Geoscience Reference
In-Depth Information
[h,p,kscalc, kscrit] = kstest(corg)
yields
h =
0
p =
0.8562
kscalc =
0.0757
kscrit =
0.1723
h e result
h=0
means that we cannot reject the null hypothesis without
another cause at a 5% signii cance level. h e
p
-value of 0.8562 or ~86%
(which is much greater than the signii cance level) means that the chances
of observing either the same result or a more extreme result from similar
experiments in which the null hypothesis is true would be 8,562 in 10,000.
h e output variable
kscalc=0.0757
corresponds to
kscalc
in our experiment
without using
kstest
. h e output variable
kscrit=1.723
dif ers slightly from
that in Table 3.1 since
kstest
uses a slightly more precise approximation for
the critical value for sample sizes larger than 40 from Miller (1956).
3.11 Mann-Whitney Test
h e Mann-Whitney test (also known as the Wilcoxon rank-sum test)
introduced by Henry B. Mann and Donald R. Whitney (1947), can be used
to determine whether two samples come from the same population, e.g.,
the same lithologic unit (
null hypothesis
), or from two dif erent populations
(
alternative hypothesis
). In contrast to the
t
-test, which compares the means
of Gaussian distributed data, the Mann-Whitney test compares the medians
without requiring a normality assumption for the underlying population, i.e.,
it is a non-parametric hypothesis test.
h e test requires that the samples have similar dispersions. We i rst combine
both sets of measurements (samples 1 and 2) and arrange them together
in ascending order. We then sum the ranks of samples 1 and 2, where the
sum of all ranks is
R
=
n
(
n
+1)/2 with
n
as the total number of measurements.
Published literature is full of dif erent versions of how to calculate the test
statistic. Here we use the version that can be found in Hedderich and Sachs
(2012, page 484):
