Geoscience Reference
In-Depth Information
p =
0.6244
stats =
chi2stat: 2.6136
df: 4
edges: [1x8 double]
O: [8 8 5 10 10 9 10]
E: [1x7 double]
h e function automatically bins the data into seven classes. 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 0.6244 or ~62% (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 6,244 in 10,000. h e structure array
stats
contains the calculated ˇ
2
value, which is 2.6136 and dif ers from our
result of 6.2489 due to the dif erent number of classes. h e array
stats
also
contains the number of degrees of freedom ʦ=7-(2+1)=4, the eight edges
of the seven classes automatically dei ned by the function
chi2gof
, and the
observed and expected frequencies of the distribution.
3.10 The Kolmogorov-Smirnov Test
h e Kolmogorov-Smirnov (K-S) test introduced by Andrei N. Kolmogorow
and Nikolai W. Smirnov is similar to the ˇ
2
-test in that it also involves the
comparison of distributions, allowing two distributions to be tested for
derivation from the same population (Kolmogorow 1933, Smirnov 1939).
h is test is independent of the type of distribution that is being used and can
therefore be used to test the hypothesis that the observations were drawn
from a specii c theoretical distribution.
Let us again assume that we have a data set that consists of multiple
chemical measurements from a sedimentary unit. We can use the K-S test
to test the null hypothesis that these measurements can be described by a
Gaussian distribution with a typical central value (the mean) and a random
dispersion around the mean (the standard deviation). h e appropriate test
statistic is then
where
F
n
(
x
) is the empirical distribution function of the
n
measurements and
F
(
x
) is the cumulative distribution function expected from the theoretical
distribution. h e null hypothesis can be rejected if the measured
KS
value is
