Geoscience Reference
In-Depth Information
p =
6.1183e-06
ci =
0.7011
1.7086
stats =
tstat: 4.7364
df: 118
sd: 1.3933
h e result
h=1
suggests that we can reject the null hypothesis. h e
p
-value
is extremely low and very close to zero suggesting that the null hypothesis
is very unlikely to be true. h e 95% coni dence interval on the mean is
[0.7011,1.7086], which again includes the theoretical dif erence between the
means of 25.5-24.3=1.2.
3.8 The F-Test
h e two-sample
F
-test by Snedecor and Cochran (1989) compares the
variances
s
a
2
and
s
b
2
of two distributions, where
s
a
2
>
s
b
2
. An example is the
comparison of the natural heterogeneity of two samples based on replicated
measurements. h e sample sizes
n
a
and
n
b
should be above 30. Both the
sample and population distributions must be Gaussian. h e appropriate test
statistic with which to compare the variances is then
h e two variances are signii cantly dif erent (i.e., we can reject the null
hypothesis without another cause) if the measured
F
value is higher than
the critical
F
value, which will in turn depend on the number of degrees of
freedom ʦ
a
=
n
a
-1 and ʦ
b
=
n
b
-1, respectively, and the signii cance level ʱ. h e
one-sample
F
-test, in contrast, virtually performs a
ˇ
2
-test of the hypothesis
that the data come from a normal distribution with a specii c variance (see
Section 3.9). We i rst apply the two-sample
F
-test to two distributions with
very similar standard deviations of 1.2550 and 1.2097.
clear
load('organicmatter_four.mat');
h e quantity
F
is the quotient of the larger variance divided by the smaller
variance. We can now compute the standard deviations, where