Geoscience Reference
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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
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