Graphics Programs Reference
In-Depth Information
hypothesized) difference of 0.2.
The second synthetic example shows the performance of the t-test on very
different distributions in the means. The means are 24.3 and 25.5, whereas
the standard deviations are again 1.3 and 1.5, respectively.
clear
load('organicmatter_three.mat');
This fi le again contains two data sets
corg1
and
corg2
. The t-test at a 5%
signifi cance level
[h,significance,ci] = ttest2(corg1,corg2,0.05)
yields
h =
1
significance =
6.1138e-06
ci =
0.7011 1.7086
The result
h=1
suggests that you can reject the null hypothesis. The signifi -
cance is extremely low and very close to zero. The 95% confi dence interval
on the mean is [0.7011 1.7086], which again includes the theoretical (and
hypothesized) difference of 1.2.
3.7 The F-Test
The 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 heterogenity of two samples based on replicated measurements. The
sample sizes
n
a
and
n
b
should be above 30. Then the appropriate test statistic
to compare variances is
The two variances are not signifi cantly different, i.e., we reject the alterna-
tive hypothesis, if the measured
F
-value is lower then the critical
F
-value,
which depends on the degrees of freedom
Φ
a
=
n
a
-1 and
Φ
b
=
n
b
-1, respec-
tively, and the signifi cance level
α
.
