Geoscience Reference
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where
w
i
(
x
) is the range of the
x
values for the
i
th
sample and
wx
is the range
of the sample means. Critical values of the test-statistic can be found in Sachs
(1972) or Kanji (2001). If computed values of the test-statistic are greater than
the critical values, the null hypothesis of equal variances is rejected at 5%
significance level. Furthermore, the critical value of the sample mean
differences (
D
) is expressed as (Kanji, 2001):
()
K
Ç
K
w
()
x
critical
i
i
1
D
=
(16)
n
k
where
K
critical
is the critical value of the test-statistic. If the mean differences
for a sample are greater than the value of '
D
', the null hypothesis of equal
means is rejected.
4.1.6 Dunnett Test
This test is used to investigate the significance of the differences in means,
when several samples are compared with a control one. This is a parametric
test with a limitation that the samples of equal sizes (
n
s
) are drawn independently
from normally distributed populations with equal variances. To apply this test
to a hydrologic record
x
t
(
t
= 1, 2, …,
n
), the entire series is divided into '
K
+ 1' subseries. The variance within the
K
+ 1 groups is calculated as (Kanji,
2001):
K
Ç
2
2
s
s
0
i
i
1
s
2
=
(17)
Kn
1
1
s
where
s
0
is the variance of the control subseries and
s
i
is variance of the
i
th
subseries. The standard deviation of the differences between control and
remaining subseries is then calculated as:
s
(
d
¯) =
2
(18)
2
sn
s
The test-statistic (
D
j
) is given by (Kanji, 2001):
i
xx
sd
0
()
D
j
=
(
i
= 1, 2, …,
K
)
(19)
Critical values of the test-statistic can be obtained from Kanji (2001). If
an observed value is larger than the tabulated value, it can be concluded that
the corresponding difference in mean between the subseries '
i
' and control is
significant. Similarly, each subseries may be considered as control and
significance of differences between all the sample means can be examined.
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