Geoscience Reference
In-Depth Information
and
s
2
log
=
1 85979
.
Then the test for homogeneity is
(
)
−
(
)
(
)
∑
∑
2
2
2
χ
(
=
(.
2 3026
) og
s
(
n
−
1
)
(
n
−
1
) lo
g
s
i
k f
−
1
)
i
i
[
]
2
χ
=
(.
2 3026
)(.
1 85979
)()
43
−
79
.
81543
3
df
= .
0 358
This value of χ
2
is now compared with the value of χ
2
in an accumulative distribution of chi-square
for the desired probability level. A value greater than that given in the table would lead us to reject
the homogeneity assumption.
Note:
The original form of this equation used natural logarithms in place of the common loga-
rithms shown here. The natural log of any number is approximately 2.3026 times its common
log—hence, the constant of 2.3026 in the equation. In computations, common logarithms are
usually more convenient than natural logarithms.
The χ
2
value given by the above equation is biased upward. If χ
2
is nonsignificant, the bias is not
important. However, if the computed χ
2
is just a little above the threshold value for significance, a
correction for bias should be applied. The correction (
C
) is
1
−
1
∑
31
(
k
−+
)
∑
n
−
1
(
n
−
1
)
i
i
C
=
31
(
k
−
)
The corrected value of χ
2
is then
1
43
34 10475
(
−+ −
)
.
=
1 0502
.
34 1
(
−
)
DID YOU KNOW?
According to Ernst Mayr (1970, 2002),
races
are distinct, generally divergent populations
within the same species with relatively small morphological and genetic differences. The pop-
ulations can be described as ecological races if they arise from adaptations to different local
habitats or geographic races when they are geographically isolated. If sufficiently different,
two or more races can be identified as subspecies, which is an official biological taxonomy
unit subordinate to species. If not, they are denoted as races, which means that a formal rank
should not be given to the group or taxonomists are unsure whether or not a formal rank
should be given. Again, according to Mayr, “a subspecies is a geographical race that is suf-
ficiently different taxonomically to be worthy of a separate name” (pp. 89-94).
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