Geoscience Reference
In-Depth Information
Group I
Group II
Group III
Subtotals
Attacked by termites
193
148
210
551
Not attacked
307
352
390
949
Subtotals
500
500
500
1500
If the data in the table can be symbolized as shown below:
Group I
Group II
Group III
Subtotals
Attacked by termites
a
1
a
2
a
3
A
Not attacked
b
1
b
2
b
3
B
Subtotals
T
1
T
2
T
3
G
then the test of independence is made by computing
3
2
1
(
aB
−
bA
)
∑
i
i
χ
2
=
( ()
AB
T
i
i
=
1
2
2
(
)
++
(
)
1
551 94
(
193
)(
949
)
−
(
307
)(
551
)
(
210
)(
949
)
−
(
290
)(
551
)
=
…
(
)(
9
)
500
500
=
17 66
.
The result is compared to the appropriate tabular accumulative distribution of chi-square values
of χ
2
with (
c
- 1) degrees of freedom, where
c
is the number of columns in the table of data. If the
computed value exceeds the tabular value given in the 0.05 column, then the difference among treat-
ments is said to be significant at the 0.05 level (i.e., we reject the hypothesis that attack classification
is independent of termite-repellent treatment).
For illustrative purposes, in this example, we say that the computed value of 17.66 (2 degrees of
freedom) exceeds the tabular value in the 0.01 column, so the difference in rate of attack among
treatments is said to be significant at the 1% level. Examination of the data suggests that this is pri-
marily due to the lower rate of attack on the Group II stakes.
7.14.2 t
est
oF
a
h
ypothesized
C
ount
A geneticist hypothesized that, if a certain cross were made, the progeny would be of four types, in
the following proportions:
A
= 0.48,
B
= 0.32,
C
= 0.12,
D
= 0.08
The actual segregation of 1225 progeny is shown below, along with the numbers expected according
to the hypothesis:
Type
A
B
C
D
Total
Number (
X
i
)
542
401
164
118
1225
Expected (
m
i
)
588
392
147
98
1225
As the observed counts differ from those expected, we might wonder if the hypothesis is false. Or,
can departures as large as this occur strictly by chance?
Search WWH ::
Custom Search