Geoscience Reference
In-Depth Information
Plot Pair
1
2
3
4
5
6
7
8
9
10
11
Sum
Mean
Race A
12
8
8
11
10
9
11
11
13
10
7
110
10.0
Race B
10
7
8
9
11
6
10
11
10
8
9
99
9.0
d
i
= A
i
- B
i
2
1
0
2
-1
3
1
0
3
2
-2
11
1.0
As before, we wish to test the hypothesis that there is no real difference between the race means.
The value of
t
when the plots have been paired is
XX
s
n
−
d
s
AB
t
=
=
,with (
n
−
1
) degrees of fre
edom
2
2
d
d
where
n
= Number of pairs of plots.
s
2
= Variance of the individual differences between A and B.
−
(
)
2
∑
d
n
2
11
11
i
∑
2
2
2
2
d
21
+++− −
…
()
2
i
2
s
=
=
= 2.
d
(
n
−
1
)
10
So, in this example we find
10 090
2611
.
−
.
t
=
=
2 057
.
10
df
.
When this value of 2.057 is compared to the tabular value of
t
in a distribution of
t
table (
t
0.05
with
10 degrees of freedom = 2.228), we find that the difference is not significant at the 0.05 level. That
is, a sample means difference of 1 cord or more could have occurred by chance more than one time
in twenty even if there is no real difference between the race means. Usually such an outcome is not
regarded as sufficiently strong evidence to reject the hypothesis.
“The method of paired observations is a useful technique. Compared with the standard two-
sample
t
test, in addition to the advantage that we do not have to assume that the two samples are
independent, we also need not assume that the variances of the two samples are equal” (Hamburg,
1987, p. 304). Moreover, the paired test will be more sensitive (capable of detecting smaller real dif-
ferences) than the unpaired test whenever the experimental units (plots, in this case) can be grouped
into pairs such that the variation between pairs is appreciably larger than the variation within pairs.
The basis for paring plots may be geographic proximity or similarity in any other characteristic that
is expected to affect the performance of the plot. In animal-husbandry studies, litter mates are often
paired, and where patches of human skin are the plots, the left and right arms may constitute the
pair. If the experimental units are very homogeneous, then there may be no advantage in pairing.
7.15.2.1 Number of Replicates
The number (
n
) of plot pairs needed to detect a true mean difference of size
D
is
=
22
2
ts
D
d
n
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