Geoscience Reference
In-Depth Information
DID YOU KNOW?
The term “block” derives from experimental design work in agriculture in which parcels of land
are referred to as
blocks
. In a randomized block design, treatments are randomly assigned to
units within each block. To test the yield of different fertilizers, for example, this design ensures
that the best fertilizer is applied to all types of soil, not just the best soil (Hamburg, 1987).
Each plot consisted of a planting of 100 cuttings of the clone assigned to that plot. When the trees
were 5 years old the heights of all survivors were measured and an average computed for each plot.
The plot averages (in feet) by clones and blocks are summarized below:
Clone
Block
Totals
Block
A
B
C
D
I
18
14
12
16
60
II
15
15
16
13
59
III
16
15
8
15
54
IV
14
12
10
12
48
V
12
14
9
14
49
Clone totals
75
70
55
70
270
Clone means
15
14
11
14
—
The hypothesis to be tested is that clones do not differ in mean height. In this design there are
two identifiable sources of variation—that attributable to clones and that associated with blocks.
The remaining portion of the total variation is used as a measure of experimental error. The outline
of the analysis is therefore as follows:
Source of Variation
Degrees of Freedom
Sums of Squares
Mean Squares
Blocks
4
Clones
3
Error
12
Total
19
The breakdown in degrees of freedom and computation of the various sums of squares follow the
same pattern as in the completely randomized design. Total degrees of freedom (19) are one less
than the total number of plots. Degrees of freedom for clones (three) are one less than the number of
clones. With five blocks, there will be four degrees of freedom for blocks. The remaining 12 degrees
of freedom are associated with the error term.
Sums-of-squares calculations proceed as follows:
2
20
X
n
2
270
20
1.
CT
=
=
=
3645
20
(
)
−=
∑
2
2
2
2
2.
Total
SS
=
XCT
− =+++
18
15
…
14
CT
37
66
−
3645
=
121
19
df
4
∑
(
2
Clone totals
No.ofplots p
)
er clone
2
2
2
2
−=
+++
−= −
75
70
55
70
3.
Clone
S
df
=
CT
CT
3690
3645
=
45
5
3
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