Geoscience Reference
In-Depth Information
7.17.5 a
nalysis
oF
C
ovarianCe
in
a
r
andomized
b
loCK
d
esign
A test was made of the effect of three soil treatments on the height growth of 2-year-old seedlings.
Treatments were assigned at random to the three plots within each of 11 blocks. Each plot was made
up of 50 seedlings. Average 5-year height growth was the criterion for evaluating treatments. Initial
heights and 5-year growths, all in feet, were as follows:
Treatment A
Treatment B
Treatment C
Block Totals
Block
Height
Growth
Height
Growth
Height
Growth
Height
Growth
1
3.6
8.9
3.1
10.7
4.7
12.4
11.4
32.0
2
4.7
10.1
4.9
14.2
2.6
9.0
12.2
33.3
3
2.6
6.3
0.8
5.9
1.5
7.4
4.9
19.6
4
5.3
14.0
4.6
12.6
4.3
10.1
14.2
36.7
5
3.1
9.6
3.9
12.5
3.3
6.8
10.3
28.9
6
1.8
6.4
1.7
9.6
3.6
10.0
7.1
26.0
7
5.8
12.3
5.5
12.8
5.8
11.9
17.1
37.0
8
3.8
10.8
2.6
8.0
2.0
7.5
8.4
26.3
9
2.4
8.0
1.1
7.5
1.6
5.2
5.1
20.7
10
5.3
12.6
4.4
11.4
5.8
13.4
15.5
37.4
11
3.6
7.4
1.4
8.4
4.8
10.7
9.8
26.5
Sums
42.0
106.4
34.0
113.6
40.0
104.4
116.0
324.4
Means
3.82
9.67
3.09
10.33
3.64
9.49
3.52
9.83
The analysis of variance of growth is
Source of Variation
Degrees of Freedom
Sums of Squares
Mean Squares
Blocks
10
132.83
—
Treatment
2
4.26
2.130
Error
20
68.88
3.444
Total
32
205.97
—
2 130
3 444
.
.
F
(
fortestingtreatments)
220
=
/
df
which is not significant at the 0.05 level.
There is no evidence of a real difference in growth due to treatments. There is, however, reason
to believe that, for young seedlings, growth is affected by initial height. A glance at the block totals
seems to suggest that plots with greatest initial height had the greatest 5-year growth. The possibil-
ity that effects of treatment are being obscured by differences in initial heights raises the question
of how the treatments would compare if adjusted for differences in initial heights.
If the relationship between height growth and initial height is linear and if the slope of the
regression is the same for all treatments, the test of adjusted treatment means can be made by
an analysis of covariance as described below. In this analysis, the growth will be labeled
Y
and
initial height
X
.
Computationally the first step is to obtain total, block, treatment, and error sums of squares of
X
(
SS
x
) and sums of products of
X
and
Y
(
SP
xy
), just as has already been done for
Y
.
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