Geoscience Reference
In-Depth Information
9
(
)
−
∑
(
2
2
2
2
Treatment totals
No.of
)
plotsper treatment
−=
++
122
63
58
Treatment
S
df
=
CT
CT
= 1970 2963
.
3
8
Error
SS
=
Total
SS
−
Treatment
SS
− lock
S
df
B
=
293 7037
.
16
df
26
df
8
df
2
Tabulating these in the usual form:
Source of Variation
Degrees of Freedom
Sums of Squares
Mean Squares
Blocks
2
11.6296
5.8148
Treatments
8
1970.2963
246.2870
Error
16
293.7037
18.3565
Total
26
2275.6296
246 2870
18 3565
.
F
=
=
13 417
.
,significantat 0.01
816
/
df
.
The next step is to analyze the components of the treatment variability. How do the species com-
pare? What is the effect of fertilization? And does fertilization affect all species the same way (i.e.,
is there a species-nitrogen interaction)? To answer these questions we have to partition the degrees
of freedom and sums of squares associated with treatments. This is easily done by summarizing the
data for the nine combinations in a two-way table:
Nitrogen Levels
Species
0
1
2
Totals
A
122
63
55
240
B
88
58
56
202
C
119
64
58
241
Totals
329
185
169
683
The nine individual values will be recognized as those that entered into the calculation of the
treatment
SS
. Keeping in mind that each entry in the body of the table is the sum of three plot values
and that the species and nitrogen totals are each the sum of nine plots, the sums of squares for spe-
cies, nitrogen, and the species-nitrogen interaction can be computed as follows:
Treatment
S
df
= .
1970 2963
,aspreviously ca
lculated
8
3
(
)
−
∑
(
2
2
2
2
Species totals
No.ofplo
)
ts perspecies
−=
+
240
202
+
241
Species
S
df
=
CT
CT
9
2
156
485
9
=
−=
CT
109 8518
.
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