Geoscience Reference
In-Depth Information
For X:
2
(
116 0
33
. )
CT
=
=
407 76
.
x
(
) −=
2
2
Total
SS
=
36
.
+
+
48
.
CT
73 26
.
x
x
2
2
11 4
.
+
9 8
.
Block
SS
=
CT
=
54 31
.
x
x
3
2
2
2
42 0 40
.
+
.
+
40 0
.
−=
Treatment
SS
=
CT
315
.
x
x
11
Error
SS
=
Total
SS
Block
SS
Treatment SS x
=
15 80
.
x
x
x
For X Y:
(
116 0 324 4
33
. )(
.)
CT
=
=
1140 32
.
xy
Total
SP
=
(.
3
6689
)( .)
++
(.)(
4 8107
.)
CT
=
103 99
.
xy
xy
(.)(
11 4320
.)
++
(.)(
98 26 5
.)
Block
SP
=
CT
=
8
2271
.
x
y
xy
3
(. )(
42 0 106 4 40 11
.) (.)(
+
336
.) (. )(
+
40 0 104 4
.)
Treatment SP xy =
CT xy
= −
330
.
11
Error
SP
=
Total
SP
Block
SP
Treatment
SP
= 24 58
.
xy
xy
xy
xy
These computed terms are arranged in a manner similar to that for the test of group regressions
(which is exactly what the covariance analysis is). One departure is that the total line is put at the top.
Residuals
Source of Variation
df
SS y
SP xy
SS x
df
SS
MS
Total
32
205.97
103.99
73.26
Blocks
10
132.83
82.71
54.31
Treatment
2
4.26
-3.30
3.15
Error
20
68.88
24.58
15.80
19
30.641
1.613
On the error line, the residual sum of squares after adjusting for a linear regression is
= (
)
2
SP
SS
2
(.
24 58
15
)
xy
Residual SS
SS
=
68 88
.
=
30 641
.
y
80
x
This sum of squares has one degree of freedom less than the unadjusted sum of squares.
To test treatments we first pool the unadjusted degree of freedom and sums of squares and prod-
ucts for treatment and error. The residual terms for this pooled line are then computed just as they
were for the error line:
Residuals
Source of Variation
df
SS y
SP xy
SS x
df
SS
Treatment plus error
22
73.14
21.28
18.95
21
49.244
 
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