Agriculture Reference
In-Depth Information
Table 10.12
ANOVA table for LSD
Sources of variation
d.f.
SS
MS
F
-ratio
TrSS
t
TrMS
ErMS
Treatment
t
1
TrSS
TrMS
¼
1
RSS
t
1
RMS
ErMS
Row
t
1
RSS
RMS
¼
Column
t
1
CSS
CSS
t
CMS
ErMS
RMS
¼
1
ErSS
Error
(
t
1)(
t
2)
ErSS
ErMS
¼
ðt
1
Þðt
2
Þ
2
Total
t
1
TSS
Hypothesis to Be Tested
against
H
0
: ð
1
Þ α
1
¼ α
2
¼¼α
i
¼¼α
t
¼
0
;
H
1
:ð
1
Þ α
's are not equal,
ð
Þ β
1
¼ β
2
¼¼β
j
¼¼β
t
¼
;
ð
Þ β
2
0
2
's are not equal,
ð
Þ γ
:
3
's are not equal
ð
3
Þ γ
1
¼ γ
2
¼¼γ
k
¼¼γ
t
¼
0
Analysis
From least square estimates
;
we have
XX
X
X
X
X
2
2
2
2
ðy
ijk
y
000
Þ
¼ t
ðy
i
00
y
000
Þ
þ t
ðy
0
j
0
y
000
Þ
þ t
ðy
00
k
y
000
Þ
i; j; k
i
j
k
X
2
þ
ðy
ijk
y
i
00
y
0
j
0
y
00
k
þ
2
y
000
Þ
;
i; j; k
TSS
¼
Tr SS
þ
RSS
þ
CSS
þ
ErSS,
P
t
i¼
where
μ ¼ y
000
; α
i
¼ y
i
00
y
000
; β
j
¼ y
0
j
0
y
000
;
γ
k
¼ y
00
k
y
000
;
y
000
¼
1
y
i
00
2
t
ð
Þ¼
Treatment sum of squares TrSS
CF
¼
y
2
100
t
þ
y
2
200
t
þ
y
2
300
t
þ
y
2
i
00
t
þþ
y
2
t
00
t
CF
2
observations,
mean of all
t
P
t
j¼
1
y
0
j
0
2
t
y
i
00
¼
mean of
t
observations from
i
th treatment,
y
0
j
0
¼
mean of
t
observations from
j
th row,
Row sum of squares RSS
ð
Þ¼
CF
y
00
k
¼
mean of
t
observations from
k
th column
:
2
0
2
010
2
020
2
030
t
þ
y
2
0
¼
y
t
þ
y
t
þ
y
t
þþ
y
j
0
0
t
t
CF
Various sums of squares are calculated using
the following formulae (Table
10.12
):
P
t
k¼
1
y
00
k
2
X
Grand total
¼
y
ijk
¼ G
Column sum of squares CSS
ð
Þ¼
CF
t
ði;j;kÞ2D
¼
y
2
001
t
þ
y
2
002
t
þ
y
2
003
t
þ
y
2
00
k
t
þþ
y
2
00
t
2
Correction factor
¼
ðGÞ
t
CF
¼
CF
t
2
X
ð
Þ
2
Error sum of squares by subtraction
Total sum of squares TSS
ð
Þ¼
y
ijk
CF
ði;j;kÞ2D
¼
TSS
TrSS
RSS
CSS
