Agriculture Reference
In-Depth Information
s
ErMS
r
2
B ¼
½R
0
ðt
1
ÞX
t
SE
d
¼
2
þ
tðt
1
Þ
ðr
1
Þðt
1
Þ
s
0
2
¼
½
106
:
30
ð
6
1
Þ
19
:
12
¼
3
:
816
:
2636
4
6
6
ð
6
1
Þ
¼
2
þ
¼
0
:
398
:
ð
4
1
Þð
6
1
Þ
Corrected TrSS
¼
TrSS
B
Thus, to compare the variety having missing
value (V5) with the other varieties having no
missing value, SE
d
t
0.025,14
¼
¼
359
:
00
3
:
816
¼
355
:
18
;
0.398
2.145
ErSS
¼
TSS
RSS
TrSS corrected
ð
Þ
¼
0.854.
¼
363
:
20
0
:
51
355
:
18
¼
7
:
50
;
Variety
Average yield
where TSS, RSS, TrSS, and ErSS are the total,
replication, treatment, and error sum of squares,
respectively.
Construct the ANOVA table as given
below with the help of the above sum of squares
values.
V3
27.28
V2
23.73
V6
22.78
V5
19.36
V1
18.03
V4
15.68
From the table of means it is clear that variety
V3 is the highest yielder followed by V2, V6, and
so on.
ANOVA
SOV
d.f.
SS
MS
F
Replication
3
0.51
0.17
0.31733
Variety
5
359.00
71.80
272.38
Error
14
3.69
0.2636
10.10.2 Missing Plot Technique in LSD
Total
22
363.20
Variety
(corrected)
5
355.18
71.036
132.51
t t
For a missing observation in
Latin square,
G
0
be the total of available observations (excluding
the missing value) of
T
0
,
R
0
,
C
0
, and
let it be denoted by
y
ijk
and let
Error
14
7.506
0.5361
Let the level of significance be
α ¼
0.05.
th
column, and all available observations, respec-
tively; then the least square estimate for the
missing value is given by
i
th treatment,
j
th row,
k
Thus, one can find that the varietal effects
differ significantly among themselves. So we
are to calculate the CD values for comparing
the treatment means.
The treatment means having no missing value
are compared by usual CD value given as
y ¼
tðT
0
þ R
0
þ C
0
Þ
G
0
2
:
ðt
1
Þðt
2
Þ
Once the estimated value for the missing obser-
vation is worked out, the usual analysis of variance
is taken up with the estimated value of the missing
observation. The treatment sum of squares is to be
corrected by subtracting the upward biased
r
2ErMS
r
CD
0
:
05
¼
t
0
:
025
;
error df
r
2
0
:
5361
¼
t
0
:
025
;
14
4
r
2
2
ÞT
0
þ R
0
þ C
0
G
0
:
½
ð
t
1
0
5361
¼
2
:
145
¼
1
:
110
:
B ¼
:
2
4
½
ð
t
1
Þ t
2
ð
Þ
The treatment means are compared with the
mean having missing values using the formula
for standard error of difference as
The degrees of freedom for both total and
error sum of squares is reduced by one in each
case. The treatment means are compared with the
