Agriculture Reference
In-Depth Information
T
0
¼
y ¼ X ¼
tðR
0
þ C
0
þ T
0
Þ
G
0
total of available entries of the variety V3
having the missing observation
C
0
¼
2
ðt
1
Þðt
2
Þ
total of available entries of the column
having the missing observation
G
0
¼
5
ð
51
:
5
þ
50
:
25
þ
56
:
5
Þ
2
311
¼
¼
14
:
104
ð
5
1
Þð
5
2
Þ
total of available entries in the whole design
Now,
G ¼ G
0
+
X ¼
311 + 14.104
¼
325.104
where
X ¼
Total of variety three
¼
56.5 +
X ¼
70.604
estimate of the missing value
Total of row three
¼
51.5 +
X ¼
65.604
R
0
¼
total of available entries of the row having
the missing observation
Total of column two
¼
50.25 +
X ¼
64.354
Calculate the following quantities:
2
t t
¼
104
2
¼
G
325
:
CF
5
¼
4227
:
704
;
5
X
Obs
2
5
2
5
2
5
2
25
2
TSS
¼
:
CF
¼
10
:
þ
9
:
þþ
10
:
þ
12
:
4227
:
704
¼
176.7634,
5
X
5
1
1
5
2
0
65
2
5
2
65
2
RSS
¼
1
y
CF
¼
þ
63
:
þþ
66
:
4227
:
704
¼
1
:
151531,
j
0
j¼
5
X
5
k¼
1
y
1
1
5
2
9
2
354
2
25
2
CSS
¼
00
k
CF
¼
65
:
þ
64
:
þþ
65
:
4227
:
704
¼
0
:
309531,
5
X
5
i¼
1
y
4227
:
704
¼
170
:
1305,
1
1
5
2
i
00
55
2
þ
86
:
5
2
þ
70
:
604
2
þ
49
2
þ
64
2
VSS
¼
CF
¼
ErSS
¼
TSS
RSS
CSS
VSS
¼
176
:
7634
1
:
151531
0
:
309531
170
:
1305
¼
5
:
171792
where TSS, RSS, CSS, VSS, and ErSS are the
total, row, column, variety, and error sum of
squares, respectively.
The upward bias is calculated as follows:
The table value of
F
0.05;4,11
¼
3.36. Thus, we
find that the calculated values of
are less than
the corresponding table value, except for variety.
So the tests for row and columns are nonsignifi-
cant. We conclude that neither the row effects
nor the column effects are significant. But the
effects of varieties are significant. So we are to
identify the best variety.
To compare the varietal means involving no
missing value, the CD(0.05) is calculated using
the following formula:
F
2
B ¼
G
0
R
0
C
0
ðt
1
ÞT
0
ð
Þ
2
½
ðt
1
Þðt
2
Þ
2
ð
311
51
:
5
50
:
25
ð
5
1
Þ
56
:
3
Þ
¼
¼
1
:
948
:
2
½
ð
5
1
Þð
5
2
Þ
Construct the ANOVA table as given below
using the above values:
r
2
MSE
t
CD
0
:
05
ð
Variety
Þ¼
t
0
:
025
;
err
:
df
:
r
2
MSE
5
ANOVA
SOV
d.f.
SS
MS
F
¼
t
0
:
025
;
11
r
Row
4
1.152
0.288
<
1
2
0
:
647286
5
Column
4
0.309
0.077
<
1
¼
2
:
201
¼
1
:
12
;
Variety
4
170.131
Error
11
5.172
and
to compare the varietal means with variety 3,
involving missing value, the CD(0.05) is calcu-
lated using the following formula:
Total
23
176.763
Variety
(corrected)
168.182
42.046
64.957
