Agriculture Reference
In-Depth Information
-ratio corresponding
to treatment is greater than the table value at
If the calculated value of
F
α
Varieties Grain weight(gm)/hill
A 150 148 145 145 140
B 162 158 150 155 148 146
C 140 142 144 146 149 140 152 150
D 130 134 135 132
E 145 135 134 140 142 137 138
Analyze the data and draw the necessary
conclusion.
This is a problem of completely randomized
design with unequal replications. The fixed effect
model
level of significance with (
t
1),(
n t
)degrees
of freedom, that is,
F
cal
> F
tab
α;ðt
1
Þ;ðntÞ
, the null
hypothesis is rejected; otherwise, one cannot
reject the null hypothesis. When the test is signifi-
cant, one should find out which pair of treatments
is significantly different and which treatment is
either the best or the worst with respect to the
particular characters under consideration. This is
accomplished with the help of the least significant
difference (critical difference) value per the given
formula below:
for
the
purpose
would
be
y
ij
¼ μ þ α
i
þ e
ij
, where
α
i
is the effect of the
r
ErMS
i
1, 2, 3, 4, 5. That means the
problem is to test
th variety,
i ¼
1
1
r
i
0
LSD
α
¼
r
i
þ
t
2
;ðntÞ
, where
i
and
i
0
refer to the treatments involved in compari-
son and
H
0
: α
1
¼ α
2
¼ α
3
¼ α
4
¼ α
5
against
H
1
: α
i
0
s are not all equal
t
is the table value of
t
distribution
at
α
level of significance with (
n t
)d.f.and
:
r
ErMS
1
1
r
i
0
r
i
þ
is the standard error of differ-
Let the level of significance be
α ¼
0.05.
ence (SE
d
) between the means for treatments
i
and
i
0
. Thus, if the absolute value of the difference
between the treatment means exceeds the
corresponding CD value, then the two treatments
are significantly different and the better treatment
is adjudged based on the mean values commensu-
rate with the nature of the character under study.
Varieties
A
B
C
D
E
150
162
140
130
145
148
158
142
134
135
145
150
144
135
134
145
155
146
132
140
140
148
149
142
146
140
137
Example 10.9.
An experiment was conducted
with five varieties of wheat. The following data
gives the weight of grains per hill (g) recorded
from different varieties:
152
138
150
Sum (
y
i
0
)
728
919
1,163
531
971
Average
y
i
ðÞ
145.6 153.167 145.375 132.75 138.714
Grand total GT
ðÞ¼
150
þ
148
þ
145
þþ
142
þ
137
þ
138
¼
4312
GT
2
n
4312
2
30
Correction factor CF
ðÞ¼
¼
¼
619778
:
1
150
2
148
2
145
2
142
2
137
2
138
2
Total sum of squares TSS
ð
Þ¼
þ
þ
þþ
þ
þ
CF
¼
1737
:
867
728
2
5
þ
919
2
6
þ
1163
2
8
þ
531
2
4
þ
971
2
7
Variety sum of squares VSS
ð
Þ¼
CF
¼
1231
:
78
Error sum of squares ErSS
ð
Þ¼
TSS
VSS
¼
1737
:
867
1231
:
78
¼
506
:
087
