Agriculture Reference
In-Depth Information
s
MSE
t
s
MSE
t
t
ðt
1
Þðt
2
Þ
t
ðt
1
Þðt
2
Þ
CD
0
:
05
ð
Variety
Þ¼
2
þ
t
0
:
025
;
err
:
df
:
¼
2
þ
t
0
:
025
;
11
s
0
:
647286
5
5
¼
2
þ
2
:
201
¼
1
:
231
:
4
3
Factors
A factor is a group of treatments. In a factorial
experiment different varieties may form a factor
and different doses of nitrogen or different irriga-
tion methods may form other factors in the same
experiment. Here variety, nitrogen (irrespective
dose), and irrigation schedule (irrespective of
types) are the factors of the experiment.
Levels of Factors
Different components of a factor are known as
the levels of the factor. Different varieties under
the factor variety form the level of the factor
variety; similarly doses of nitrogen, types of irri-
gation, etc., are the levels of the factors nitrogen,
irrigation, etc., respectively.
Variety Mean yield
V2 17.30
V3 14.12
V5 12.80
V1 11.00
V4 9.80
Comparing the varietal differences with
appropriate CD values, it can be inferred that
all the varieties are significantly different from
each other. Variety V2 is the best yielder, while
variety V4 is the lowest yielder.
10.11 Factorial Experiment
Instead of conducting many single-factor
experiments to fulfill the objectives, a researcher
is always in search of experimental method in
which more than one set of treatments could be
tested or compared. Moreover, if the experi-
menter not only wants to know the level or the
doses of individual factor giving better result but
also wants to know the combination/interaction
of the levels of different factors which is produc-
ing the best result, factorial experiment is the
answer. For example, an experimenter may be
interested to know not only the best dose of
nitrogen, phosphorus, and potassium but also
the best dose combination of these three essential
plant nutrients to get the best result in guava.
This can be done by designing his experiment
in such a way that the best levels of all these three
factors, N, P, and K, can be identified along with
the combination of N, P, and K to get the best
result. Factorial experiments are the methods
for inclusions of more than one factor to be
compared for their individual effects as well as
interaction effects in a single experiment. The
essential analysis of factorial experiments is
accomplished through two-way analysis of vari-
ance, as already discussed and other methods.
10.11.1 m n Factorial Experiment
The dimension of a factorial experiment is
indicated by the number of factors and the num-
ber of levels of each factor. Thus, a 3
4 facto-
rial experiment means an experiment with
2 factors, one with 3 levels and another with 4
levels.
Let us assume that an
experiment is
conducted in a randomized block design with
m n
r
replication. So there would be two factors: the
first factor is having
m
levels and the second
factor is having
m n
treatment combinations in each replication.
Thus, the model for the design can be presented
as
n
levels and, all together,
y
ijk
¼ μ þ α
i
þ β
j
þ αð
ij
þ γ
k
þ e
ijk
where
i ¼
...
m
j ¼
...
n
k ¼
1, 2,
,
;
1, 2,
,
;
1,
2,
...
,
r
y
ijk
¼
th observation due to the
i
th level of the first factor A and the
j
th level
of the second factor B
μ ¼
response in the
k
general effect
α
i
¼
additional effect due to the
i
th level of first
factor A,
P
α
i
¼
0
