Agriculture Reference
In-Depth Information
11
Analysis Related to Breeding
Researches
Variability is one of the major concerns of any
research. In a real-life situation, we are to deal
with a number of variables at a time, so co-
variability plays an important role. In social,
agricultural, and other fields, the biophysical
features in any experiment rarely behave inde-
pendently; rather these are found to be function-
ally related to each other. There are several
examples where the analysis of covariance can
be used effectively in augmenting the precession
of the experimental results. For example, in yield
component analysis of paddy, the yield compo-
nents, namely, the number of hills per unit area,
the number of effective tillers per hill, and the
number of grains per panicles, can be used as
covariates or concomitant variables. In a study of
health drinks on the growth and physique of
school-going children, initial body weight,
height, age, physical agility, etc., can be taken
as concomitant variables during the analysis of
covariance. In the analysis of covariance, there
are two types of variables: the characteristic of
the main interest and the information on the
secondary or auxiliary interest or the covariates.
In the analysis of covariance, the expected (true)
value of the response is the resultant of two
components, one because of the linear combina-
tion of the values of the concomitant variables
which are functionally related with the response
and another one already obtained in the analysis
of variance. Thus, the analysis of covariance is
the synthesis of the analysis of variance and the
regression. Similar to that of the partitioning of
variances into different components, one can also
partition the covariance among the variables
into different components like genotypic and
environmental.
11.1 Analysis of Covariance
The analysis of covariance can be taken up for
one-way and two-way layouts and other specific
types of experimental design. In the analysis of
covariance, there is one dependent variable (
)
and one or more concomitant variables. The
basic difference between the analysis of variance
and the analysis of covariance models is that in
the former, each response (
y
) is partitioned into
two components, one because of its true value
and the error part. The model in its simplest form
may be written as
y
X
X
y
i
¼
α
ij
τ
j
þ
β
k
x
ik
þ e
i
;
where
α
ij
are known
;
j
k
x
ik
is the value of the
k
th concomitant variable
corresponding to
y
i
,
β
k
's are the regression coefficients of
y
on the
x
k
's,
τ
j
's are the effects (main, interaction, blocks,
etc.),
covariates
e
i
is the random component in the model.
