Agriculture Reference
In-Depth Information
10
Analysis of Variance
and Experimental Designs
systematic approach of partitioning the variance
of a variable into assignable and non-assignable
parts
τ
or
t
-test. Problem arises when one wants to compare
more than two populations at a time. One of the
possible solutions to this problem is to take
m
C
2
no. of pairs of samples and test these using the
τ
. Through ANOVA one can investigate one
or more factors (variety, type of irrigation, fertil-
izer doses, social groups, business houses, etc.)
with varying levels (e.g., five or six varieties at a
time; three or more irrigation types; different
levels of NPK; social groups like innovators,
early adopters, early majority, late majority, and
laggards; more than one business house) that are
hypothesized to influence the dependent variable.
Depending upon the nature, type, and classifica-
tion of data, the analysis of variance is developed
for
-test as applicable. Another important pro-
cedure is to use the analysis of variance tech-
nique. The analysis of variance technique, in
short ANOVA, is a powerful technique used in
the field of agriculture, social science, business,
education, medicine, and several other fields.
Using this tool the researcher can draw inference
about the samples whether these have been
drawn from the same population or they belong
to different populations. Using this technique
the researcher can establish whether a no. of
varieties differ significantly among themselves
with respect to their different characteristics
like yield, susceptibility to diseases and pests,
nutrient acceptability, and stress tolerance and
efficiency of different salesmen; for example,
one can compare different plant protection
chemicals, different groups of people with
respect to their innovativeness, and different
drugs against a particular disease, different
programs of poverty reduction, performances of
different business houses, and so on.
In statistical studies variability and measures
of variability are the major focal points of atten-
tion. The essence of ANOVA lies in partitioning
the variance of a set of data into a number of
components associated with the type, classifica-
tion, and nature of data.
or
t
one-way classified data, two-way classified
data with one observation per cell
two-way clas-
sified data with more than one observation per
cell
,
. Before taking up the analysis of vari-
ance in detail, let us discuss about linear model,
which is mostly being used in the analysis of
variance.
,
etc
10.1
Linear Models
Taken observation on any dependent variable
Y
,
y
i
can be assumed as
y
i
¼ α
i
þ e
i
, where
α
i
is its
true value and
e
i
is the error part, which may be
because of chance factor. This
α
i
again may be
the linear combination of
m
unknown quantities
γ
1
; γ
2
; ...; γ
m
as
α
i
¼ a
i
1
γ
1
þ a
i
2
γ
2
þþa
im
γ
m
,
where
a
ij
(
j ¼
1, 2,
...
,
m
) is the constant and take
the values 0 or 1.
Thus,
Analysis of variance is a
y
i
¼ a
i
1
γ
1
þ a
i
2
γ
2
þþa
im
γ
m
þ e
i
.
