Agriculture Reference
In-Depth Information
nonsignificant and the null hypothesis cannot be
rejected. That means the two attributes, namely,
the grain shape and aroma are independent of
each other.
behavior which is supposed to be valid under the
specific situation. In nonparametric tests instead
of the normality assumption, one assumes the
continuity of the distribution function and the
probability density function of the variable and
independence of the sample observations.
Nonparametric methods are synonymously
used as “distribution-free” methods, etc., as men-
tioned above but is nonparametric if the parent
distribution is dependent on some general assum-
ption like continuity. A distribution-free method
depends neither on the form nor on the para-
meters of the parent distribution.
Merits nonparametric methods are as follows
Example 9.29.
2 table gives
the frequency distribution of rice varieties based
on two attributes, namely, shape of grain and the
aroma of rice. Test whether the two attributes are
independent or not.
The following 2
Rice aroma
Grain type
Scented
Non-scented
Elongated
15
30
:
1. Nonparametric statistical tests are exact
irrespective of the nature of the population
distribution.
2. For unknown population distribution and for
very small (say, 6) sample size, then tests are
useful.
3. Nonparametric tests are also available for a
sample made up of observations from differ-
ent populations.
4. Nonparametric tests are useful both for inher-
ent by ranked/qualified data and for the data
which are potential to be ranked from numer-
ical figure.
5. Data measured in nominal scales, mostly in
socioeconomic studies can also be put under
nonparametric tests.
Demerits of nonparametric methods
Short
3
42
Solution.
Under the given condition, we are to
test whether the two attributes, namely, “aroma”
and “grain shape” in rice are independent of each
other or not.
So
H
0
: Aroma and grain shape in rice are
independent of each other, against
H
1
: Aroma and grain shape in rice are not
independent of each other.
The test statistic for the problem will be
2
with 1 d.f. Seeing the data that a cell frequency
will be less than five, so we are to adopt the
formula for
χ
2
with Yates's correction. Thus,
χ
2
j
2
j
ad bc
N
2
χ
corr
:
¼
ða þ bÞðc þ dÞða þ cÞðb þ dÞ
:
1. Probability of type II error is more in nonpara-
metric method. If all the assumptions of the
parametric model are valid, then a parametric
test is superior.
2. Suitable non parametric method corres-
ponding to interaction effect
2
90
2
j
15
42
30
3
j
90
¼
ð
30
þ
15
Þð
15
þ
3
Þð
3
þ
42
Þð
30
þ
42
Þ
¼
8
:
402
:
Let the level of significance be 0.05 and the
corresponding table value at 1 d.f. is 3.84. So the
calculated value of
estimation
through ANOVA is lacking.
3. Estimation of population parameters cannot
be done by non-parametric method.
4. Disregard the actual scale of measurement.
We discuss below some of the nonparametric
tests widely used in agriculture and allied field.
2
χ
corr
:
is more than the table
2
at 1 d.f. at 5% level of significance.
Hence, the test is significant and the null hypoth-
esis is rejected. We can conclude that the two
attributes, aroma and grain shape in rice, are not
independent of each other.
value of
χ
9.5.1 One-Sample Tests
9.5
Nonparametric Tests
1.
Sign Test
For a random sample
x
1
,
x
2
,
x
3
,
... x
n
of
In parametric tests discussed so far, there is one
or more
