Agriculture Reference
In-Depth Information
Table 9.1
Table of
types of decision in statistical
2
value from an
example, in calculating
χ
r s
inference
table, the degrees of freedom will be (
r
1)
(
s
1).
Decision taken
Reject
Null
hypothesis (
H
0
)
H
Accept
H
0
0
True
Incorrect
decision
(type I error)
Correct decision
9.2.5 Steps in Testing of Statistical
Hypothesis
False
Correct
decision
Incorrect decision
(type II error)
Holistic and meticulous approach is required
in each and every step of testing of statistical
hypothesis so as to draw fruitful and correct
decision about the population parameter based
on sample observations. Some of the important
steps to be followed in testing of statistical
hypothesis are as follows:
(a)
value of a test statistic lies in the critical region,
the null hypothesis is said to be rejected at
level
of significance. Generally, the level of signifi-
cance is taken as 5 or 1%. This depends on the
objective of the study. Sometimes we may have
to opt for 0.01 or 0.001% level of significance,
particularly in relation to medical studies. The
researcher has the freedom to select the appropri-
ate level of significance depending upon the
objective of the study. Nowadays in many statis-
tical software, the actual level of significance is
provided instead of saying whether a particular
null hypothesis is rejected or accepted at a par-
ticular prefixed level of significance or not.
α
Objective of the study
: There should not be
any ambiguity in fixing the objective of the
study, that is, to test whether the equality of
two population means from two different
samples drawn from the same parent popula-
tion or from two different populations or to
test whether population mean can be taken as
μ
0
(a specified value) or not and so on.
(b)
Knowledge about population
: Extensive
information or knowledge about the popula-
tion and its distribution for which the
parameters under study have been taken is
essential and useful.
9.2.3 Types of Test
Based on the nature of alternative hypothesis,
a test is
Hypothesis
(c)
: Commensurating with the objec-
tive of the study and the knowledge about the
population under study selection or fixing of
appropriate null hypothesis and alternative
hypothesis will lead us to the type of test
(i.e., one sided or two sided) to be performed.
one sided (one tailed) or both sided
(two tailed)
. For example,
if we are to test
6
0
, then the test against alternative
hypothesis (1)
H
0
:
μ ¼
5
:
50 is a both-sided or two-
tailed test while the test
μ 6¼
H
1
: against either
H
1
:
μ >
50 or
μ <
50 is a one-sided or one-
(d)
Selection of test statistic
: While deciding the
appropriate sampling distribution vis-a-vis
the suitable test statistic, one should be very
careful to select such a statistic which can
best reflect the probability of the null hypoth-
esis and the alternative hypothesis based on
available information under study. A faulty
selection of test statistic may lead to the
wrong conclusion about the population
parameter under study. Similarly, instead of
a small sample test, if we go for a large
sample test in a case where the number of
observations is low, we may lead to an erro-
neous conclusion.
tailed test.
9.2.4 Degrees of Freedom
Degree of freedom is
actually the number of
observations less the number of restrictions
.
Generally, the degrees of freedom are
1for
asamplew th
n
number of observations, but
it should be kept in mind that the degrees of
freedom are not necessarily be
n
n
observations. Depending upon the restrictions,
the degrees of freedom are worked out, for
n
1for
