Agriculture Reference
In-Depth Information
2
test for goodness of fit as given
below:
χ
Yates's Correction
Validity of the
2
depends on the con-
dition that the expected frequency in
each cell should be sufficiently large;
generally the expected frequency is
required to be at least five. One can
overcome the problem of lower cell
frequency by coalescing or merging
consecutive rows or columns. In
doing so, one has to compromise with
the basic concept of the classification
of the particular subject on hand. In a
2
χ
2
4
3
5
n
o
2
o
A
i
B
j
e
A
i
B
j
X
r
X
s
2
χ
¼
e
A
i
B
j
i¼
1
j¼
1
2
X
r
X
s
f
ij
e
ij
2
ðr
1
Þðs
1
Þ
¼
: χ
e
ij
i¼
1
j¼
1
where
f
ij
¼
observed cell frequency of
i
th
2 table, the possibility of merging
cell frequencies is ruled out, rather we
adopt Yates's corrected formula for
χ
row and
th column combination and
e
ij ¼
expected cell frequency of
j
i
th row
j
and
th column combination.
2
as given below:
2
Test
Under the special case, the
2. “2
2”
χ
r s
con-
2
tingency table becomes a 2
2 con-
tingency table, in which both the
attributes are classified into two groups
each. The test of independence of
attributes can be performed in the sim-
ilar way as in the case of
N
ða þ bÞðc þ dÞða þ cÞðb þ dÞ
;
j
ad bc
j
2
2
1
χ
¼
N
a
b
where
is the total frequency and
,
,
c
, and
d
are as usual.
contin-
gency table. Moreover, the value of
χ
r s
Example 9.27.
The following table gives the
frequency distribution of education standard
and type occupation for 280 persons. Test
whether the type of occupation is independent
of education standard or not.
2
can also be calculated directly from
the observed frequency table. Let us
suppose we have the following 2
2
contingency Table
9.4
as given below:
The formula for calculating
2
value is
χ
Govt.
service Others
Cultivation Teaching
2
Nðad bcÞ
2
χ
¼
HS
65
5
12
8
ða þ cÞðb þ dÞða þ bÞðc þ dÞ
χ
Graduation
35
25
15
10
2
2
1
ð
2
1
Þð
2
1
Þ
χ
:
Postgraduation 25
40
25
15
Solution.
Under the given condition
H
0
: Educational standard and occupation are
independent against
H
1
: Educational standard and occupation are not
independent.
Under the given
2
at
1 degree of freedom at a prefixed
χ
Now comparing the table value of
α
level of significance with the calcu-
lated value of
2
, one can arrive at a
definite conclusion about the indepen-
dence of the two attributes.
χ
H
0
, the test statistic is
2
4
3
5
n
o
2
o
A
i
B
j
e
Table 9.4
“2
2” contingency table
A
i
B
j
X
r
X
s
2
ð
e
χ
Þ
¼
Attribute
B
Attribute
A
1
3
1
Þð
3
1
A
i
B
j
i¼
1
j¼
1
B
2
Total
2
A
1
a
b
a
+
b
X
r
X
s
f
ij
e
ij
A
2
c
d
c
+
d
¼
:
e
ij
Total
a
+
c
b
+
d
a
+
b
+
c
+
d ¼ N
i¼
1
j¼
1
