Non Parametric
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} Where h=.5 if r < 2mn/N+1 and }
h= -.5 if r > 2mn/N+1
} irection of ifference between the two measures
rather than quantitative measure of the data.
1
83
89
2
85
87
3
75
70
4
91
93
5
80
85
6
75
75
7
90
80
8
65
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80
10
85
88
11
83
82
12
75
79
13
78
75
14
80
85
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82
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16
88
85
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18
80
87
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78
78
20
81
84
21
70
85
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81 }he above data is of80the 22 workers working in a company (before vacation and after vacation ) Find out whether a period of vacation has increased workers productivity or not ?
} 0 =VACA} N AS N EFFEC} N }E
PRC} V } F WRKERS. } 1 = VACA} N AS A S N F CAN} EFFEC} N }E PRC} V } F WRKERS.
} F N }E REC} N F FFERENCE BE}WEEN
EVER Xi AN i
(-X)
1
83
89
6
+
2
85
87
2
+
3
75
70
5
-
4
91
93
2
+
5
80
85
5
+
6
75
75
0
0
7
90
80
10
-
8
65
71
6
+
9
78
80
2
+
10
85
88
3
+
11
83
82
1
-
12
75
79
4
+
13
78
75
3
-
14
80
85
3
-
15
82
86
4
-
16
88
85
3
-
17
85
82
3
-
18
80
87
7
+
19
78
78
0
0
20
81
84
3
+
21
70
85
15
+
22
80
81
1
+
(-X)
} ERE }}AL + S N = 12 } }}AL Ȃve S N = 8 } ZERES = 2 (RPE) } S ǮNǯ = 22-2 =20
} S}EP 5: CNSL} }ABLE Ȃ ( WE SEE }E VALE
NER ǮNǯ ACRSS }E CALCLA}E FEW S N We see the value of N= 20 across K = 8 from table Ȃd which comes to be .252 which is more than our level of significance(0.05) So, we accept the null hypothesis
} } L SE NL }E REC} N F }E
FFERENCES W } N }E PA RS.
} }ES} N }W FFEREN} BRANS }ES} }E
P}ES S }A} }ERE S N FFERENCE BE}WEEN }E PERC EVE QAL } F }W SAMPLES(Ʉ = 0.05)
1
75
68
2
65
40
3
55
57
4
56
44
5
34
57
6
52
58
7
47
24
8
43
43
9
73
51
} S}EP 1: }AKE FFERENCE B/W }W RPS (i} } } }
Xi) AN ASS N RANKS } EAC FFERENCES. S}EP 2 AF}ER RANK N }E FFERENCE }E S N SL BE A}}ACE } EAC RANK. S}EP 3 }E VALE F Dz } S CMPA RE FRM }ABLE VALE. }EN WE }AKE EC SS N VALE DzL R LEVEL F S N F CANCE AVE SE} S}EP 5 WE ASSEP} R REJEC} R NLL P}ES S
} S SE } }ES} WE}ER }W NEPENEN}
SAMPLES AVE }AKEN FRM }E PPLA} N AV N }E SAME ME AN.
} S}EP1 FRMLA}E NLL P}ES S } 0 = }E ME AN F WAES F MALE WRKER
S EQAL } }A} F FEMALE WRKER } 1 = }E ME AN WAES F MALE S MRE }AN FEMALE WRKERS
ABVE }E ME AN BELW }E ME AN
9(a)
6(b)
15
5(C)
10(d)
15
N1= 14
N2 =16
} } S }ES} S SE } }ES} }E
NEPENENCE F A}}R B}ES } sed to test the significant difference between the observed and expected no. } AS 5 S}EPS } PERFRM
} ata of a movie viewer test whether liking or disliking is
independent of age group
NER 20
20-39
40 -59
60 AN ABVE
L KE
320
80
110
200
710
SL KE
50
15
70
60
195
N FFEREN} 30
05
20
40
95
100
200
300
1000
}}AL
400
}
-
- 0 = L K N AN SL K N S NEPENEN} F AE RP 1 = N} NEPENEN} F AE RP
} WERE R = }}AL RWS } C = CLMN }AL N W C }E BSERVE
FREQENC L ES. } N = N F }}AL BSERVA} NS
!
! "
300
284
36
1296
4.56
80
71
9
81
1.14
110
142
-32
1024
7.21
200
2.3
-13
169
0.793
50
213
-28
784
10.051
15
78
4.50
20.25
1.038
70
19.5
31
961
24.641
60
39
1.50
2.25
0.038
30
58.5
-8
64
1.684
5
38
-4.50
20.25
2.136
20
9.5
1
1
0.052
40
19
11.50
132.25
4.640
}}AL
1000
1000
0
57.987
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} }
.
}
!"# $ } !% & '!!! ! ! ( !$ } ( (()*& ! ! $
} }
} ' + &&!!"#
! ' " $ ,
- .
- - -
$
/,
- 0
- $
1 2 3 4 / 4
} 5,
$
$ 1246 #7, 8!% #9, * :;(! ! < *". (! *!% ;;&! # )# &
} But if our sample size is more than 20 then we use the
formula
Æ Æ Æ Æ
} Where h=.5 if r < 2mn/N+1 and }
h= -.5 if r > 2mn/N+1
} irection of ifference between the two measures
rather than quantitative measure of the data.
1
83
89
2
85
87
3
75
70
4
91
93
5
80
85
6
75
75
7
90
80
8
65
71
9
78
80
10
85
88
11
83
82
12
75
79
13
78
75
14
80
85
15
82
86
16
88
85
17
85
82
18
80
87
19
78
78
20
81
84
21
70
85
22
81 }he above data is of80the 22 workers working in a company (before vacation and after vacation ) Find out whether a period of vacation has increased workers productivity or not ?
} 0 =VACA} N AS N EFFEC} N }E
PRC} V } F WRKERS. } 1 = VACA} N AS A S N F CAN} EFFEC} N }E PRC} V } F WRKERS.
} F N }E REC} N F FFERENCE BE}WEEN
EVER Xi AN i
(-X)
1
83
89
6
+
2
85
87
2
+
3
75
70
5
-
4
91
93
2
+
5
80
85
5
+
6
75
75
0
0
7
90
80
10
-
8
65
71
6
+
9
78
80
2
+
10
85
88
3
+
11
83
82
1
-
12
75
79
4
+
13
78
75
3
-
14
80
85
3
-
15
82
86
4
-
16
88
85
3
-
17
85
82
3
-
18
80
87
7
+
19
78
78
0
0
20
81
84
3
+
21
70
85
15
+
22
80
81
1
+
(-X)
} ERE }}AL + S N = 12 } }}AL Ȃve S N = 8 } ZERES = 2 (RPE) } S ǮNǯ = 22-2 =20
} S}EP 5: CNSL} }ABLE Ȃ ( WE SEE }E VALE
NER ǮNǯ ACRSS }E CALCLA}E FEW S N We see the value of N= 20 across K = 8 from table Ȃd which comes to be .252 which is more than our level of significance(0.05) So, we accept the null hypothesis
} } L SE NL }E REC} N F }E
FFERENCES W } N }E PA RS.
} }ES} N }W FFEREN} BRANS }ES} }E
P}ES S }A} }ERE S N FFERENCE BE}WEEN }E PERC EVE QAL } F }W SAMPLES(Ʉ = 0.05)
1
75
68
2
65
40
3
55
57
4
56
44
5
34
57
6
52
58
7
47
24
8
43
43
9
73
51
} S}EP 1: }AKE FFERENCE B/W }W RPS (i} } } }
Xi) AN ASS N RANKS } EAC FFERENCES. S}EP 2 AF}ER RANK N }E FFERENCE }E S N SL BE A}}ACE } EAC RANK. S}EP 3 }E VALE F Dz } S CMPA RE FRM }ABLE VALE. }EN WE }AKE EC SS N VALE DzL R LEVEL F S N F CANCE AVE SE} S}EP 5 WE ASSEP} R REJEC} R NLL P}ES S
} S SE } }ES} WE}ER }W NEPENEN}
SAMPLES AVE }AKEN FRM }E PPLA} N AV N }E SAME ME AN.
} S}EP1 FRMLA}E NLL P}ES S } 0 = }E ME AN F WAES F MALE WRKER
S EQAL } }A} F FEMALE WRKER } 1 = }E ME AN WAES F MALE S MRE }AN FEMALE WRKERS
ABVE }E ME AN BELW }E ME AN
9(a)
6(b)
15
5(C)
10(d)
15
N1= 14
N2 =16
} } S }ES} S SE } }ES} }E
NEPENENCE F A}}R B}ES } sed to test the significant difference between the observed and expected no. } AS 5 S}EPS } PERFRM
} ata of a movie viewer test whether liking or disliking is
independent of age group
NER 20
20-39
40 -59
60 AN ABVE
L KE
320
80
110
200
710
SL KE
50
15
70
60
195
N FFEREN} 30
05
20
40
95
100
200
300
1000
}}AL
400
}
-
- 0 = L K N AN SL K N S NEPENEN} F AE RP 1 = N} NEPENEN} F AE RP
} WERE R = }}AL RWS } C = CLMN }AL N W C }E BSERVE
FREQENC L ES. } N = N F }}AL BSERVA} NS
!
! "
300
284
36
1296
4.56
80
71
9
81
1.14
110
142
-32
1024
7.21
200
2.3
-13
169
0.793
50
213
-28
784
10.051
15
78
4.50
20.25
1.038
70
19.5
31
961
24.641
60
39
1.50
2.25
0.038
30
58.5
-8
64
1.684
5
38
-4.50
20.25
2.136
20
9.5
1
1
0.052
40
19
11.50
132.25
4.640
}}AL
1000
1000
0
57.987
V
V
C
C
C C
}
5 8
O
C
C
4 1=/2 1=/2 4 $ 4 $
J
}
5* !< ( (! !% ! ( * < * ! * '< * *' "
>5 !% !'!? '$*$! '@A ( * < * ! " %/5$@B
1 2
$
$
- C $
$
5
} >
$ C
-
D
-
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