Product Moment Method

1. Correlation
lg&lEcU/k
By
Product Moment Method
xq.ku vk?kwZ.k fof/k
MkW- vfHk’ksd
JhokLro
,lksfl,V izksQslj
vo/kwr Hkxoku jke ih- th- dkyst
vuijk] lksuHknz
9415921915

2. Some Importent Product Moment Methods
dqN egRoiw.kZa xq.ku vk?kwZ.k
fof/k
• vad de djus dh fof/k (Reduced Score
Method)
• dfYir ek/; fof/k (Assumed Mean Method)
• okLrfod e/;eku fof/k (Real Mean Method)
• vUrj fof/k (Difference Method)

3. vad de djus dh fof/k
(Reduced Score Method)

5. • Calculate ‘r’ from Below Table
Students 1 2 3 4 5 6 7 8 9 10 11 12
Subject 1 45 48 35 32 36 30 38 39 46 48 40 42
Subject2 40 39 36 42 40 36 35 40 34 36 39 33

6. Sl.No. Subject1 Subject2 X Y X2
Y2
X.Y
1 45 40
2 48 39
3 35 36
4 32 42
5 36 40
6 30 36
7 38 35
8 39 40
9 46 34
10 48 36
11 40 39
12 42 33
Total

7. Consider Coefficient for Sub.1 and Sub.2 are 38 &35 Respectively
Sl.No. Subject1 Subject2 X Y X2
Y2
X.Y
1 45 40 7 5
2 48 39 10 4
3 35 36 -3 1
4 32 42 -6 7
5 36 40 -2 5
6 30 36 -8 1
7 38 35 0 0
8 39 40 1 5
9 46 34 8 -1
10 48 36 10 1
11 40 39 2 4
12 42 33 4 -2
Total ∑X=23 ∑Y=30

8. Sl.No. Subject1 Subject2 X Y X2
Y2
X.Y
1 45 40 7 5 49
2 48 39 10 4 100
3 35 36 -3 1 9
4 32 42 -6 7 36
5 36 40 -2 5 4
6 30 36 -8 1 64
7 38 35 0 0 0
8 39 40 1 5 1
9 46 34 8 -1 64
10 48 36 10 1 100
11 40 39 2 4 4
12 42 33 4 -2 16
Total ∑X=23 ∑Y=30 ∑X2
=447

9. Sl.No. Subject1 Subject2 X Y X2
Y2
X.Y
1 45 40 7 5 49 25
2 48 39 10 4 100 16
3 35 36 -3 1 9 1
4 32 42 -6 7 36 49
5 36 40 -2 5 4 25
6 30 36 -8 1 64 1
7 38 35 0 0 0 0
8 39 40 1 5 1 25
9 46 34 8 -1 64 1
10 48 36 10 1 100 1
11 40 39 2 4 4 16
12 42 33 4 -2 16 4
Total ∑X=23 ∑Y=30 ∑X2
=447 ∑Y2
=164

10. Sl.No. Subject1 Subject2 X Y X2
Y2
X.Y
1 45 40 7 5 49 25 35
2 48 39 10 4 100 16 40
3 35 36 -3 1 9 1 -3
4 32 42 -6 7 36 49 -42
5 36 40 -2 5 4 25 -10
6 30 36 -8 1 64 1 -8
7 38 35 0 0 0 0 0
8 39 40 1 5 1 25 5
9 46 34 8 -1 64 1 -8
10 48 36 10 1 100 1 10
11 40 39 2 4 4 16 8
12 42 33 4 -2 16 4 -8
Total ∑X=23 ∑Y=30 ∑X2
=447 ∑Y2
=164 ∑X.Y=-3

11. From Table -
lkfj.kh ls&
• N=12,
• ∑X=23
• ∑Y=30
• ∑X2
=447
• ∑Y2
=164
• ∑X.Y=-3
12x(-3)-23x30 .
√[12x447-(23)2
] [12x164-(30)2
]
-36-690 .
√(5364-529)(1964-900)
-726 .
√4835x1064

12. -726 ,
√5163780
-726 ,
2272.40
r=-0.32
Low Negative Correlation
fuEu udkjkRed lg&lEcU/k