Karl pearson's coefficient of correlation (1)

CORRELATION
– KARL PEARSON’S
COEFFICIENT OF
CORRELATION
- INTERPRETATION OF
CORRELATION
COEFFICIENT

MEANING OF CORRELATION
 The method of correlation is developed
by Francis Galton in 1885.
 It is the relationship between two sets of
scores or variables.

DEFINITION OF CORRELATION
 Whenever two variables of the same
group are so related that the increase or
decrease are correspond to the increase
or decrease to another or conversely ,
increase or decrease corresponds to the
decrease or increase to another ,they
are said to be correlated.

TYPES OF CORRELATION
On the basis of direction of the
relation between variables, there are
three types of correlation. That are ,
1. POSITIVE CORRELATION
2. NEGATIVE CORRELATION
3 . ZERO CORRELATION

POSITIVE CORRELATION
If when the first variable increases or
decreases the other also increases or
decreases respectively their relationship
is said to be Positive correlation ,
because they move in the same
direction.
Eg. Intelligence and Achievement

NEGATIVE CORRELATION
If when the first variable increases or
decreases , the other respectively
decreases or increases their relationship
is said to be Negative correlation ,
because they move in the opposite
direction.
Eg. Anxiety and Performance

ZERO CORRELATION
If there exists no relationship between
two sets of measures or variables.
Eg. Intelligence and Height.

COEFFICIENT OF CORRELATION
 The ratio indicating the degree of
relationship between two related variables.
 For a perfect POSITIVE CORRELATION the
coefficient of correlation is +1.
 For a perfect NEGATIVE CORRELATION the
coefficient of correlation is -1.
 Positive coefficient of correlation varies
from 0 to +1.
 Negative coefficient of correlation varies
from 0 to -1.

USES OF CORRELATION
 It helps to determine the validity of a
test.
 It helps to determine the reliability of a
test.
 It indicates the nature of the relationship
between two variables.
 It helps to ascertain the traits and
capacities of pupils.

COMPUTATION OF COEFFICIENT
OF CORRELATION
There are two different methods of
computing coefficient of correlation .
They are ,
 RANK DIFFERENCE METHOD
 PRODUCT MOMENT METHOD

PRODUCT MOMENT METHOD
 Most widely used measure of
correlation.
 This method is also known as Pearson’s
product moment method in honour of
Karl Pearson , who is said to be the
inventor of this method.
 The coefficient of correlation computed
by this method is known as the product
moment coefficient of correlation or
Pearson’s correlation coefficient.
 It is represented as ‘r’ .

The standard formula used in the computation of
Pearson’s product moment correlation coefficient is as
follows :
])(][)([
)(N
r
2222
YYNXXN
YXXY




Where,
 N - the total no: of scores or cases
 Ʃ - the summation of the items indicated
 ƩX - the sum of all X scores
 ƩX² - each X score should be squared and then
those squares summed{the sum of the X
squared scores}
 (ƩX)² - X scores should be summed and the
total squared(the squares of the sum of all the
X scores)
])(][)([
)(N
r
2222
YYNXXN
YXXY




 ƩY – the sum of all Y scores
 ƩY² - each Y score should be squared and then
those squares summed
 (ƩY)² - Y score should be summed and the
total squared

CALCULATE THE CORRELATION OF THE
FOLLOWING DATA
SUBJECT SCORES IN TEST 1 SCORES IN TEST 2
A 5 12
B 3 15
C 2 11
D 8 10
E 6 18

SUBJECT SCORES
IN TEST 1
(X)
SCORES
IN TEST 2
(Y)
XY X² Y²
A 5 12
B 3 15
C 2 11
D 8 10
E 6 18
N= ƩX= ƩY= ƩXY= ƩX²= ƩY²=

SUBJECT SCORES IN
TEST 1 (X)
SCORES IN
TEST 2 (Y)
XY X² Y²
A 5 12 60 25 144
B 3 15 45 9 225
C 2 11 22 4 121
D 8 10 80 64 100
E 6 18 108 36 324
N=5 ƩX=24 ƩY=66 ƩXY=315 ƩX²=138 ƩY²=914

]669145][241385[
)6624()3155(
22


r
])(][)([
)(N
r
2222
YYNXXN
YXXY



)43564570)(576690(
15841575


r

214114
9


r
24396
9
r
2.156
9
r
0576.0r

0576.0
2.156
9
24396
9
214114
9
)43564570)(576690(
15841575
]669145][241385[
)6624()3155(
22














r
r
r
r
r
r
])(][)([
)(N
r
2222
YYNXXN
YXXY




r= -0.0576
ie, product moment correlation
coefficient= -0.0576

CALCULATE THE CORRELATION OF THE
FOLLOWING DATA
INDIVIDUALS SCORE IN TEST
X
SCORES IN TEST
Y
A 15 60
B 25 70
C 20 40
D 30 50
E 35 30

INDIVIDU
AL
SCORES
IN TEST
X
SCORES
IN TEST
Y
XY X² Y²
A 15 60
B 25 70
C 20 40
D 30 50
E 35 30
N= ƩX= ƩY= ƩXY= ƩX²= ƩY²=

INDIVIDU
AL
SCORES
IN TEST
X
SCORES
IN TEST
Y
XY X² Y²
A 15 60 900 225 3600
B 25 70 1750 625 4900
C 20 40 800 400 1600
D 30 50 1500 900 2500
E 35 30 1050 1225 900
N=5 ƩX=125 ƩY=250 ƩXY=
6000
ƩX²=
3375
ƩY²=
13500

]250135005][12533755[
)250125()60005(
22


r
])(][)([
)(N
r
2222
YYNXXN
YXXY



]6250067500][1562516875[
3125030000


r

50001250
1250


r
6250000
1250
r
2500
1250
r
5.0r

])(][)([
)(N
r
2222
YYNXXN
YXXY



5.0
2500
1250
6250000
1250
50001250
1250
]6250067500][1562516875[
3125030000
]250135005][12533755[
)250125()60005(
22














r
r
r
r
r
r

Product moment correlation coefficient =
-0.5

INTERPRETATION OF
CORRELATION COEFFICIENT
The correlation coefficient ‘r’ value was verbally
interpreted as per the criteria suggested by
Garret(2010). The details were as follows:
 ‘r’ from 0.00 to ±0.20 denotes negligible
correlation.
‘r’ from ±0.20 to ±0.40 denotes low correlation.
‘r’ from ±0.40 to ±0.70 denotes substantial or
marked correlation.
‘r’ from ±0.70 to ±1.00 denotes high to very
high correlation.

ADVANTAGES OF PRODUCT
MOMENT CORRELATION
It gives a precise and quantitative figure
which can be interpreted meaningfully.
It helps in establishing the value of the
dependent variable from the known
value of independent variable.

LIMITATIONS OF PRODUCT
MOMENT CORRELATION
 This method assumes that there is a
linear relationship between the variables
under study regardless of the fact
whether it exists or not.
 Compared to other methods , the
computation of correlation coefficient by
this method is time consuming.
 The value of the coefficient is unduly
affected by extreme items.

Karl pearson's coefficient of correlation (1)

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