created by Name Roll Batch Md. Topu Kawser 28 58thB Azizul Haque Bhuiyan 07 58thB Md Maidul Islam Chowdhury 06 58thB Kaptusha akter monisha 26 59thB Ramnunsang bawm 37 58thB students of (BBA) Dhaka International University

1. Pearson's correlation coefficient

2. Submitted by: Group B
Name Roll Batch
Md. Topu Kawser 28 58thB
Azizul Haque Bhuiyan 07 58thB
Md Maidul Islam Chowdhury 06 58thB
Kaptusha akter monisha 26 59thB
Ramnunsang bawm 37 58thB
Department of Business Administration
Dhaka International University.

3. 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.

4. 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.

5. 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.

6. Uses Of
Correlation
• IT HELPS TO DETERMINE
THE VALIDITY OF A TEST.
• IT HELPS TO DETERMINE
THE RELIABILITY OF A TEST.
• IT CAN BE USED TO
ASCERTAIN THE DEGREE OF
THE OBJECTIVITY OF A TEST.
• IT CAN ANSWER THE
VALIDITY OF ARGUMENTS
FOR OR AGAINST A
STATEMENT.
• IT INDICATES THE NATURE
OF THE RELATIONSHIP
BETWEEN TWO VARIABLES.
• IT PREDICTS THE VALUE OF
ONE VARIABLE GIVEN THE
VALUE OF ANOTHER
RELATED VARIABLE.
• IT HELPS TO ASCERTAIN
THE TRAITS AND CAPACITIES
OF PUPILS.

7. Types Of
Correlation
On the basis of direction of the relation
between variables, there are three types
of correlation. That are
POSITIVE CORRELATION
NEGATIVE CORRELATION
ZERO CORRELATION

8. POSITIVE CORRELATION NEGATIVE 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.
Example . Intelligence and Achievement.
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.
Example . Anxiety and Performance.

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

10. Computation Of Coefficient Of Correlation
There are two different methods of computing
coefficient of correlation . they are ,
• Rank difference method
• PRODUCT MOMENT METHOD or pearson's
correlation coefficient .

11. 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’ .
Pearson's correlation coefficient (r) is a measure of the linear association of two
variables. Correlation analysis usually starts with a graphical representation of the relation of
data pairs using a scatter diagram. The values of correlation coefficient vary from –1 to +1.

12. The standard formula used in the computation of
Pearson’s product moment correlation coefficient
is as follows :

13. Where,
• N - the number: of pairs of data
• 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)
• 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

14. Calculate the
correlation of
the following data
INDIVIDUALS
SCOREIN TEST
X
SCORES
IN TEST
Y
A 15 60
B 25 70
C 20 40
D 30 50
E 35 30

15. INDIVIDUAL
SCORES I
N TEST X
SCORES I
N TEST Y
XY X² Y²
A 15 60
B 25 70
C 20 40
D 30 50
E 35 30
N= ƩX= ƩY=
ƩX
Y=
ƩX²= ƩY²=

16. INDIVIDUAL SCORES INTEST X SCORES INTEST 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

19. Pearson's correlation
coefficient = -0.5

20. How to evaluate a correlation
• The values of ‘r’ always fall between -1 and +1 and the value
does not change if all values of either variable are converted to a
different scale.
• For eg. If the weights of the students were given in pounds
instead of kilograms , the value of ‘r’ would not change.

21. Advantages of pearson's correlation coefficient
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.

22. Limitations of pearson's correlation coefficient
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.

23. Thank you