Coefficient of correlation meaning, definition, types of correlation, methods for calculating coefficient of correlation, Karl Pearson coefficient formula, spearman rank correlation, correlation coefficient properties

1. S U B M IT T E D B Y
C .H E N A J O IC E
7 2 0 8 2 2 2 0 8 0 2 4
I M B A

2. DEFINITION
 A C O R R E L AT I O N C O E F F I C I E N T
I S A S TAT I S T I C A L M E A S U R E O F
T H E D E G R E E TO W H I C H
C H A N G E S TO T H E VA L U E O F
O N E VA R I A B L E P R E D I C T
C H A N G E TO T H E VA L U E O F
A N O T H E R
 A C O R R E L AT I O N C A N O N LY
I N D I C AT E T H E P R E S E N C E O R
A B S E N C E O F A R E L AT I O N S H I P,
N O T T H E N AT U R E O F T H E
R E L AT I O N S H I P. C O R R E L AT I O N

3. TYPES OF CORRELATION
POSITIVE AND NEGATIVE
CORRELATION
LINEAR AND NON -LINEAR
CORRELATION
SIMPLE, MULTIPLE AND
PARTIAL CORRELATION

4. POSITIVE CORRELATION
W H E N T H E VA L U E S O F T W O VA R I A B L E S
M O V E S A M E D I R E C T I O N , C O R R E L AT I O N
I S S A I D TO B E P O S I T I V E .
E G . T E M P E R AT U R E A N D V O L U M E
NEGATIVE CORRELATION
W H E N T H E VA L U E S O F T W O VA R I A B L E S
M O V E S O P P O S I T E D I R E C T I O N ,
C O R R E L AT I O N I S S A I D TO B E
N E G AT I V E .
E G . P R E S S U R E A N D V O L U M E

5. LINEAR CORRELATION
W H E N T H E A M O U N T O F C H A N G E I N
O N E VA R I A B L E L E A D S TO A C O N S TA N T
R AT I O O F C H A N G E I N T H E O T H E R
VA R I A B L E , C O R R E L AT I O N I S S A I D TO
B E L I N E A R .
NON LINEAR CORRELATION
C O R R E L AT I O N I S S A I D TO B E N O N
L I N E A R ( C U RV E L I N E A R ) W H E N T H E
A M O U N T O F C H A N G E I N O N E
VA R I A B L E I S N O T I N C O N S TA N T R AT I O
TO T H E C H A N G E I N T H E O T H E R
VA R I A B L E .

6. SIMPLE CORRELATION
I N T H E S T U D Y O F R E L AT I O N S H I P
B E T W E E N T H E VA R I A B L E S , I F T H E R E
A R E O N LY T W O VA R I A B L E S , T H E
C O R R E L AT I O N I S S A I D TO B E S I M P L E .
MULTIPLE CORRELATION
I N T H E S T U D Y O F M U LT I P L E
C O R R E L AT I O N W E M E A S U R E T H E
D E G R E E O F A S S O C I AT I O N B E T W E E N
O N E VA R I A B L E O N O N E S I D E A N D A L L
T H E O T H E R VA R I A B L E TO G E T H E R O N
T H E O T H E R S I D E .

7. PARTIAL CORRELATION
I N PA RT I A L C O R R E L AT I O N W E
S T U D Y T H E R E L AT I O N S H I P O F O N E
VA R I A B L E W I T H O N E O F T H E O T H E R
VA R I A B L E S P R E S U M I N G T H AT T H E
O T H E R VA R I A B L E R E M A I N S
C O N S TA N T.

8. METHODS FOR CALCULATING
COEFFICIENT OF CORRELATION
KARL PEARSON’S
METHOD
SPEARMAN’S METHOD
CONCURRENT
DEVIATION METHOD

9. KARL PEARSON’S CORRELATION
COEFFICIENT FORMULA:
T H E C O E F F I C I E N T C O R R E L AT I O N
B E T W E E N X A N D Y I S D E F I N E D A S :
W H E N A C T U A L D ATA I S G I V E N
C O R R E L AT I O N A N D R E G R E S S I O N :

10. SPEARMAN’S RANK CORRELATION
R = R A N K C O R R E L AT I O N
C O E F F I C I E N T
N = N U M B E R O F
O B S E RVAT I O N S
D = D I F F E R E N C E B E T W E E N 2
R A N K S ( R 1 - R 2 )

11. Correlation Coefficient properties
1) Correlation coefficient remains in the same measurement as in which the two
variables are.
2) The sign which correlations of coefficient have will always be the same as the
variance.
3) The numerical value of correlation of coefficient will be in between -1 to + 1. It is
known as real number value.
4) The negative value of coefficient suggests that the correlation is strong and
negative. And if ‘r’ goes on approaching toward -1 then it means that the relationship
is going towards the negative side.
When ‘r’ approaches to the side of + 1 then it means the relationship is strong and
positive. By this we can say that if +1 is the result of the correlation then the
relationship is in a positive state.
5) The weak correlation is signaled when the coefficient of correlation approaches to
zero. When ‘r’ is near about zero then we can deduce that the relationship is weak.
6) Correlation coefficient can be very dicey because we cannot say that the
participants are truthful or not

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