Correlation measures the strength and direction of association between two variables. It ranges from -1 to 1, where 0 indicates no association and values closer to 1 or -1 indicate stronger positive or negative associations, respectively. The document provides examples of positive correlation between variables such as height and weight that increase together, and negative correlation where variables such as TV time and grades move in opposite directions. Formulas and different types of correlation including partial and multiple correlation are also defined in the document.

2. Correlation
By
RANI SUMMEYA
SEME
Roll no.
33

3. Outline
O Definition
O Formula
O Features
O Types
O Example

4. Definition
Correlation:-
‘’Mutual relationship or connection between
two variables.’’
O It measures the strength of association between
two variables & the direction of relationship.
O It is a statistical method which enables the
researcher to find out whether two variables are
related & to what extent they are related.

5. Formula

6. Features
O Association between two factors
O Our data should be in the form of pairs
O Value shown by r = Pearson
O Value lies between 0 -1
O Value can be - or +
O Value greater than 1 ans wrong
O 0 = no association
O Value close to 1= strong association

7. Types
Following are the types of correlation
O Positive correlation
O Negative correlation
O Partial correlation
O Zero correlation
O Linear correlation
O Non linear correlation

8. Positive Correlation
A relationship b/w 2 variables in which both variables
move in the same direction
O if one variable decrease other also decrease, vice
versa
O Example:-
O Height & weight
O water consumption & temperature
O study time & grades

9. Positive Correlation Types
O Strong Positive Correlation:-
It has the same change, points are more close
together & form a line.
O Weak Positive Correlation:-
it has variables that has same change but points on
graph are dispersed.

10. Negative Correlation
O A relationship b/w 2 variables in which both
variables move in the opposite direction
O if one variable increase other decrease, vice versa
O Example:-
O TV time increases & grade decreases
O Alcohol consumption increases & driving ability
decrease
O Price increases & Quantity demand decreases

12. Simple Correlation
When we study the relation between two
variables only then it is known as simple
correlation,
Example:-
Correlation is said to be
simple when it is
between income
and expenditure.

13. Partial Correlation
When three or more variables are taken but
relationship between any two variables is study,
assuming other variables as constant, then it is called
partial correlation

14. Multiple Correlation
When we study the relationship among
three or more variables then it is called
multiple correlation.

15. Linear Correlation
Change in one variable result
constant change of other variable
Non Linear Correlation
Change in one variable do not result constant change
of other variable

16. Zero Correlation
O A correlation of zero means there is no
relationship between the two variables

17. Spearman's rank-
order correlation
O The Spearman's rank-order correlation is the
nonparametric version of the Pearson product-
moment correlation. Spearman's
correlation coefficient, (ρ, also signified by rs)
measures the strength and direction of association
between two ranked variables.

18. Interpretation of r
Some
r value =
+.70 or higher Very strong positive relationship
+.40 to +.69 Strong positive relationship
+.30 to +.39 Moderate positive relationship
+.20 to +.29 weak positive relationship
+.01 to +.19 No or negligible relationship
0 No relationship [zero correlation]
-.01 to -.19 No or negligible relationship
-.20 to -.29 weak negative relationship
-.30 to -.39 Moderate negative relationship
-.40 to -.69 Strong negative relationship
-.70 or higher Very strong negative relationship

19. A random sample of junior high school is selected
& each student height (in inches) and weight (in
pounds) is recorded. Test whether height & weight
are related
HEIGHT WEIGHT
15 13
5 6
16 14
10 13
11 11
3 5
12 10

20. HEIGHT
(X)
WEIGHT
(Y) XY X2
Y2
15 13
5 6
16 14
10 13
11 11
3 5
12 10

21. HEIGHT
(X)
WEIGHT
(Y) XY X2
Y2
15 13 195
5 6 30
16 14 224
10 13 130
11 11 121
3 5 15
12 10 120

22. HEIGHT
(X)
WEIGHT
(Y) XY X2
Y2
15 13 195 225 169
5 6 30 25 36
16 14 224 256 196
10 13 130 100 169
11 11 121 121 121
3 5 15 9 25
12 10 120 144 100

23. HEIGHT
(X)
WEIGHT
(Y) XY X2
Y2
15 13 195 225 169
5 6 30 25 36
16 14 224 256 196
10 13 330 100 169
11 11 121 121 121
3 5 15 9 25
12 10 120 124 100
€X= 72 €Y= 72 €XY= 835 €X2= 880 €Y2= 816

25. Interpretation of r