3. Introduction
• Definition:
• Correlation is the relationship which can reveal whether the
change in one variable would cause change in the
other or not.
• Such relationship between the two sets of charac-
ters or variables can be expressed quantitatively by the
degree of relationship, called Correlation Coefficient.
• Correlation is a LINEAR association between two random
variables.
• Correlation analysis show us how to determine both the nature and
strength of relationship between two variables.
• When variables are dependent on time correlation is applied.
4. Introduction • Correlation lies between +1 to -1.
• A zero correlation indicates that
there is no
• relationship between the
variables.
• A correlation of –1 indicates a
perfect negative correlation.
• A correlation of +1 indicates a
perfect positive
correlation.
6. Types of Correlation
Type 1:
It is further divided into three categories :
1. Positive
2. Negative
3. No
4. Perfect
If two related variables are such that when
one increases (decreases), the other also
increases (decreases), then it is called positive correlatio
7. Types of Correlation
• If both the variables are independent
,then there is no correlation.
• Perfect correlation occurs when there is a
functional dependency between the
variables.
In this case all the points are in a straight
line.
• If two variables are such that when one
increases (decreases), the other
decreases(increases) , then it is called
negative correlation.
8. Types of correlation
• Type 2:
• Linear
• Non-Linear
• When all the points on the scatter diagram tend to
lie near a line which looks like a straight line,
the correlation is said to be linear.
• Correlation is said to be non -linear if the ratio of
change is not constant. In other words, when all
the points on the scatter diagram tend to lie near a
smooth curve, the correlation is said to be non -
linear (curvilinear).
9. Types of
Correlation• Type 3:
• Simple
• Multiple
• Partial
• Simple correlation is a measure used to
determine the strength and the direction
of the relationship between two
variables, X and Y.
• Multiple correlation is
the correlation between the variable's
values and the best predictions that can
be computed linearly from the predictive
variables.
• Partial correlation measures the strength
of a relationship between two variables,
while controlling for the effect of one or
more other variables.
• For example, you might want to see if
there is a correlation between amount of
food eaten and blood pressure, while
controlling for weight or amount of
exercise.
10. Methods of studying Correlation
• Scatter Diagram Method
• Karl Pearson Coefficient Correlation of
Method
• Spearman’s Rank Correlation Method
11. Coefficient of Correlation
• A measure of the strength of the linear relationship
between two variables that is defined in terms of
the (sample) covariance of the variables divided
by their (sample) standard deviations.
• Represented by “r”
• r lies between +1 to –1
• Magnitude and Direction
• -1 < r < +1
• The + and – signs are used for positive linear
correlations and negative linear
correlations, respectively
13. Interpreting correlation
coefficient (r)
• Strong correlation: r > .70 or r < –.70
• Moderate correlation: r is between .30 &
.70
• or r is between –.30 and –.70
• Weak correlation: r is between 0 and .30
or r is between 0 and –.30 .
14. Spearman's rank coefficient
• A method to determine correlation when the data
is not available in numerical form and as an
alternative the method, the method of rank
correlation is used. Thus when the values of the
two variables are converted to their ranks, and
there from the correlation is obtained, the
correlations known as rank correlation.
15. Computation of Rank correlation
coefficient
Spearman's rank correlation coefficient ρ
can be calculated when
1. Actual ranks given
Ranks are not given but grades are given
but not repeated.
3. Ranks are not given and grades are given
and repeated.
16. Computation of rank
correlation coefficient
• The Spearman correlation coefficient, ρ, can
take values from +1 to -1.
• A ρ of +1 indicates a perfect association of ranks
• A ρ of zero indicates no association between
ranks and
A ρ of -1 indicates a perfect negative association
of ranks.
The closer ρ is to zero, the weaker
the association between the ranks.
