Correlationanalysis

Meaning of Correlation
Analysis  The degree of relationship between the
variables under consideration is measure
through the correlation analysis.
 The measure of correlation called the
correlation coefficient
 The degree of relationship is expressed by
coefficient which range from correlation (-1≥ r
≤ +1)
 The direction of change is indicated by a sign.
 The correlation analysis enable us to have an
idea about the degree & direction of the
relationship between the two variables under
study.

 Correlation is a statistical tool that helps
to measure and analyze the degree of
relationship between two variables.
 Correlation analysis deals with the
association between two or more
variables.
 Indicated by sign; (+) or (-)

Correlation and Causation
 Causation means cause & effect relation.
Correlation denotes the interdependency among the
variables for correlating two phenomenon, it is
essential that the two phenomenon should have
cause-effect relationship,& if such relationship does
not exist then the two phenomenon can not be
correlated.
 If two variables vary in such a way that movement
in one are accompanied by movement in other, these
variables are called cause and effect relationship.
 Causation always implies correlation but correlation
does not necessarily implies causation.

Uses of Correlation Analysis
 It is used in deriving the degree and
direction of relationship within the
variables.
 It is used in reducing the range of
uncertainty in matter of prediction.
 It I used in presenting the average
relationship between any two variables
through a single value of coefficient of
correlation.

Uses of Correlation
Analysis
 In the field of science and philosophy
these methods are used for making
progressive conclusions.
 In the field of nature also, it is used in
observing the multiplicity of the inter
related forces.

Types of correlation
On the basis of
degree of
correlation
On the basis of
number of variables
On the basis of
linearity
•Positive
correlation
•Negative
correlation
•Simple
correlation
•Partial correlation
•Multiple
correlation
•Linear
correlation
•Non – linear
correlation

Correlation : On the basis of
degree
 Positive Correlation
 The correlation is said to be positive
correlation if the values of two variables
changing with same direction.
 Ex. Pub. Exp. & sales, Height & weight.
 Variables change in the same direction.
 As X is increasing, Y is increasing. As X
is decreasing, Y is decreasing
 E.g., As height increases, so does weight.

degree
 Negative correlation
• The correlation is said to be negative
correlation when the values of variables
change with opposite direction.
Ex. Price & qty. demanded.
• Variables change in opposite directions.
• As X is increasing, Y is decreasing
• As X is decreasing, Y is increasing

number of variables
 Simple correlation
Under simple correlation problem there are
only two variables are studied.

number of variables
 Partial correlation :
analysis recognizes more than two variables
but considers only two variables keeping the
other constant.
 Total correlation:
based on all the relevant variables, which is
normally not feasible.

number of variables
 Multiple correlation :
Under Multiple Correlation three or more
than three variables are studied.

linearity
 Linear correlation :
 Correlation is said to be linear when the
amount of change in one variable tends to
bear a constant ratio to the amount of
change in the other. The graph of the
variables having a linear relationship will
form a straight line.

linearity
 Non - Linear correlation :
The correlation would be non linear if the
amount of change in one variable does not
bear a constant ratio to the amount of change
in the other variable.

Methods of correlation
 Scatter Diagram method
 Karl Pearson coefficient correlation
method
 Spearman’s Rank correlation

Scatter Diagram
 Scatter Diagram is a graph of observed
plotted points where each points
represents the values of X & Y as a
coordinate. It portrays the relationship
between these two variables graphically.
 Advantages
◦ Simple & Non Mathematical method
◦ Not influenced by the size of extreme item
◦ First step in investing the relationship
◦ between two variables

 Disadvantages:
◦ Can not adopt the an exact degree of
correlation

Karl Pearson's
 Pearson’s ‘r’ is the most common
correlation coefficient.
 Karl Pearson’s Coefficient of Correlation
denoted by- ‘r’ The coefficient of
correlation ‘r’ measure the degree of
linear relationship between two variables
say x & y.
 Karl Pearson’s Coefficient of Correlation
denoted by- r -1≥ r ≤ +1

Advantages
It summarizes in one value, the degree of
correlation & direction of correlation also.
Disadvantages
Always assume linear relationship
Interpreting the value of r is difficult.
Value of Correlation Coefficient is affected
by the extreme values.
Time consuming methods

Spearman’s rank
 When statistical series in which the
variables under study are not capable of
quantitative measurement but can be
arranged in serial order, in such situation
Pearson's correlation coefficient can not
be used in such case Spearman Rank
correlation can be used.

 Advantages
◦ This method is simpler to understand and
easier to apply compared to karl pearson’s
correlation method.
◦ This method is useful where we can give the
ranks and not the actual data.
◦ This method is to use where the initial data in
the form of ranks.
 Disadvantages
◦ Cannot be used for finding out correlation in a
grouped frequency distribution.

Importance of correlation
analysis :
 Measures the degree of relation i.e.
whether it is positive or negative.
 Estimating values of variables i.e. if
variables are highly correlated then we
can find value of variable with the help of
gives value of variable.
 Helps in understanding economic
behavior.

Correlationanalysis

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