Covariance is a measure of how two random variables change together, taking any value from -∞ to +∞. Covariance can be affected by changing the units of the variables. Correlation is a scaled version of covariance that indicates the strength of the relationship between two variables on a scale of -1 to 1. Unlike covariance, correlation is not affected by changes in the location or scale of the variables and provides a standardized measure of their relationship. Correlation is therefore preferred over covariance as a measure of the relationship between two variables.

1. Covariance vs Correlation
By: Aniruddha Deshmukh – M. Sc. Statistics, MCM

2. Covariance
• A systematic relationship between a pair of random variables
wherein a change in one variable reciprocated by an equivalent
change in another variable.
• Covariance can take any value between -∞ to +∞, wherein the
negative value is an indicator of negative relationship whereas a
positive value represents the positive relationship and when the
value is zero, it indicates no relationship.
• In addition to this, when all the observations of the either variable
are same, the covariance will be zero.
• When we change the unit of observation on any or both the two
variables, then there is no change in the strength of the
relationship between two variables but the value of covariance is
changed.
By Aniruddha Deshmukh - M. Sc. Statistics, MCM 2
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3. Correlation
By Aniruddha Deshmukh - M. Sc. Statistics, MCM 3
• A measure which determines the change in one variable due to
change in other variable.
• Correlation is of two types, i.e. positive correlation or negative
correlation.
• Correlation can take any value between -1 to +1, wherein values
close to +1 represents strong positive correlation and values close
to -1 is an indicator of strong negative correlation.
• There are four measures of correlation:
– Scatter diagram
– Product-moment correlation coefficient
– Rank correlation coefficient
– Coefficient of concurrent deviations
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4. Key Differences
By Aniruddha Deshmukh - M. Sc. Statistics, MCM 4
Key Covariance Correlation
Meaning
Covariance is a measure indicating
the extent to which two random
variables change in tandem.
Correlation is a statistical measure
that indicates how strongly two
variables are related.
What is it? Measure of correlation Scaled version of covariance
Values Lie between -∞ and +∞ Lie between -1 and +1
Change in scale Affects covariance Does not affects correlation
Unit free
measure
No Yes

5. • Correlation is a special case of covariance which can be
obtained when the data is standardized.
• Now, when it comes to making a choice, which is a better
measure of the relationship between two variables,
correlation is preferred over covariance, because it remains
unaffected by the change in location and scale, and can also
be used to make a comparison between two pairs of
variables.
By Aniruddha Deshmukh - M. Sc. Statistics, MCM 5
Summary

6. Aniruddha Deshmukh – M. Sc. Statistics, MCM
email: annied23@gmail.com
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