Difference Between Covariance and Correlation (With Table)

Covariance vs Correlation

The key difference between covariance and correlation lies in the fact that covariance measures the strength or weakness of the correlation between two or more sets of random variables. On the other hand, correlation means to serve as an extended form of covariance.

The term covariance means it will try to look for the measurement of how many variables can change together.

To simply put it when both variables are capable of changing in the same way without creating or making any relationship then it is called covariance.

Studies show that in covariance sign is the only important thing. If there is a positive value, it means that both variables will change in the same direction and in the case of negative value, it means that they vary in the opposite direction.

Covariance only shows the direction which may not be enough to get the relationship totally. This is the reason why we prefer to separate covariance with the basic change of x and y.  And this will help us to have the correlation coefficient in the process.


Parameter of ComparisonCovarianceCorrelation
DefinitionCovariance is known as an indicator of the extent to which two random variables will be dependent on each other. And higher number tends to denote higher dependency.Correlation is also known as an indicator that shows how strongly two variables are related two to each other, provided other conditions are there. Its maximum value is +1
ValuesCovariance is limited to values between -∞ and +∞.Correlation lies in the range between -1 and +1.
What is their relationship?Correlation is capable of getting deduced from covariance.If we consider a standard scale, the correlation will provide a measure of covariance. In this case, correlation can be deduced with standard deviation by dividing the calculated covariance.
How scale range affects?Covariance gets affected by any change in scales.On the other hand, correlation does not get affected by the change in scales.
UnitsCovariance has units when it is deduced by the multiplication of two numbers and units they have.A correlation has no unit, as it is a number between -1 and +1.

 

What is Covariance?

When two variables are measured by something to see how they move with respect to each other and which is also an extension of the variance concept is called covariance.

If one says that two items vary together then it means that there is a covariance between the two items which can be either positive or negative covariance.

Positive covariance tends to indicate that higher than average values of one variable pair with higher than average values of the other variable.

On the other hand, negative covariance tends to say that higher than average values of one variable pair with lower than average values of the other variable.

In this case, covariance’s number is depending on the data. To compare covariance will become difficult among data sets with different ranges of scales.

There can be a value sometimes that is capable of symbolizing a relationship that is strong and limited in one set of data. At the same time, it will show the opposite result in another set of data.

In this case, the correlation coefficient deals with the issue by adjusting the values of the covariance. They also create a dimensionless quantity which will assist the comparison of different data sets.

Covariance formula
Covariance formula
 

What is the Correlation?

Correlation is known as the statistic measurement which signifies the extent of two or more variables that fluctuates together.

A positive correlation is the indicator of the extent to which those variables parallelly increase or decrease, whereas a negative correlation is the indicator of the extent to which one variable increases and the other one decreases at the same time.

In statistics, to test the relationship between quantitative variables or categorical variables we use correlation. To put it simply, it is a measurement of how things are related to each other. According to a study, we know how variables are correlated and it is called correlation analysis.

In advanced portfolio management, correlations are used and also computed as the correlation coefficient, which contains a value in between -1 and +1. To know what the future holds is a vital thing in social sciences such as- government and healthcare.

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For that correlations are useful as it can help to find out what relationship variables have, and also let us know if we can make predictions about the upcoming pattern of behavior.

These statistics are being used for budgets and business plans by businesses.

Correlation formula
Correlation formula

Main Differences Between Covariance and Correlation

  1. The expected value of variation between two random variables from their expected values is known as covariance. On the other hand, a correlation does not have variation like covariance, even when the definition of correlation is almost as same as covariance.
  2. Covariance measures two random variables that vary together. At the same time, correlation measures how far or close two variables are from being independent of each other.
  3. In statistics, covariance tends to vary from negative infinity to positive infinity while correlation does it from -1 to 1.
  4. Covariance is not a unit-free measure. On the other hand, correlation is a unit-free measure of the inter-dependency of two variables. Also, this makes it less hard for calculated correlation values to be compared across any 2 variables that are irrespective of their units and dimensions.
  5. Covariance is known to be scale-dependent while correlation is known to be the opposite. Meaning, the difference in scale can deliver a different covariance.

 

Frequently Asked Questions (FAQ) About Covariance and Correlation

🌕 Is covariance always positive?

Covariance refers to two variables that are related. A covariance is not always positive. When a covariance is positive, it means the variables are in a positive linear relationship.

If the covariance is negative, the variables will be inversely related. Hence, covariance can be both positive or negative depends on the relationship between the variables.

🌕 What is the range for covariance?

A covariance range can be from negative infinity to positive infinity. A covariance range totally depends on the data.

🌈 What does a covariance of 0 mean?

A covariance of 0 refers to two variables that are not dependent on anyone. These variables are basically independent in nature.

Even if the covariance is 0, it does not mean that both the variables are independent. There may be a nonlinear relationship that will also conclude in the covariance of 0.

🌞 What does a correlation of 1 mean?

Correlation of 1 indicates a perfect correlation between two variables. It shows a perfect positive linear relationship.

It means that every time the first variable moves in a direction, the second variable moves the same amount in the same direction.

If variable A increases by 10%, variable B will also increase by 10%.

Some examples are:

  1. Relationship between Fahrenheit and Celsius, if one rises other rises as well.
  2. Relationship between a person and his image in the mirror; image will do similar movements as the person.

Is covariance the same as standard deviation?

Covariance is used to measure the relationship between two variables. It shows how two variables move or change with respect to each other.

Standard deviation calculates the amount of dispersion or variation of a dataset. This dispersion is measured with respect to the mean of the dataset.

Standard deviation = square root of variance

Hence covariance and standard deviation are not the same.

What is an example of a negative correlation?

A negative correlation is the correlation of -1. It is the opposite of the correlation of 1. In a negative correlation, an increase in one variable causes a decrease in the other variable.

Example of a negative correlation:
When the speed of a car is increased, it will take less time to reach the destination. In a similar manner, if the speed of the car is reduced, it would take more time to reach the destination.


 

Infographic

Covariance vs Correlation

 

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Conclusion

The fact is covariance and correlation are very closely related to each other and also at the same time they have so many differences.

Covariance tends to define the type of interaction between variables, and correlation does the same too but it also defines the strength of the relationship.

For this, plenty of time correlation is called as the special case of covariance. Though if anyone has to pick between the two, so many analysts prefer to choose correlation as it does not get affected by the changes in dimensions, locations, and scale.


 

Word Cloud for Difference Between Covariance and Correlation

The following is a collection of the most used terms in this article on Covariance and Correlation. This should help in recalling related terms as used in this article at a later stage for you.

Covariance and Correlation
Word Cloud for Covariance and Correlation

 

References

  1. https://www.researchgate.net/profile/Karl_Joereskog/publication/24062332_Structural_Analysis_of_Covariance_and_Correlation_Matrices/links/0046352b8b078d34d6000000.pdf
  2. https://projecteuclid.org/download/pdf_1/euclid.aos/1176349937
  3. https://academic.oup.com/biomet/article-abstract/87/3/603/293706

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