Covariance vs Correlation: Understanding top Differences

Covariance vs Correlation is two of the most common statistical concepts. However, many people use these terms interchangeably. And this is leading to confusion. In this article, we will explain the differences between covariance and correlation first. And we will show when to use each of them for you.

What is Covariance? covariance function in excel

Covariance is a measure of how two variables change together. It measures the relationship between two variables. Hence, it tells us how much the variables vary from their means. In other words, it shows how much the variables are related. If the variables move in the same direction, the covariance is positive. And if they move in opposite directions, then, it is negative.

Formula for Covariance: how to find covariance on excel

The formula for covariance is below.

Where X and Y are two variables, n is the number of observations. And xi and yi are the values of X and Y, respectively. So,  x̄ and ȳ are the means of X and Y.

What is Correlation?

Correlation measures the strength and direction of the relationship between two variables. It measures the degree to which two variables are linearly related. Correlation coefficients range from -1 to +1. Here -1 indicates a perfect negative correlation. While +1 indicates a perfect positive correlation and 0 indicates no correlation.

Formula for Correlation: correlation function in excel

The formula for correlation is:

Where ρX,Y is the correlation coefficient between X and Y. And cov(X,Y) is the covariance between X and Y. While σX is the standard deviation of X and σY is the standard deviation of Y.

Key Differences between Covariance vs Correlation

Covariance and correlation are two statistical concepts used together. But they are not the same thing. Here are some key differences between covariance and correlation below.

difference between correlation and covariance Definition

Covariance measures the extent to which two variables are linearly related to each other. It is a measure of the joint variability of two random variables. Correlation measures the strength and direction of the linear relationship of same those.

Range of values

Covariance can take on any value. This is including negative values. And it’s not bounded between -1 and 1. Correlation, on the other hand, always takes on values between -1 and 1.

Interpretation: relationship between correlation and covariance

Covariance does not give any information about the strength or direction of the relationship between two variables. It only shows the extent to which they are related. Correlation tough provides information about both the strength and direction of that relationship.

Units of measurement

Covariance is measured in terms of the units of the two variables. For example, if you are comparing the height and weight of people, the covariance will be in terms of inches and pounds. Correlation is a unitless measure. And it is standardized by the standard deviation of each variable.

Relationship between variables

Covariance can be positive, negative or zero depending on the relationship between the two variables. A positive covariance indicates that the two variables tend to increase or decrease together. While a negative covariance indicates they move in opposite directions. A covariance of zero indicates that there is no linear relationship between those. Correlation coefficients have the same interpretation. But they are standardized to be between -1 and 1.

what is the difference between correlation and covariance

In summary, covariance and correlation are both measures of the relationship between two variables. But they have different properties and provide different types of information. While covariance can describe the extent of the relationship correlation provides more useful information about the strength and direction between those.

When to Use Covariance and Correlation

Covariance

Covariance is useful when we want to know the direction of the relationship of variables at hand. It tells us whether the variables move in the same direction or in opposite directions. Covariance is also useful for calculating regression equations. So that, we can predict one variable based on another.

Correlation

Correlation is useful when we want to know the strength and direction of the relationship between them. It tells us how much two variables are related to each other. Correlation is also useful for identifying outliers and influential observations. It is also good for selecting variables for multivariate analysis.

Examples on covariance versus correlation

Here we suppose we have two variables as X and Y. And their values are as follows:

Covariance

To calculate the covariance between X and Y, we first need to calculate the means of X and Y.

x̄ = (1 + 2 + 3 + 4 + 5) / 5 = 3

ȳ = (2 + 3 + 4 + 5 + 6) / 5 = 4

Then, we use the covariance formula like below.

cov(X,Y) = [(1-3)(2-4) + (2-3)(3-4) + (3-3)(4-4) + (4-3)(5-4) + (5-3)(6-4)] / 5

cov(X,Y) = 2

The covariance between X and Y is 2. And this means variables are positively related.

Correlation

To calculate the correlation between X and Y, we also need to calculate the standard deviations of X and Y.

σX = √[(1-3)² + (2-3)² + (3-3)² + (4-3)² + (5-3)²] / 5 ≈ 1.41

σY = √[(2-4)² + (3-4)² + (4-4)² + (5-4)² + (6-4)²] / 5 ≈ 1.41

Then, we use the correlation formula as below.

ρX,Y = cov(X,Y) / (σX σY)

ρX,Y = 2 / (1.41 x 1.41) ≈ 1

The correlation between X and Y is approximately 1. So it means that the variables have a strong positive relationship.

Excel Examples

covariance function in excel

To calculate the covariance between two variables in Excel, you can use the COVARIANCE.P or COVARIANCE.S function. The COVARIANCE.P function calculates the population covariance. While the COVARIANCE.S calculates the sample covariance.

For example, let’s say we have two variables X and Y in columns A and B. To calculate the covariance between X and Y using the COVARIANCE.P function, you can use the formula below.

=COVARIANCE.P(A:A, B:B)

To calculate the covariance between X and Y using the COVARIANCE.S function, you can apply below formula.

=COVARIANCE.S(A:A, B:B)

correlation function in excel

If you wanna get correlation between two variables in Excel, you can use the CORREL function.

If you have variables of X and Y in columns A and B, you can use the formula.

=CORREL(A:A, B:B)

The output of the CORREL function will be a correlation coefficient between -1 and 1.

You should note that while Excel provides these functions for calculating covariance and correlation, it’s still important to understand the underlying concepts.

Conclusion: is covariance the same as correlation

In summary, covariance and correlation are two different measures of the relationship between two variables. Covariance function in excel tells us how much two variables vary together. While correlation function in excel is about the strength and direction of their relationship. Knowing the differences between these two concepts can help us choose the appropriate statistical method. We hope it helps you for future analyses. You can read this article on the subject or you can read this article we found for you from another site.