The most common way to quantify the linear association between two variables is to use the Pearson Correlation Coefficient, which always takes on a value between -1 and 1 where:

- -1 indicates a perfectly negative linear correlation
- 0 indicates no linear correlation
- 1 indicates a perfectly positive linear correlation

However, this type of correlation coefficient works best when the true underlying relationship between the two variables is *linear*.

There is another type of correlation coefficient known as **Spearman’s rank correlation** that is better to use in two specific scenarios:

**Scenario 1**: When working with ranked data.

- An example could be a dataset that contains the rank of a student’s math exam score along with the rank of their science exam score in a class.

**Scenario 2**: When one or more extreme outliers are present.

- When extreme outliers are present in a dataset, Pearson’s correlation coefficient is highly affected.

The following examples show how to calculate the Spearman Rank Correlation in each of these scenarios.

**Scenario 1: Spearman’s Rank Correlation with Ranked Data**

Consider the following dataset (and corresponding scatter plot) that shows the relationship between two variables:

Using statistical software, we can calculate the following correlation coefficients for these two variables:

- Pearson’s correlation:
**0.79** - Spearman’s rank correlation:
**1**

In this scenario, if we only care about the ranks of the data values (when the rank of x increases, does the rank of y also increase?) then Spearman’s rank correlation would provide us with a better idea of the correlation between the two variables.

In this particular dataset, as the rank of x increases the rank of y *always* increases.

Spearman’s rank correlation captures this behavior perfectly by telling us that there is a perfect positive relationship (**ρ = 1**) between the ranks of x and the ranks of y.

By contrast, Pearson’s correlation tells us the that there is a strong linear relationship (**r = 0.79**) between the two variables.

This is true, but it’s not useful if we only care about the relationship between the ranks of x and the ranks of y.

**Scenario 2: Spearman’s Rank Correlation with Extreme Outliers**

Consider the following dataset (and corresponding scatter plot) that shows the relationship between two variables:

Using statistical software, we can calculate the following correlation coefficients for these two variables:

- Pearson’s correlation:
**0.86** - Spearman’s rank correlation:
**0.85**

The correlation coefficients are nearly identical because the underlying relationship between the variables is roughly linear and there are no extreme outliers.

Now suppose we change the last y value in the dataset to be an extreme outlier:

Using statistical software, we can calculate the correlation coefficients once again:

- Pearson’s correlation:
**0.69** - Spearman’s rank correlation:
**0.85**

Pearson’s correlation coefficient changed dramatically while Spearman’s rank correlation coefficient remained the same.

Using statistical jargon, we would say that the relationship between x and y is monotonic (as x increases, y generally increases) but not linear since the outlier influences the data so much.

In this scenario, Spearman’s rank correlation does a good job of quantifying this monotonic relationship, while Pearson’s correlation does a poor job because it’s attempting to calculate the linear relationship between the two variables.

**Related:** How to Report Spearman’s Rank Correlation in APA Format

**Additional Resources**

The following tutorials explain how to calculate the Spearman Rank Correlation using different software:

How to Calculate Spearman Rank Correlation in Excel

How to Calculate Spearman Rank Correlation in Google Sheets

How to Calculate Spearman Rank Correlation in R

How to Calculate Spearman Rank Correlation in Python