Pearson vs Spearman Correlation Coefficients – Difference and Applications

In data science, statistics, and machine learning, it is important to understand how variables are related to make good decisions and find useful insights. Two common ways to measure these relationships are the Pearson correlation versus Spearman. Both methods help show how two variables are connected, but they are quite different in what they assume and how they are used. Pearson correlation works best for continuous data that has a normal pattern and shows straight-line relationships. In contrast, Spearman correlation is great for ranked or ordered data and doesn’t assume anything about the data’s shape. This article looks at the main differences between Pearson vs Spearman correlation and their uses. As well as provide tips for choosing the right method based on the data type.

What is Correlation?

Before going towards the comparison of Pearson vs Spearman correlation it is important to understand what is Correlation. So, the correlation is a way to measure how two things are related. It shows if one thing changes when another thing changes. The correlation value can be between -1 and 1:

• +1 means both things increase together.
• -1 means one thing goes up while the other goes down.
• 0 means there’s no connection between them.

We can use Correlation in areas like data science, economics, and research to find patterns and relationships. However, it only shows how things are linked, not whether one causes the other. Let’s start with the differentiation of Correlation Pearson vs Spearman below.

Pearson Correlation Coefficient

The Pearson correlation coefficient measures how two continuous things are related in a straight line. It is shown as r and is found by comparing how both things change together with their overall variation. It assumes the data is normally spread out and the relationship between the two is straight, not curved.

Formula:

Where:

• cov(X, Y) is the covariance between X and Y.
• σ_X and σ_Y are the standard deviations of X and Y, respectively.

Example of Pearson Correlation

In the realm of the Pearson vs Spearman correlation example, If you want to check the link between height and weight, both being continuous, you can use the Pearson correlation. So, it will show if taller people tend to weigh more (positive correlation) or if there is no straight-line relationship.

When should I use Pearson correlation?

Use Pearson correlation when:

• Both things are continuous.
• The relationship is straight (linear).
• The data follows a normal pattern.
• There are no big outliers.

It is good for situations where you expect a straight-line connection. Like checking the link between temperature as well as how much electricity is used.

Spearman Correlation Coefficient

In the conflict of Pearson vs Spearman correlation, the Spearman correlation coefficient measures how two things are related based on their rank or order. It checks if the relationship between them moves in one direction, even if it is not in a straight line. Unlike Pearson, Spearman doesn't need the data to follow a normal pattern and works well with ranked or ordered data.

Formula:

Where:

• d_i is the difference in ranks between corresponding values of X and Y.
• n is the number of data points.

Example of Spearman Correlation

If you want to check the link between students' test scores and their rank in class, even if the data is not in a straight line, you can use the Spearman correlation to see if higher scores lead to better ranks.

When to Use Spearman Correlation?

Use Spearman correlation when:

• The data is ordered or not following a normal pattern.
• The relationship moves in one direction but not in a straight line.
• Some outliers might affect Pearson's results.
• You are working with ranked data.

This makes Spearman great for things like customer satisfaction ratings or the link between study time and class rank.

Key Differences Between Pearson vs Spearman Correlation

The Pearson and Spearman correlation coefficients are commonly used to measure how two things are related to each other, but they work in slightly different ways. So, here are the key differences between correlation Spearman vs Pearson:

1. Nature of Relationship 

• Pearson looks at straight-line (linear) relationships
• While Spearman checks for general direction (monotonic), which doesn't have to be straight.

2. Assumptions About Data

• Pearson needs the data to be normally spread out, 
• But Spearman doesn’t need any specific data patterns.

3. Handling Outliers

• Pearson can be affected by extreme values (outliers), which can change results. 
• While Spearman is better at handling outliers since it uses ranks.

4. Type of Data

• Pearson is for continuous data. 
• While Spearman can be used with ordered data (ordinal), as well as interval or ratio data.

Importance of Pearson Correlation Coefficient and Spearman Coefficients

The Pearson and Spearman coefficients are important. Because they help us understand how different things are related. Which aids researchers and analysts in making smart choices. As well as Pearson correlation is great for finding straight-line relationships in continuous data, making it useful in areas like finance and health where exact measurements are important. In contrast, Spearman correlation helps look at relationships in ordered data or when the data doesn't follow a normal pattern. This allows for analyzing rankings. Both coefficients assist in spotting patterns, and trends, and making predictions, leading to better decisions based on data. Their use in many fields shows how important they are in statistics and research.

Pearson vs Spearman Correlation Application Scenarios

When deciding between Pearson and Spearman correlation coefficients, it’s important to think about the type of data and the context. Here are some simple examples of how Pearson correlation vs Spearman correlation is used in real life:

• Finance: In finance, analysts use Pearson to check the linear relationship between the returns of two assets. Spearman is useful for looking at ranked data, like bond ratings or investment choices.
• Biology and Medicine: In biology, researchers often use Pearson to study the relationship between two continuous variables, such as height and weight. If they want to see how a patient’s health rank affects survival rates, they would use Spearman.
• Machine Learning: In machine learning, Pearson helps find linear relationships between features and the target variable. If the relationship is nonlinear or if the data is ranked, Spearman also can provide better insights.

Conclusion

In conclusion, knowing the differences between Pearson vs Spearman correlation is important for analyzing data relationships effectively. Pearson works best for continuous data that follows a normal pattern. It also shows a straight-line relationship, making it useful in finance and healthcare. On the other hand, Spearman is better for ordered data or when the relationship isn’t straight, which is helpful in psychology and social sciences. So, by choosing the right method based on the data and research goals, analysts can gain better insights and make smarter decisions. The Pearson correlation coefficient vs Spearman is key in finding patterns and trends, helping us understand complex relationships in different fields.

Frequently Asked Questions (FAQs)