Spearman’s Rank Correlation: A Simple Guide

Introduction

In statistics, we often want to find out whether two variables are related. For example, do students who study more get better marks? Do taller people tend to weigh more? To answer such questions, we use correlation. One type of correlation is Spearman’s Rank Correlation.

This article explains Spearman’s Rank Correlation in simple words, with examples and formulas.

What is Spearman’s Rank Correlation?

Spearman’s Rank Correlation is a method used to measure the strength and direction of the relationship between two sets of ranked data. It tells us how well the relationship between two variables can be described using a monotonic function (i.e., when one variable increases, the other tends to increase or decrease consistently).

It is especially useful when:

• The data is ordinal (ranked).
• The relationship between variables is not linear.
• The values are not normally distributed.

• +1: Perfect positive correlation (as one increases, the other also increases).
• -1: Perfect negative correlation (as one increases, the other decreases).
• 0: No correlation.

When to Use Spearman Instead of Pearson

Use Spearman’s correlation when:

• Data is ordinal or in ranks.
• Data has outliers or is not normally distributed.
• Relationship is non-linear but monotonic (increasing or decreasing consistently).

Use Pearson’s correlation when:

• Data is interval or ratio scale.
• Relationship is linear.
• Data is normally distributed.

Advantages of Spearman’s Rank Correlation

• Simple to calculate.
• Does not require normal distribution.
• Can be used for non-linear data.
• Suitable for ranked data and small samples.

Limitations

• It only detects monotonic relationships, not all kinds.
• Less accurate than Pearson’s correlation if data is linear and normal.
• Ranking can be difficult with tied values (though corrections exist).

Conclusion

Spearman’s Rank Correlation is a valuable tool when dealing with ranked or non-linear data. It helps researchers, teachers, and analysts understand whether two sets of observations move together. By following simple steps, you can find how strongly two variables are related — even without complicated mathematics.