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What is Spearman Rank Correlation

# What is Spearman Rank Correlation

• 29 Jun 2023

A mathematical metric called correlation can be used to assess how closely two variables change.  A positive correlation demonstrates how closely the variables rise or fall together. The range in which one variable rises while the other falls is indicated by a negative correlation. In this post, we'll talk about the Spearman Rank correlation.

When it comes to online Share trading, Spearman's rank correlation may be used to look at the relationship between the rankings of various stocks or financial instruments over a certain time frame.

## What Does Monotonic Function Mean?

It's critical to understand the monotonic function in order to understand Spearman's rank correlation. In response to changes in its independent variable, a monotonic function never either rises or decreases.

For monotonic functions, there are two categories:

Monotonic rising function: This kind of function keeps the output values constant or grows as the input values rise, maintaining a non-decreasing order.

Monotonic declining function: This kind of function keeps the output values constant or continuously falls as the input values rise, maintaining a non-increasing order.

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### Table of Content

1. What Does Monotonic Function Mean?
2. Spearman Rank Correlation
3. Why does Spearman's correlation need a monotonic relationship?
4. Spearman's Rank Correlation Illustration
5. Conclusion

## Spearman Rank Correlation

The degree and direction of the link between two ranked variables are measured by Spearman's rank correlation. It simply provides a measure of how monotonically a relationship between two variables can be expressed, or how effectively a monotonic function can capture that relationship.

The Spearman's rank correlation formula is as follows:

ρ = 1 - [(6Σd²) / (n(n² - 1))]

Spearman's rank correlation coefficient is equal to 𝝆

di = The difference between each observation's two rankings

n is the number of observations.

The Spearman Rank Correlation might range from +1 to -1 depending on the following:

• A value of +1 indicates a perfect rank relationship.
• If a value is 0, there is no correlation between rankings.
• A complete negative correlation of rank is represented by a value of -1

## Why does Spearman's correlation need a monotonic relationship?

The intensity and direction of the monotonic relationship between two variables are measured using Spearman's correlation. The "less restrictive" nature of monotonicity contrasts with that of a linear connection.

Spearman's correlation does not always presuppose a monotonic connection. To find out if there is a monotonic component to a connection, you can use Spearman's correlation on a non-monotonic relationship.

However, you would often use a measure of connection that matches the pattern of the observed data, such as Spearman's correlation. In other words, you would do a Spearman's correlation if a scatterplot indicated that the connection between your two variables appeared monotonic since this will then determine the strength and direction of this monotonic association.

On the other hand, you would use Pearson's correlation to determine the strength and direction of any linear relationship if, for instance, the relationship seems linear. Since you won't always be able to visually determine if you have a monotonic connection, you could still conduct a Spearman's correlation in this situation.

## Spearman's Rank Correlation Illustration

Take a look at the maths and science test results for the five kids listed in the table.

Step 1: Make a table for the provided data.

Step 2: Descend the rankings of both sets of data. The greatest marks will receive a rating of 1, while the lowest marks will receive a rank of 5.

Step 3: Determine the square value of d and the difference between the ranks (d).

Step 5: Add these values to the formula.

ρ = 1 - [(6Σd²) / (n(n² - 1))]

= 1 - (6 * 14) / 5(25 - 1)

= 0.3

For the provided data, the Spearman's Rank Correlation is 0.3. Since the value is close to 0, there is only a little connection between the two ranks.

## Conclusion

A statistical tool for evaluating the strength and direction of a monotonic relationship between two variables is Spearman's rank correlation. It is especially helpful in situations when the variables don't necessarily have a linear relationship but nevertheless fluctuate in a predictable fashion.

Spearman's rank correlation should, however, be used in combination with other analytic methods and factors because it does not always suggest causality. Additionally, the formula may take different forms in other statistical software programmes, but the fundamental idea is the same. You can use the blinkX trading App to learn how to trade by comprehending technical charts and making wise financial decisions.

## Spearman's Rank Correlation Coefficient FAQs

The degree and direction of the monotonic link between two variables are quantified by Spearman's Rank Correlation Coefficient, a statistical metric.

If you have ordinal or non-normally distributed data and wish to evaluate the monotonic correlation between two variables, Spearman's Rank Correlation Coefficient is helpful. It does not presume a linear connection and is resistant to outliers.

The magnitude and axis of the monotonic link between two variables are measured using Spearman's rank correlation coefficient. Instead of evaluating the actual values, it evaluates how well the rankings of the variables match one another.

The coefficient may fall between -1 and 1. A value of -1 denotes an idealised negative monotonic connection, a value of 1 denotes an idealised positive monotonic relationship, and a value of 0 denotes an idealised absence of monotony.

Hypothesis testing can be used to determine the statistical significance of Spearman's Rank Correlation Coefficient.

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