# Calculate Spearman’s Correlation Coefficient for Beginners – NumPy Tutorial

By | September 15, 2019

Spearman’s Correlation Coefficient is widely used in deep learning right now, which is very useful to estiment the correlation of two variables. In this  tutorial, we will introduce how to calculate spearman’s correlation coefficient.

## Preliminaries

from scipy.stats import spearmanr

Create a pair of data (x, y)

x = [1, 8, 3, 4, 5, 6, 7, 2, 9, 10]
y = [1, 5, 8, 7, 10, 9, 3,6 , 2, 4]

This pair data is like:

You can learn how to implement a scatter plot with matplotlib in:

Best Practice to Implement Scatter Plot with Matplotlib – Matplotlib Tutorial

## Calculate spearman correlation coefficient

value = spearmanr(x, y)
print value[0]

The output is:

-0.175757575758

This value mean that x and y is week monotonic relationship.

## Method 2: Calculate it with its formula

Spearman’s correlation coefficient is defined:

We can calculate it with code:

n = len(x)
total = 0
for i in range(n):
total += (x[i]-y[i])**2
spearman = 1 - float(6 * total) / (n * (n ** 2 - 1))
print spearman

The output is:

-0.175757575758