Spearman Correlation in Python

Ever wondered how to compute the statistical relationship between two datasets? Well, one of the go-to methods for that is Spearman correlation, specifically in Python. This non-parametric measure gives insights into the degree and direction of association between two ranked variables.

What is Spearman Correlation?

Spearman Correlation is a statistical measure that evaluates the strength and direction of monotonic relationships between variables. Unlike Pearson correlation, it doesn’t assume that both datasets are normally distributed.

Key insights about Spearman Correlation:

• Non-parametric: It’s used when data doesn’t follow a normal distribution.
• Monotonic relationship: Both variables move in the same or opposite directions, but not necessarily at a constant rate.
• Rank-based: Uses the rank values instead of original observations.

Let’s look at how to interpret Spearman’s coefficient (ρ):

Remember:

1. A perfect spearman correlation of +1 or -1 means ranks are the same.
2. A spearman correlation of zero indicates no monotonic trend between the two datasets.
3. The closer to +1 or -1, the stronger the relationship; closer to zero implies a weaker link.

In Python, we use spearmanr() a function from the Scipy library for calculating this!

How to Calculate Spearman Correlation in Python

To calculate the Spearman correlation coefficient in Python, here’s a step-by-step guide:

1. Import necessary libraries

import pandas as pd
from scipy.stats import spearmanr

2. Create/load your data.

We’ll create a simple DataFrame for illustration.

data = {'X': [1, 2, 3, 4], 'Y': [4, 5, 6,7]}
df = pd.DataFrame(data)

3. Use spearmanr function from scipy package

This function calculates the Spearman correlation coefficient between two datasets.

corr,_ = spearmanr(df['X'], df['Y'])
print('Spearmans correlation: %.3f' % corr)

Note:

• The resulting value lies between -1 and +1 where +1 indicates perfect positive correlation and -1 perfect negative.
• Only monotonic relationships are considered by this method.
• Variable scales do not affect the score, unlike Pearson’s Coefficient.

And there you have it! That’s how you calculate Spearman Correlation in Python using scipy library functions.

Understanding the Results of Spearman Correlation

Spearman correlation in Python measures how related two sets of data are. The result is interpreted as follows:

• Close to +1: Strong positive relationship
• Close to -1: Strong negative relationship
• Around 0: No relationship.

Let’s take an example output from the spearman correlation method spearmanr(). It returns two values:

# Example output:
# SpearmanrResult(correlation=0.7, pvalue=0.02)

Here’s what these values mean:

• correlation (rho or r_s): This tells us the strength and direction of the association between two ranked variables.
  • A value close to 1 means strong positive relation.
  • A value close to -1 indicates strong negative relation.
  • A value near zero signifies no relation.
• pvalue: This shows the statistical significance of our calculated correlation coefficient (the probability that we would observe such an extreme correlation coefficient under the null hypothesis).
  • If p-value < 0.05, there’s a statistically significant correlation.

Consider these points when interpreting your results:

• Always look at both rho and p-value for complete analysis.
• Don’t forget about sample size; larger samples can make weak correlations seem more significant than they truly are!

Interpreting Negative and Positive Correlations

When working with Spearman correlation in Python, interpreting the results is straightforward:

• A positive correlation coefficient indicates that both variables increase or decrease together. As one variable gets larger, so does the other.
• A negative correlation coefficient suggests an inverse relationship between two variables. Meaning, as one variable grows larger, the other gets smaller.

Let’s dive into more details:

1. Positive Correlation:

Positive correlations are represented by values between +0.01 to +1.00.

• +0.01 - +0.20: Slight positive relationship
• +0.21 - +0.50: Low positive relationship
• +0.51 - +1:00: High positive relationship

Example: The number of hours studied and exam scores generally have a high positive correlation (+0.85).

2. Negative Correlation:

Negative correlations are represented by values from -0.01 to -1.

• **-0 .01-  -   ‎ ‎ ‎ ‏‎ ‏‎ ‏‎ ‏ minus;  minus; minus; minus;          **
• Slight negative relationship
• **minus;-                                       
• Low negative relation
• “Minus;-*           

For instance, time spent watching TV could have a low negative correlation (-3) with exam scores—the more TV watched (increase), the lower your grades (decrease).

Handling Missing Values in Spearman Correlation Analysis

When performing a Spearman correlation analysis, missing values can create issues. Here are a few strategies to tackle this problem:

• Eliminate Rows or Columns: Remove any rows or columns with missing data. This is quick and easy but potentially removes valuable information.

df.dropna(inplace=True)

• Imputation: Replace missing values with a statistical measure such as mean, median, mode etc.

from sklearn.impute import SimpleImputer
imputer = SimpleImputer(strategy='mean')
df_imputed = pd.DataFrame(imputer.fit_transform(df), columns=df.columns)

• Prediction Models: Use machine learning models to predict the missing values from other data.

Remember:

1. Always back up your original dataset before making changes.
2. Carefully consider the nature of your dataset when choosing an approach for handling missing values.
3. Test different methods and compare results to decide which strategy works best for you.

Use these techniques wisely, depending on your specific use case and requirements!

Comparing Pearson and Spearman Correlation Methods

While both Pearson and Spearman correlation methods are used to define the relationship between two variables, they have key differences:

• Pearson Correlation
• Measures linear relationships.
• Assumes that each dataset is normally distributed.
• More sensitive to outliers.

• Spearman Correlation
• Non-parametric measure of rank correlation.
• Does not assume any specific distribution in the data.
• Less sensitive to outliers.

The choice between using the Pearson or Spearman correlation method depends on your data set:

• Use Pearson if your data is normally distributed and has a linear relation.
• Choose Spearman for ordinal variables or when there’s no assumption about distribution type.

In Python, you can compute correlations using numpy’s corrcoef function for Pearson, and scipy.stats.spearmanr Spearman.

# Calculate Pearsons correlation
from numpy.random import randn
from numpy.random import seed
from scipy.stats import pearsonr

seed(1)
dataA = randn(100)
dataB = randn(100)

corr,_= pearsonr(dataA,dataB)
print('Pearsons correlation: %.3f' % corr)

# Calculate Spearmans Rank Correlation
from scipy.stats import spearmanr

corrs,_= spearmanr(dataA,dataB)
print('Spearmans Rank Coefficient: %.3f' % corrs)

Note: Be sure to handle missing values before performing these calculations, as they could affect outcomes negatively!

Tips for Effective Use of Spearman Correlation in Python

• Ensure Data is Ordinal: Spearman correlation focuses on ordinal data. Make sure your dataset has variables that can be ranked.
• Nonparametric Analysis: Unlike Pearson, Spearman doesn’t assume a normal distribution. So, it’s great for nonparametric data analysis.
• Use SciPy Library: Import the spearmanr function from the scipy.stats module: from scipy.stats import spearmanr
• Correct Syntax: To calculate and return a correlation matrix and p-value, coef, p = spearmanr(data1, data2)

• Interpret Results Correctly:

1. If coef is close to +1 or -1: Strong relationship.
2. If coef hovers towards zero: Weak relationship.
3. The closer p is to zero: The more statistically significant results are.

Remember, these tips help make effective use of Spearman Correlation in Python!

Wrapping Up

We’ve successfully navigated the path of understanding and implementing Spearman correlation in Python. It’s a powerful tool that helps us uncover relationships between variables when we can’t assume normality.

By leveraging packages like pandas and scipy, we managed to simplify our data analysis journey. Remember, every dataset is unique, with specific challenges. So, always stay open to exploring various statistical methods for different scenarios. Happy coding!