Spearman correlation in SciPy

Introduction

Spearman correlation helps us find how two things move together in order, even if the exact numbers don't match perfectly.

When you want to see if taller people tend to weigh more, without assuming exact weight differences.

When your data is ranked or ordered, like race positions or customer satisfaction ratings.

When the relationship between two variables is not straight but still follows a pattern.

When your data has outliers that might confuse other correlation methods.

When you want to check if two sets of exam scores are related by their ranks.

Syntax

SciPy

from scipy.stats import spearmanr
correlation, p_value = spearmanr(x, y)

x and y are lists or arrays of numbers of the same length.

The function returns two values: the Spearman correlation coefficient and a p-value to test significance.

Examples

Calculate Spearman correlation between two simple lists.

SciPy

from scipy.stats import spearmanr
x = [1, 2, 3, 4, 5]
y = [5, 6, 7, 8, 7]
correlation, p_value = spearmanr(x, y)
print(correlation)

Calculate Spearman correlation for numpy arrays with a perfect negative rank relationship.

SciPy

from scipy.stats import spearmanr
import numpy as np
x = np.array([10, 20, 30, 40])
y = np.array([40, 30, 20, 10])
correlation, p_value = spearmanr(x, y)
print(correlation)

Sample Program

This code finds the Spearman correlation between hours studied and exam ranks. It shows how strongly the order of hours studied relates to exam performance.

SciPy

from scipy.stats import spearmanr

# Sample data: hours studied and exam ranks
hours_studied = [2, 3, 5, 8, 13]
exam_ranks = [5, 4, 3, 2, 1]

correlation, p_value = spearmanr(hours_studied, exam_ranks)

print(f"Spearman correlation: {correlation:.2f}")
print(f"P-value: {p_value:.4f}")

Important Notes

A Spearman correlation of 1 means perfect increasing order match, -1 means perfect decreasing order match.

The p-value helps check if the correlation is likely due to chance; a small p-value means it's probably real.

Spearman correlation works well even if the data is not normally distributed.

Summary

Spearman correlation measures how well two variables relate by their order or rank.

It is useful when data is not linear or has outliers.

Use scipy.stats.spearmanr to calculate it easily in Python.

Practice

1. What does the Spearman correlation measure between two variables?

easy

A. The variance of a single variable

B. The strength and direction of a monotonic relationship based on ranks

C. The difference in means of two variables

D. The linear relationship between two variables

Solution

1. Step 1: Understand correlation types

   Spearman correlation measures how two variables move together based on their rank order, not their actual values.

2. Step 2: Compare with other correlations

   Unlike Pearson correlation, which measures linear relationships, Spearman focuses on monotonic relationships using ranks.

3. Final Answer:

   The strength and direction of a monotonic relationship based on ranks -> Option B

4. Quick Check:

   Spearman = monotonic rank correlation [OK]

Hint: Spearman uses ranks, not raw values, to find monotonic links [OK]

Common Mistakes:

• Confusing Spearman with Pearson correlation
• Thinking it measures linear relationships only
• Assuming it compares means or variances

2. Which of the following is the correct way to import the Spearman correlation function from scipy?

easy

A. from scipy.stats import spearmanr

B. import scipy.spearmanr

C. from scipy import spearmanr

D. import spearmanr from scipy.stats

Solution

1. Step 1: Recall scipy.stats module structure

   The Spearman correlation function is inside the stats submodule of scipy, so it must be imported from scipy.stats.

2. Step 2: Check correct import syntax

   The correct Python syntax to import a function is 'from module import function', so 'from scipy.stats import spearmanr' is correct.

3. Final Answer:

   from scipy.stats import spearmanr -> Option A

4. Quick Check:

   Correct import syntax = from scipy.stats import spearmanr [OK]

Hint: Use 'from scipy.stats import spearmanr' to import correctly [OK]

Common Mistakes:

• Trying to import spearmanr directly from scipy
• Using incorrect import syntax like 'import spearmanr from ...'
• Missing the stats submodule in import

3. What is the output of this code snippet?

from scipy.stats import spearmanr
x = [1, 2, 3, 4, 5]
y = [5, 6, 7, 8, 7]
result = spearmanr(x, y)
print(round(result.correlation, 2))

medium

A. 0.5

B. 0.9

C. 1.0

D. 0.82

Solution

1. Step 1: Understand the data ranks

   x is increasing from 1 to 5, y mostly increases but has a slight drop at the end (7 instead of 9), so ranks are similar but not perfect.

2. Step 2: Calculate Spearman correlation

   Spearman correlation measures rank similarity; here it is less than 1 but still strong, about 0.82 after rounding.

3. Final Answer:

   0.82 -> Option D

4. Quick Check:

   Spearman correlation ≈ 0.82 [OK]

Hint: Spearman close to 1 means strong rank similarity [OK]

Common Mistakes:

• Assuming perfect correlation (1.0) without checking data
• Confusing Pearson and Spearman correlation values
• Ignoring the slight rank difference in y

4. Identify the error in this code that calculates Spearman correlation:

from scipy.stats import spearmanr
x = [1, 2, 3]
y = [4, 5]
result = spearmanr(x, y)
print(result.correlation)

medium

A. Missing import for numpy

B. spearmanr function is misspelled

C. Lists x and y have different lengths

D. result.statistic attribute does not exist

Solution

1. Step 1: Check input data lengths

   Spearman correlation requires both input lists to have the same length. Here, x has 3 elements, y has 2.

2. Step 2: Understand function requirements

   Because lengths differ, spearmanr will raise an error. Other options are incorrect as spelling and attribute usage are correct.

3. Final Answer:

   Lists x and y have different lengths -> Option C

4. Quick Check:

   Input length mismatch causes error [OK]

Hint: Ensure input lists have equal length before correlation [OK]

Common Mistakes:

• Ignoring length mismatch of input lists
• Thinking spearmanr needs numpy import explicitly
• Assuming result.statistic is invalid

5. You have two variables with many tied ranks and some missing values (NaNs). Which approach using scipy.stats.spearmanr is best to get a valid Spearman correlation?

hard

A. Use spearmanr with nan_policy='omit' to ignore NaNs and handle ties automatically

B. Replace NaNs with zeros and then use spearmanr without extra parameters

C. Remove all tied values manually before using spearmanr

D. Use spearmanr with nan_policy='raise' to get an error for NaNs

Solution

1. Step 1: Handle missing values properly

   Spearman correlation in scipy can handle NaNs if nan_policy='omit' is set, which ignores NaNs safely.

2. Step 2: Understand tied ranks handling

   Spearman correlation automatically manages tied ranks, so no manual removal is needed.

3. Step 3: Evaluate other options

   Replacing NaNs with zeros or removing tied values manually can bias results; raising errors is not helpful for analysis.

4. Final Answer:

   Use spearmanr with nan_policy='omit' to ignore NaNs and handle ties automatically -> Option A

5. Quick Check:

   nan_policy='omit' + automatic tie handling = Use spearmanr with nan_policy='omit' to ignore NaNs and handle ties automatically [OK]

Hint: Use nan_policy='omit' to skip NaNs safely in spearmanr [OK]

Common Mistakes:

• Replacing NaNs with zeros causing bias
• Trying to remove tied ranks manually
• Not setting nan_policy causing errors