Spearman correlation in SciPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Spearman correlation output for simple arrays

What is the output of the following code that calculates Spearman correlation between two arrays?

SciPy

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

A 1.0

B -0.9

C 0.7

D 0.9

💡 Hint

Spearman correlation measures monotonic relationship, not linear.

The Spearman correlation here is about 0.9, showing a strong positive monotonic relationship.

❓ data_output

intermediate

Spearman correlation matrix from DataFrame columns

Given a DataFrame with columns A, B, and C, what is the Spearman correlation matrix output?

SciPy

import pandas as pd
from scipy.stats import spearmanr

data = {'A': [1, 2, 3, 4], 'B': [4, 3, 2, 1], 'C': [1, 3, 2, 4]}
df = pd.DataFrame(data)
correlation, _ = spearmanr(df)
print(correlation)

A

[[ 1.  -1.   0.8]
 [-1.   1.  -0.8]
 [ 0.8 -0.8  1. ]]

B

[[ 1.   1.  -0.8]
 [ 1.   1.  -0.8]
 [-0.8 -0.8  1. ]]

C

[[ 1.   0.8 -1. ]
 [ 0.8  1.  -1. ]
 [-1.  -1.   1. ]]

D

[[ 1.   0.5  0.5]
 [ 0.5  1.   0.5]
 [ 0.5  0.5  1. ]]

💡 Hint

Spearman correlation matrix is symmetric with 1s on diagonal.

Column A and B are perfectly negatively correlated (-1), A and C have 0.8 positive correlation.

🔧 Debug

advanced

Identify the error in Spearman correlation code

What error does this code raise when trying to calculate Spearman correlation?

SciPy

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

A ValueError: x and y must have the same length

B TypeError: spearmanr() missing 1 required positional argument

C IndexError: list index out of range

D No error, returns correlation

💡 Hint

Check if input arrays have the same length.

Spearman correlation requires inputs of equal length; otherwise, ValueError is raised.

🧠 Conceptual

advanced

Understanding Spearman correlation properties

Which statement about Spearman correlation is TRUE?

A It is sensitive to outliers more than Pearson correlation.

B It measures linear relationships only.

C It uses ranks of data values to measure monotonic relationships.

D It requires data to be normally distributed.

💡 Hint

Think about how Spearman correlation handles data values.

Spearman correlation uses ranks to measure monotonic relationships, not just linear.

🚀 Application

expert

Interpreting Spearman correlation p-value

You calculate Spearman correlation between two variables and get correlation=0.6 and p-value=0.07. What is the correct interpretation?

A There is no relationship because p-value is greater than 0.05.

B There is a moderate monotonic relationship but it is NOT statistically significant at 0.05 level.

C There is a strong monotonic relationship and it is statistically significant at 0.05 level.

D The correlation is weak and p-value indicates strong significance.

💡 Hint

Check both correlation strength and p-value significance.

Correlation 0.6 is moderate positive, but p-value 0.07 is above 0.05 threshold, so not significant.