Spearman correlation in SciPy - Mini Project: Build & Apply

Calculate Spearman Correlation with SciPy

📖 Scenario: You are a data analyst working with two sets of related data points. You want to find out how strongly these two sets are related in terms of their rank order, not just their actual values.

🎯 Goal: Build a small Python program that calculates the Spearman correlation coefficient between two lists of numbers using the scipy library.

📋 What You'll Learn

Create two lists of numbers named data1 and data2 with exact values.

Create a variable named alpha to set the significance level.

Use scipy.stats.spearmanr to calculate the Spearman correlation coefficient and p-value.

Print the Spearman correlation coefficient and the p-value.

💡 Why This Matters

🌍 Real World

Spearman correlation is used when you want to measure how well two variables relate in terms of their order or rank, such as customer satisfaction rankings or survey responses.

💼 Career

Data analysts and scientists use Spearman correlation to find relationships in data that are not necessarily linear, helping in decision making and reporting.

1

Create the data lists

Create two lists called data1 and data2 with these exact values: data1 = [10, 20, 30, 40, 50] and data2 = [12, 24, 33, 47, 52].

SciPy

# Create the two data lists
# Your code here

Hint

Use square brackets to create lists and separate numbers with commas.

2

Set the significance level

Create a variable called alpha and set it to 0.05 to represent the significance level for the correlation test.

SciPy

data1 = [10, 20, 30, 40, 50]
data2 = [12, 24, 33, 47, 52]
# Create the alpha variable
# Your code here

Hint

Use a simple assignment statement to create alpha.

3

Calculate Spearman correlation

Import spearmanr from scipy.stats. Then use spearmanr(data1, data2) to calculate the Spearman correlation coefficient and p-value. Store the results in variables called corr and p_value.

SciPy

data1 = [10, 20, 30, 40, 50]
data2 = [12, 24, 33, 47, 52]
alpha = 0.05
# Import spearmanr and calculate correlation and p-value
# Your code here

Hint

Use from scipy.stats import spearmanr to import the function.

4

Print the Spearman correlation and p-value

Print the Spearman correlation coefficient stored in corr and the p-value stored in p_value using two separate print statements.

SciPy

from scipy.stats import spearmanr
data1 = [10, 20, 30, 40, 50]
data2 = [12, 24, 33, 47, 52]
alpha = 0.05
corr, p_value = spearmanr(data1, data2)
# Print the correlation and p-value
# Your code here

Hint

Use print(corr) and print(p_value) to show the results.

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