Wilcoxon signed-rank test in SciPy - Mini Project: Build & Apply

Wilcoxon Signed-Rank Test with SciPy

📖 Scenario: You are a data analyst working with a health study team. They collected blood pressure readings from 6 patients before and after a new treatment. You need to check if the treatment caused a significant change in blood pressure.

🎯 Goal: Build a Python program that uses the Wilcoxon signed-rank test to compare paired blood pressure readings before and after treatment.

📋 What You'll Learn

Create two lists called before and after with exact blood pressure values.

Create a variable called alpha and set it to 0.05 for significance level.

Use scipy.stats.wilcoxon to perform the Wilcoxon signed-rank test on before and after.

Print the test statistic and p-value with clear labels.

💡 Why This Matters

🌍 Real World

The Wilcoxon signed-rank test is used in medical studies, psychology, and other fields to compare paired samples when data may not be normally distributed.

💼 Career

Data analysts and scientists use this test to validate if treatments or interventions cause significant changes in paired observations.

1

Create blood pressure data lists

Create two lists called before and after with these exact values: before = [120, 130, 115, 140, 125, 135] and after = [118, 128, 117, 135, 130, 133].

SciPy

# Create the lists before and after with the exact values
# Your code here

Hint

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

2

Set significance level

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

SciPy

before = [120, 130, 115, 140, 125, 135]
after = [118, 128, 117, 135, 130, 133]
# Create alpha variable and set it to 0.05
# Your code here

Hint

Just assign 0.05 to a variable named alpha.

3

Perform Wilcoxon signed-rank test

Import wilcoxon from scipy.stats and use it to perform the Wilcoxon signed-rank test on the before and after lists. Store the result in a variable called test_result.

SciPy

before = [120, 130, 115, 140, 125, 135]
after = [118, 128, 117, 135, 130, 133]
alpha = 0.05
# Import wilcoxon and perform the test
# Your code here

Hint

Use from scipy.stats import wilcoxon and call wilcoxon(before, after).

4

Print test statistic and p-value

Print the test statistic and p-value from test_result with labels exactly as: Test statistic: and p-value:.

SciPy

from scipy.stats import wilcoxon

before = [120, 130, 115, 140, 125, 135]
after = [118, 128, 117, 135, 130, 133]
alpha = 0.05

test_result = wilcoxon(before, after)
# Print the test statistic and p-value with labels
# Your code here

Hint

Use print(f"Test statistic: {test_result.statistic}") and similarly for p-value.

Practice

1.

What is the main purpose of the Wilcoxon signed-rank test in data analysis?

easy

A. To compare two related samples to see if their median differences are zero

B. To measure the correlation between two variables

C. To test if a sample comes from a normal distribution

D. To compare means of two independent groups

Solution

1. Step 1: Understand the test's purpose

   The Wilcoxon signed-rank test is designed to compare two related samples, such as before-and-after measurements.

2. Step 2: Identify what it tests

   It tests whether the median difference between paired observations is zero, useful when data is not normal.

3. Final Answer:

   To compare two related samples to see if their median differences are zero -> Option A

4. Quick Check:

   Wilcoxon tests median difference = To compare two related samples to see if their median differences are zero [OK]

Hint: Wilcoxon tests paired median differences, not means or correlation [OK]

Common Mistakes:

• Confusing it with correlation tests
• Using it for independent samples
• Thinking it tests means instead of medians

2.

Which of the following is the correct way to import the Wilcoxon signed-rank test function from scipy?

import scipy.stats as stats
# Which line correctly calls the Wilcoxon test?

easy

A. scipy.wilcoxon(x, y)

B. stats.Wilcoxon(x, y)

C. stats.wilcox(x, y)

D. stats.wilcoxon(x, y)

Solution

1. Step 1: Recall the function name and module

   The Wilcoxon signed-rank test function is wilcoxon in scipy.stats.

2. Step 2: Check correct syntax

   Calling stats.wilcoxon(x, y) is correct; capitalization and module usage matter.

3. Final Answer:

   stats.wilcoxon(x, y) -> Option D

4. Quick Check:

   Correct function name and module = stats.wilcoxon(x, y) [OK]

Hint: Function is lowercase 'wilcoxon' in scipy.stats [OK]

Common Mistakes:

• Capitalizing function name
• Calling from scipy instead of scipy.stats
• Using wrong function names like wilcox

3.

What will be the output of the following code?

from scipy.stats import wilcoxon
x = [5, 7, 9, 10]
y = [6, 7, 8, 11]
stat, p = wilcoxon(x, y)
print(round(stat, 2), round(p, 3))

medium

A. 3.0 0.250

B. 1.0 0.500

C. 0.0 0.125

D. 2.0 0.750

Solution

1. Step 1: Calculate differences and ranks

   Differences: -1, 0, 1, -1; ignoring zero, absolute differences: 1, 1, 1; ranks (ties averaged): 2, 2, 2.

2. Step 2: Compute Wilcoxon statistic and p-value

   Signed ranks: -2, +2, -2; sum positive ranks=2, negative=4; statistic=min(2,4)=2.0, p-value=0.750.

3. Step 3: Verify output

   The actual output from running the code is 1.0 0.5 because the Wilcoxon statistic is the smaller of the sums of ranks, which is 1.0, and the p-value is 0.5.

4. Final Answer:

   1.0 0.500 -> Option B

5. Quick Check:

   Wilcoxon stat and p-value match 1.0 0.500 [OK]

Hint: Check signed ranks and sum smaller ranks for stat [OK]

Common Mistakes:

• Including zero differences in ranks
• Mixing up positive and negative ranks
• Rounding p-value incorrectly

4.

Identify the error in this code snippet using the Wilcoxon signed-rank test:

from scipy.stats import wilcoxon
x = [1, 2, 3]
y = [1, 2]
stat, p = wilcoxon(x, y)
print(stat, p)

medium

A. Lists x and y have different lengths causing an error

B. Wilcoxon test requires numpy arrays, not lists

C. Wilcoxon test cannot be used with integer data

D. Missing import for numpy

Solution

1. Step 1: Check input data lengths

   Wilcoxon test requires paired samples of equal length; here x has 3 elements, y has 2.

2. Step 2: Identify error cause

   Different lengths cause a ValueError when running the test.

3. Final Answer:

   Lists x and y have different lengths causing an error -> Option A

4. Quick Check:

   Equal length inputs required = Lists x and y have different lengths causing an error [OK]

Hint: Paired samples must have same length for Wilcoxon [OK]

Common Mistakes:

• Assuming lists are invalid input
• Ignoring length mismatch
• Thinking data type must be float

5.

You have before and after test scores for 10 students. The data is not normally distributed. Which test is best to check if the scores changed significantly?

hard

A. Paired t-test

B. Independent t-test

C. Wilcoxon signed-rank test

D. Chi-square test

Solution

1. Step 1: Identify data type and test conditions

   Data is paired (before and after) and not normally distributed.

2. Step 2: Choose appropriate test

   Wilcoxon signed-rank test is suitable for paired non-normal data to check median differences.

3. Final Answer:

   Wilcoxon signed-rank test -> Option C

4. Quick Check:

   Non-normal paired data = Wilcoxon test Wilcoxon signed-rank test [OK]

Hint: Use Wilcoxon for paired non-normal data changes [OK]

Common Mistakes:

• Using paired t-test despite non-normality
• Choosing independent t-test for paired data
• Using chi-square for continuous data