Wilcoxon signed-rank test in SciPy - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the Wilcoxon signed-rank test used for?

It is a test to compare two related samples to see if their population median ranks differ. It helps check if there is a difference between paired data without assuming normal distribution.

beginner

What kind of data is suitable for the Wilcoxon signed-rank test?

Paired or matched samples where you want to compare differences, especially when data is not normally distributed or sample size is small.

beginner

Which Python library provides the Wilcoxon signed-rank test function?

The 'scipy.stats' module provides the function 'wilcoxon()' to perform the Wilcoxon signed-rank test.

intermediate

What does a low p-value from the Wilcoxon signed-rank test indicate?

It suggests that there is a significant difference between the paired samples, so we reject the idea that their median differences are zero.

intermediate

How do you interpret the test statistic returned by the Wilcoxon signed-rank test?

The test statistic is the sum of ranks of the differences with positive or negative signs. Smaller values indicate stronger evidence against the null hypothesis of no difference.

What type of test is the Wilcoxon signed-rank test?

A Test for correlation between variables

B Non-parametric test for paired samples

C Parametric test for independent samples

D Test for normality of data

The Wilcoxon signed-rank test is a non-parametric test used to compare two related or paired samples.

Which Python function runs the Wilcoxon signed-rank test?

A scipy.stats.ttest_rel()

B scipy.stats.kruskal()

C scipy.stats.mannwhitneyu()

D scipy.stats.wilcoxon()

The function 'wilcoxon()' in scipy.stats performs the Wilcoxon signed-rank test.

When should you use the Wilcoxon signed-rank test instead of a paired t-test?

A When data is not normally distributed

B When samples are independent

C When data is normally distributed

D When sample size is very large

The Wilcoxon signed-rank test is used when the paired data is not normally distributed, unlike the paired t-test which assumes normality.

What does a p-value less than 0.05 in the Wilcoxon test usually mean?

A No difference between samples

B Test is invalid

C Significant difference between samples

D Samples are independent

A p-value less than 0.05 typically means we reject the null hypothesis and conclude there is a significant difference between paired samples.

Which of these is NOT a requirement for the Wilcoxon signed-rank test?

A Samples must be independent

B Differences should be symmetrically distributed

C Data must be paired

D Data can be ordinal or continuous

Samples must be paired, not independent, for the Wilcoxon signed-rank test.

Explain the Wilcoxon signed-rank test and when you would use it.

Think about comparing before and after measurements without assuming normal data.

Describe how to perform the Wilcoxon signed-rank test using scipy and interpret its output.

Focus on the function name, inputs, and what the p-value tells you.

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