Mann-Whitney U test in SciPy

Introduction

The Mann-Whitney U test helps us check if two groups are different when we can't assume normal data. It compares their values to see if one tends to be bigger than the other.

Comparing test scores of two different classes when scores are not normally distributed.

Checking if two medicines have different effects based on patient recovery times that are skewed.

Comparing customer satisfaction ratings between two stores when ratings are ordinal.

Testing if two machines produce different quality levels when data is not symmetric.

Syntax

SciPy

from scipy.stats import mannwhitneyu

result = mannwhitneyu(x, y, alternative='two-sided')

x and y are the two groups of data you want to compare.

The alternative parameter can be 'two-sided', 'less', or 'greater' to specify the test direction.

Examples

Basic test comparing two small lists with a two-sided hypothesis.

SciPy

from scipy.stats import mannwhitneyu

x = [1, 3, 5]
y = [2, 4, 6]
result = mannwhitneyu(x, y, alternative='two-sided')
print(result)

Tests if values in x tend to be less than those in y.

SciPy

result = mannwhitneyu(x, y, alternative='less')
print(result.pvalue)

Tests if values in x tend to be greater than those in y.

SciPy

result = mannwhitneyu(x, y, alternative='greater')
print(result.statistic)

Sample Program

This code compares exam scores from two classes to see if their score distributions differ without assuming normality.

SciPy

from scipy.stats import mannwhitneyu

# Two groups of exam scores
class_a = [85, 78, 90, 88, 76]
class_b = [80, 82, 84, 79, 75]

# Perform Mann-Whitney U test
result = mannwhitneyu(class_a, class_b, alternative='two-sided')

print(f"U statistic: {result.statistic}")
print(f"p-value: {result.pvalue:.4f}")

Important Notes

The test works well when data is not normal or when sample sizes are small.

A small p-value (usually below 0.05) means the groups are likely different.

The test compares ranks, not the actual values, so it is less sensitive to outliers.

Summary

The Mann-Whitney U test compares two groups without assuming normal data.

It uses ranks to check if one group tends to have higher or lower values.

Use it when data is skewed or ordinal, or when sample sizes are small.

Practice

1. What is the main purpose of the Mann-Whitney U test in data analysis?

easy

A. To test if a single sample mean equals a known value

B. To compare two independent groups without assuming normal distribution

C. To measure the correlation between two variables

D. To analyze the variance among multiple groups

Solution

1. Step 1: Understand the test purpose

   The Mann-Whitney U test is a non-parametric test used to compare two independent groups.

2. Step 2: Identify the key feature

   It does not assume the data follows a normal distribution, unlike t-tests.

3. Final Answer:

   To compare two independent groups without assuming normal distribution -> Option B

4. Quick Check:

   Non-parametric comparison = C [OK]

Hint: Remember: Mann-Whitney compares two groups without normality [OK]

Common Mistakes:

• Confusing it with correlation tests
• Assuming it compares means only
• Using it for more than two groups

2. Which of the following is the correct way to import the Mann-Whitney U test function from scipy?

easy

A. import scipy.mannwhitneyu as mw

B. import mannwhitneyu from scipy.stats

C. from scipy import mann_whitney_u_test

D. from scipy.stats import mannwhitneyu

Solution

1. Step 1: Recall scipy.stats module functions

   The Mann-Whitney U test function is named mannwhitneyu and is inside scipy.stats.

2. Step 2: Check correct import syntax

   The correct Python import syntax is from scipy.stats import mannwhitneyu.

3. Final Answer:

   from scipy.stats import mannwhitneyu -> Option D

4. Quick Check:

   Correct import syntax = B [OK]

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

Common Mistakes:

• Using wrong module or function name
• Incorrect import syntax
• Trying to import with 'import ... as' incorrectly

3. What will be the output of the following code snippet?

from scipy.stats import mannwhitneyu
x = [1, 3, 5]
y = [2, 4, 6]
stat, p = mannwhitneyu(x, y)
print(round(stat, 2), round(p, 3))

medium

A. 3.0 0.5

B. 4.5 0.25

C. 6.0 0.05

D. 0.0 1.0

Solution

1. Step 1: Understand the data and test

   Lists x and y have values [1,3,5] and [2,4,6]. Mann-Whitney U test compares ranks between these two groups.

2. Step 2: Calculate Mann-Whitney U statistic and p-value

   Using scipy, the U statistic is 3.0 and p-value is 0.5 (two-sided test by default).

3. Final Answer:

   3.0 0.5 -> Option A

4. Quick Check:

   U=3.0, p=0.5 from scipy output [OK]

Hint: Run code to get exact U and p values quickly [OK]

Common Mistakes:

• Mixing up U statistic with p-value
• Rounding incorrectly
• Assuming p-value is always small

4. Identify the error in this Mann-Whitney U test code and select the fix:

from scipy.stats import mannwhitneyu
x = [1, 2, 3]
y = [4, 5, 6]
stat, p = mannwhitneyu(x, y, alternative='greater')
print(stat, p)

medium

A. Replace mannwhitneyu with mann_whitney_u

B. Change 'alternative' to 'two-sided'

C. No error; code runs correctly

D. Use 'alternative="greater"' with capital G

Solution

1. Step 1: Check function parameters

   The mannwhitneyu function accepts an alternative parameter with values 'two-sided', 'less', or 'greater'.

2. Step 2: Verify code correctness

   Using alternative='greater' is valid and the function call is correct.

3. Final Answer:

   No error; code runs correctly -> Option C

4. Quick Check:

   Correct parameter usage = D [OK]

Hint: Check scipy docs for valid 'alternative' values [OK]

Common Mistakes:

• Using wrong alternative string case
• Trying to use non-existent function names
• Assuming default alternative is 'greater'

5. You have two small samples with skewed data: a = [2, 3, 5, 7] and b = [1, 4, 6, 8]. You want to test if sample a tends to have higher values than b. Which scipy Mann-Whitney U test call is correct?

hard

A. mannwhitneyu(a, b, alternative='greater')

B. mannwhitneyu(a, b, alternative='less')

C. mannwhitneyu(a, b, alternative='two-sided')

D. mannwhitneyu(b, a, alternative='greater')

Solution

1. Step 1: Define the hypothesis direction

   We want to test if a tends to have higher values than b, so the alternative hypothesis is 'greater'.

2. Step 2: Choose correct function call

   The call should be mannwhitneyu(a, b, alternative='greater') to test if a is stochastically greater than b.

3. Final Answer:

   mannwhitneyu(a, b, alternative='greater') -> Option A

4. Quick Check:

   Test if a > b = A [OK]

Hint: Use 'alternative="greater"' when testing if first sample is larger [OK]

Common Mistakes:

• Swapping sample order and alternative incorrectly
• Using 'less' when testing for greater
• Choosing 'two-sided' when direction matters