Mann-Whitney U test in SciPy - Mini Project: Build & Apply

Mann-Whitney U Test with SciPy

📖 Scenario: You are a data analyst working with two groups of patients. You want to check if the two groups have different distributions of recovery times without assuming the data follows a normal distribution.

🎯 Goal: Perform the Mann-Whitney U test using SciPy to compare recovery times between two patient groups and interpret the test result.

📋 What You'll Learn

Create two lists of recovery times for two patient groups

Set a significance level variable

Use SciPy's mannwhitneyu function to perform the test

Print the U statistic and p-value

💡 Why This Matters

🌍 Real World

The Mann-Whitney U test is used in medical research, social sciences, and other fields to compare two groups when data is not normally distributed.

💼 Career

Data analysts and scientists use this test to make decisions about differences between groups without relying on assumptions of normality.

1

Create recovery time data for two patient groups

Create two lists called group1 and group2 with these exact recovery times: group1 = [5, 7, 8, 6, 9] and group2 = [10, 12, 9, 11, 13].

SciPy

# 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 test.

SciPy

group1 = [5, 7, 8, 6, 9]
group2 = [10, 12, 9, 11, 13]
# Your code here

Hint

Use a simple assignment to create the variable alpha.

3

Perform the Mann-Whitney U test

Import mannwhitneyu from scipy.stats and use it to perform the test on group1 and group2. Store the results in variables u_statistic and p_value.

SciPy

group1 = [5, 7, 8, 6, 9]
group2 = [10, 12, 9, 11, 13]
alpha = 0.05
# Your code here

Hint

Use alternative='two-sided' to test for difference in either direction.

4

Print the test results

Print the values of u_statistic and p_value using two separate print statements.

SciPy

from scipy.stats import mannwhitneyu

group1 = [5, 7, 8, 6, 9]
group2 = [10, 12, 9, 11, 13]
alpha = 0.05

u_statistic, p_value = mannwhitneyu(group1, group2, alternative='two-sided')
# Your code here

Hint

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

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