Mann-Whitney U test in SciPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Mann-Whitney U test on two small samples

What is the output of the Mann-Whitney U test for the following two samples using scipy.stats.mannwhitneyu with default parameters?

SciPy

from scipy.stats import mannwhitneyu
sample1 = [1, 3, 5]
sample2 = [2, 4, 6]
result = mannwhitneyu(sample1, sample2)
print((result.statistic, round(result.pvalue, 4)))

A (4.0, 0.5)

B (3.0, 1.0)

C (4.0, 1.0)

D (3.0, 0.5)

💡 Hint

Remember that the Mann-Whitney U statistic counts how many times values in one sample exceed values in the other.

The Mann-Whitney U statistic for these samples is 3.0, and the two-sided p-value is 0.5. The default alternative hypothesis is 'two-sided'.

❓ data_output

intermediate

Number of items in the output of mannwhitneyu

How many values are returned by scipy.stats.mannwhitneyu when called on two samples?

SciPy

from scipy.stats import mannwhitneyu
sample1 = [10, 20, 30]
sample2 = [15, 25, 35]
result = mannwhitneyu(sample1, sample2)
print(len(result))

A 2

B 4

C 3

D 1

💡 Hint

Check the type of the result and what attributes it has.

The mannwhitneyu function returns an object with two main values: the U statistic and the p-value.

🔧 Debug

advanced

Identify the error in this Mann-Whitney U test code

What error does the following code raise when run?

SciPy

from scipy.stats import mannwhitneyu
sample1 = [1, 2, 3]
sample2 = [4, 5]
result = mannwhitneyu(sample1, sample2, alternative='greater')
print(result.statistic, result.pvalue)

A ValueError: alternative must be 'two-sided', 'less' or 'greater'

B No error, prints the statistic and p-value

C TypeError: mannwhitneyu() got an unexpected keyword argument 'alternative'

D IndexError: list index out of range

💡 Hint

Check the scipy.stats.mannwhitneyu documentation for valid parameters.

The 'alternative' parameter is valid and 'greater' is accepted. The code runs without error and prints the statistic and p-value.

🧠 Conceptual

advanced

Interpretation of Mann-Whitney U test p-value

If the Mann-Whitney U test returns a p-value of 0.03 for two independent samples, what does this mean?

A The samples have exactly the same median values.

B There is no evidence to reject the null hypothesis that the two samples come from the same distribution.

C There is strong evidence that the two samples come from populations with different distributions.

D The test is invalid because p-value must be greater than 0.05.

💡 Hint

Recall that a p-value below 0.05 usually means rejecting the null hypothesis.

A p-value of 0.03 means the observed difference is unlikely under the null hypothesis, so we reject it and conclude the distributions differ.

🚀 Application

expert

Choosing the correct Mann-Whitney U test alternative hypothesis

You want to test if sample A tends to have larger values than sample B. Which 'alternative' parameter should you use in scipy.stats.mannwhitneyu?

A 'greater'

B 'less'

C 'two-sided'

D 'equal'

💡 Hint

Think about the direction of the hypothesis you want to test.

The 'greater' alternative tests if values in sample A tend to be larger than those in sample B.