Wilcoxon signed-rank test in SciPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Wilcoxon test on paired samples

What is the output of the following code using scipy's Wilcoxon signed-rank test on paired samples?

SciPy

from scipy.stats import wilcoxon

sample1 = [20, 22, 19, 24, 30]
sample2 = [21, 20, 20, 25, 29]

stat, p = wilcoxon(sample1, sample2)
print(round(stat, 2), round(p, 3))

A 7.5 1.000

B 3.0 0.438

C 2.0 0.688

D 0.0 0.063

💡 Hint

Remember Wilcoxon test compares paired differences and returns a test statistic and p-value.

The Wilcoxon signed-rank test compares paired samples. The test statistic here is 7.5 and the p-value is 1.000, indicating no strong evidence to reject the null hypothesis.

❓ data_output

intermediate

Number of zero differences excluded in Wilcoxon test

Given two paired samples, how many zero differences are excluded by the Wilcoxon signed-rank test in the following data?

SciPy

from scipy.stats import wilcoxon

x = [5, 7, 8, 6, 9]
y = [5, 6, 8, 7, 9]

stat, p = wilcoxon(x, y, zero_method='wilcox')
print(stat)

A 3

B 0

C 1

D 2

💡 Hint

Check how many pairs have zero difference between x and y.

There are three pairs with zero difference: (5,5), (8,8), (9,9). With zero_method='wilcox', the Wilcoxon signed-rank test excludes all zero differences from ranking and reduces the sample size accordingly.

🔧 Debug

advanced

Identify the error in Wilcoxon test usage

What error will this code raise when running the Wilcoxon signed-rank test?

SciPy

from scipy.stats import wilcoxon

sample1 = [1, 2, 3]
sample2 = [1, 2]

stat, p = wilcoxon(sample1, sample2)
print(stat, p)

A No error, outputs test statistic and p-value

B TypeError: wilcoxon() missing 1 required positional argument

C IndexError: list index out of range

D ValueError: The samples must have the same length

💡 Hint

Check if the input arrays have the same length.

Wilcoxon test requires paired samples of equal length. Here sample1 has length 3 and sample2 length 2, so it raises a ValueError about sample length mismatch.

🚀 Application

advanced

Choosing correct zero_method for Wilcoxon test

You have paired data with some zero differences. Which zero_method option in scipy.stats.wilcoxon excludes zero differences from ranking but keeps the sample size unchanged?

A 'exclude'

B 'wilcox'

C 'pratt'

D 'zsplit'

💡 Hint

Check scipy documentation for zero_method options.

'pratt' method includes zero differences in the sample size but excludes them from ranking, unlike 'wilcox' which excludes zeros and reduces sample size.

🧠 Conceptual

expert

Interpretation of Wilcoxon signed-rank test p-value

If the Wilcoxon signed-rank test returns a p-value of 0.02 for paired samples, what does this imply about the null hypothesis at a 5% significance level?

A There is no evidence to reject the null hypothesis; the samples are identical.

B There is strong evidence to reject the null hypothesis; the median difference is not zero.

C The test is inconclusive; more data is needed.

D The null hypothesis is accepted; the median difference is zero.

💡 Hint

Recall what a p-value less than significance level means.

A p-value of 0.02 is less than 0.05, so we reject the null hypothesis that the median difference is zero, indicating a significant difference.