Kolmogorov-Smirnov test in SciPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of KS test on two identical samples

What is the output of the Kolmogorov-Smirnov test when comparing two identical samples using scipy.stats.ks_2samp?

SciPy

from scipy.stats import ks_2samp
sample = [1, 2, 3, 4, 5]
result = ks_2samp(sample, sample)
print((round(result.statistic, 2), round(result.pvalue, 2)))

A (0.5, 0.5)

B (1.0, 0.0)

C (0.0, 1.0)

D (0.2, 0.8)

💡 Hint

Think about what happens when two samples are exactly the same.

When two samples are identical, the maximum difference between their cumulative distributions is zero, so the KS statistic is 0. The p-value is 1, indicating no evidence to reject the null hypothesis that samples come from the same distribution.

❓ data_output

intermediate

Number of items in KS test result object

How many attributes does the result object returned by scipy.stats.ks_2samp contain?

SciPy

from scipy.stats import ks_2samp
sample1 = [1, 2, 3]
sample2 = [4, 5, 6]
result = ks_2samp(sample1, sample2)
print(len(result._fields))

A 1

B 3

C 4

D 2

💡 Hint

Check the attributes of the namedtuple returned by ks_2samp.

The ks_2samp function returns a namedtuple with two fields: statistic and pvalue.

🧠 Conceptual

advanced

Interpretation of KS test p-value

If the Kolmogorov-Smirnov test returns a p-value of 0.03 when comparing two samples, what does this mean?

A The two samples definitely come from the same distribution.

B There is strong evidence that the two samples come from different distributions at the 5% significance level.

C The test is inconclusive because p-value is less than 0.05.

D The samples are identical.

💡 Hint

Recall what a p-value less than 0.05 usually indicates in hypothesis testing.

A p-value of 0.03 means we reject the null hypothesis at the 5% level, suggesting the samples likely come from different distributions.

🔧 Debug

advanced

Identify error in KS test usage

What error will this code raise? from scipy.stats import ks_2samp sample1 = [1, 2, 3] sample2 = 'abc' result = ks_2samp(sample1, sample2) print(result)

A TypeError: unsupported operand type(s) for -: 'int' and 'str'

B TypeError: object of type 'str' has no len()

C ValueError: sample sizes must be equal

D No error, prints KS test result

💡 Hint

Check what happens when comparing numeric and string data in ks_2samp.

The ks_2samp function tries to compute differences between numeric values. Passing a string sample causes a TypeError when subtracting int and str.

🚀 Application

expert

Using KS test to compare sample to normal distribution

Which code correctly performs a Kolmogorov-Smirnov test to check if a sample comes from a normal distribution with mean 0 and std 1?

A

from scipy.stats import kstest
import numpy as np
sample = np.random.normal(0, 1, 100)
result = kstest(sample, 'norm', args=(0, 1))
print(round(result.pvalue, 3))

B

from scipy.stats import ks_2samp
import numpy as np
sample = np.random.normal(0, 1, 100)
result = ks_2samp(sample, 'norm')
print(round(result.pvalue, 3))

C

from scipy.stats import kstest
import numpy as np
sample = np.random.normal(0, 1, 100)
result = kstest(sample, 'norm')
print(round(result.pvalue, 3))

D

from scipy.stats import ks_2samp
import numpy as np
sample = np.random.normal(0, 1, 100)
result = ks_2samp(sample, np.random.normal(0, 1, 100))
print(round(result.pvalue, 3))

💡 Hint

Use kstest with distribution name and parameters to test against a theoretical distribution.

The kstest function tests a sample against a given distribution. Passing 'norm' with args=(0,1) tests against standard normal. ks_2samp compares two samples, not sample vs distribution.