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.

Practice

1. What is the main purpose of the scipy.stats.ks_2samp function in data analysis?

easy

A. To generate random numbers from a normal distribution

B. To calculate the mean of a dataset

C. To perform linear regression between two variables

D. To compare two samples and check if they come from the same distribution

Solution

1. Step 1: Understand the function purpose

   ks_2samp is designed to compare two independent samples.

2. Step 2: Identify what it tests

   It tests if the two samples come from the same continuous distribution.

3. Final Answer:

   To compare two samples and check if they come from the same distribution -> Option D

4. Quick Check:

   Kolmogorov-Smirnov test compares distributions [OK]

Hint: Remember KS test compares distributions, not means or regressions [OK]

Common Mistakes:

• Confusing KS test with mean calculation
• Thinking KS test performs regression
• Assuming KS test generates random data

2. Which of the following is the correct way to import the Kolmogorov-Smirnov two-sample test from scipy?

easy

A. import ks_2samp from scipy.stats

B. import scipy.ks_2samp

C. from scipy.stats import ks_2samp

D. from scipy import ks_2samp

Solution

1. Step 1: Recall correct import syntax

   Functions inside scipy.stats are imported using from scipy.stats import function_name.

2. Step 2: Match the function name

   The function for KS two-sample test is ks_2samp, so the correct import is from scipy.stats import ks_2samp.

3. Final Answer:

   from scipy.stats import ks_2samp -> Option C

4. Quick Check:

   Correct import uses 'from scipy.stats import' [OK]

Hint: Import functions from scipy.stats using 'from scipy.stats import' [OK]

Common Mistakes:

• Using 'import scipy.ks_2samp' which is invalid
• Trying 'from scipy import ks_2samp' which misses stats
• Using wrong import order like 'import ks_2samp from scipy.stats'

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

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

medium

A. 0.999

B. 0.500

C. 0.317

D. 0.050

Solution

1. Step 1: Understand the samples and test

   Samples are close but not identical; KS test compares their distributions.

2. Step 2: Run the KS test and check p-value

   Running the code shows p-value approximately 0.999, indicating no strong evidence to reject similarity.

3. Final Answer:

   0.999 -> Option A

4. Quick Check:

   Close samples give very high p-value ~0.999 [OK]

Hint: Close samples usually yield high p-values, not moderate or low [OK]

Common Mistakes:

• Assuming p-value is always very small for different samples
• Confusing p-value with test statistic
• Rounding errors leading to wrong choice

4. Identify the error in this code snippet that attempts to perform a KS test:

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

medium

A. Incorrect import statement for ks_2samp

B. Missing second sample argument in ks_2samp call

C. Using print instead of return to show result

D. Samples contain integers instead of floats

Solution

1. Step 1: Check function call parameters

   ks_2samp requires two sample arguments, but only one is given.

2. Step 2: Identify the error cause

   Missing second sample causes a TypeError because the function expects two inputs.

3. Final Answer:

   Missing second sample argument in ks_2samp call -> Option B

4. Quick Check:

   ks_2samp needs two samples [OK]

Hint: ks_2samp always needs two sample inputs [OK]

Common Mistakes:

• Forgetting the second sample argument
• Thinking print causes error
• Assuming integer samples cause error

5. You have two datasets representing customer wait times from two stores. You want to check if their wait times differ significantly. Which approach using scipy is best?

hard

A. Use ks_2samp to compare the two samples' distributions

B. Calculate the mean wait time of each and compare with subtraction

C. Use linear regression to predict wait times from store ID

D. Use ttest_ind to compare the two samples assuming normality

Solution

1. Step 1: Understand the data and goal

   We want to check if two samples (wait times) differ in distribution, not just means.

2. Step 2: Choose appropriate test

   ks_2samp compares full distributions without assuming normality, ideal for wait times.

3. Step 3: Evaluate other options

   Mean subtraction ignores distribution shape; regression is unrelated; ttest_ind assumes normality which may not hold.

4. Final Answer:

   Use ks_2samp to compare the two samples' distributions -> Option A

5. Quick Check:

   KS test compares distributions best for this case [OK]

Hint: KS test compares distributions without normality assumptions [OK]

Common Mistakes:

• Using mean difference which ignores distribution shape
• Applying t-test without checking normality
• Using regression for distribution comparison