Kolmogorov-Smirnov test in SciPy - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the Kolmogorov-Smirnov test used for?

It is a statistical test used to compare a sample distribution with a reference probability distribution, or to compare two sample distributions, to check if they differ significantly.

beginner

What does the KS test statistic represent?

The KS test statistic is the maximum distance between the cumulative distribution functions (CDFs) of the two distributions being compared.

beginner

In scipy, which function is used to perform the Kolmogorov-Smirnov test for one sample against a distribution?

The function is scipy.stats.kstest(). It compares a sample against a given distribution.

beginner

What does a small p-value in the KS test indicate?

A small p-value means there is strong evidence that the sample distribution is different from the reference distribution.

beginner

How do you interpret the KS test result when comparing two samples?

If the p-value is large, it suggests the two samples come from the same distribution; if small, they likely come from different distributions.

What does the Kolmogorov-Smirnov test compare?

A Two distributions or a sample against a distribution

B Means of two samples

C Variances of two samples

D Correlation between two variables

The KS test compares the cumulative distributions of two samples or a sample and a reference distribution.

Which scipy function performs the KS test for one sample?

A scipy.stats.ttest_1samp

B scipy.stats.chisquare

C scipy.stats.kstest

D scipy.stats.ks_2samp

scipy.stats.kstest compares one sample against a reference distribution.

What does a KS test statistic measure?

A Difference in means

B Maximum difference between CDFs

C Sum of squared errors

D Correlation coefficient

The KS statistic is the largest vertical distance between two cumulative distribution functions.

If the KS test p-value is 0.01, what does it mean?

A Distributions are likely different

B Distributions are likely the same

C Test is inconclusive

D Sample size is too small

A small p-value (like 0.01) suggests strong evidence against the null hypothesis that distributions are the same.

Which test compares two samples directly using KS test?

A scipy.stats.mannwhitneyu

B scipy.stats.kstest

C scipy.stats.ttest_ind

D scipy.stats.ks_2samp

scipy.stats.ks_2samp compares two independent samples using the KS test.

Explain how the Kolmogorov-Smirnov test works and what it measures.

Think about how you compare two shapes of data distributions.

Describe how to use scipy to perform a KS test on a sample against a normal distribution.

Remember the function name and what arguments it needs.

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