Kolmogorov-Smirnov test in SciPy

Introduction

The Kolmogorov-Smirnov test helps us check if two sets of numbers come from the same pattern or if one set matches a known pattern.

To see if your sample data fits a normal distribution before using other tests.

To compare two groups of data and check if they behave similarly.

To test if a new batch of products matches the quality of an old batch.

To check if website visitors' behavior changed after a redesign.

To verify if a random number generator produces numbers like a uniform distribution.

Syntax

SciPy

from scipy.stats import ks_2samp

result = ks_2samp(data1, data2)

# or for one sample vs a distribution
from scipy.stats import kstest

result = kstest(data, 'distribution_name')

ks_2samp compares two data samples.

kstest compares one sample to a known distribution like 'norm' for normal.

Examples

Compare two small samples to see if they come from the same distribution.

SciPy

from scipy.stats import ks_2samp

sample1 = [1, 2, 3, 4, 5]
sample2 = [2, 3, 4, 5, 6]
result = ks_2samp(sample1, sample2)
print(result)

Check if a sample fits a normal distribution.

SciPy

from scipy.stats import kstest

import numpy as np
sample = np.random.normal(0, 1, 100)
result = kstest(sample, 'norm')
print(result)

Sample Program

This code compares exam scores from two classes to see if their score distributions differ.

SciPy

from scipy.stats import ks_2samp

# Two samples of exam scores
scores_classA = [88, 92, 85, 91, 87, 90, 89]
scores_classB = [78, 82, 80, 79, 81, 77, 83]

# Perform Kolmogorov-Smirnov test
result = ks_2samp(scores_classA, scores_classB)

print(f"KS statistic: {result.statistic:.3f}")
print(f"p-value: {result.pvalue:.3f}")

Important Notes

A small p-value (usually less than 0.05) means the two samples likely come from different distributions.

The KS test is sensitive to differences in both the center and shape of distributions.

Samples should be independent and continuous for best results.

Summary

The Kolmogorov-Smirnov test compares two samples or a sample to a known distribution.

It helps check if data follows a pattern or if two groups behave similarly.

Look at the p-value to decide if differences are meaningful.

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