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.