The Kolmogorov-Smirnov test is used to test whether or not or not a sample comes from a certain distribution.
To perform a Kolmogorov-Smirnov test in Python we can use the scipy.stats.kstest() for a one-sample test or scipy.stats.ks_2samp() for a two-sample test.
This tutorial shows an example of how to use each function in practice.
Example 1: One Sample Kolmogorov-Smirnov Test
Suppose we have the following sample data:
from numpy.random import seed from numpy.random import poisson #set seed (e.g. make this example reproducible) seed(0) #generate dataset of 100 values that follow a Poisson distribution with mean=5 data = poisson(5, 100)
The following code shows how to perform a Kolmogorov-Smirnov test on this sample of 100 data values to determine if it came from a normal distribution:
from scipy.stats import kstest #perform Kolmogorov-Smirnov test kstest(data, 'norm') KstestResult(statistic=0.9072498680518208, pvalue=1.0908062873170218e-103)
From the output we can see that the test statistic is 0.9072 and the corresponding p-value is 1.0908e-103. Since the p-value is less than .05, we reject the null hypothesis. We have sufficient evidence to say that the sample data does not come from a normal distribution.
This result also shouldn’t be surprising since we generated the sample data using the poisson() function, which generates random values that follow a Poisson distribution.
Example 2: Two Sample Kolmogorov-Smirnov Test
Suppose we have the following two sample datasets:
from numpy.random import seed from numpy.random import randn from numpy.random import lognormal #set seed (e.g. make this example reproducible) seed(0) #generate two datasets data1 = randn(100) data2 = lognormal(3, 1, 100)
The following code shows how to perform a Kolmogorov-Smirnov test on these two samples to determine if they came from the same distribution:
from scipy.stats import ks_2samp #perform Kolmogorov-Smirnov test ks_2samp(data1, data2) KstestResult(statistic=0.99, pvalue=4.417521386399011e-57)
From the output we can see that the test statistic is 0.99 and the corresponding p-value is 4.4175e-57. Since the p-value is less than .05, we reject the null hypothesis. We have sufficient evidence to say that the two sample datasets do not come from the same distribution.
This result also shouldn’t be surprising since we generated values for the first sample using the standard normal distribution and values for the second sample using the lognormal distribution.
Additional Resources
How to Perform a Shapiro-Wilk Test in Python
How to Perform an Anderson-Darling Test in Python