SciPy · Function

stats.kstest

Performs a one-sample or two-sample Kolmogorov–Smirnov test. It compares a sample with a continuous reference distribution or compares two independent continuous samples.

How it works

kstest compares one sample with a specified continuous distribution, or compares two independent samples when both inputs represent samples. It returns a result containing the KS statistic and p-value; the selected alternative determines the hypothesis direction, while method controls p-value calculation.

Syntax

scipy.stats.kstest(rvs, cdf, args=(), N=20, alternative='two-sided', method='auto', *, axis=0, nan_policy='propagate', keepdims=False)

Parameters

Name	Type	Description
`rvs`	`array_like, str, or callable`	Sample data, a distribution name, or a callable generating random variables, depending on the selected form.
`cdf`	`str, array_like, or callable`	Reference distribution name, callable CDF, or the second sample in the two-sample form.
`args`	`tuple or sequence, optional`	Distribution parameters used when `rvs` or `cdf` is a string.
`N`	`int, optional`	Sample size when `rvs` is a string or callable; default is 20.
`alternative`	`{‘two-sided’, ‘less’, ‘greater’}, optional`	Alternative hypothesis: `two-sided`, `less`, or `greater`; default is `two-sided`.
`method`	`{‘auto’, ‘exact’, ‘approx’, ‘asymp’}, optional`	Method used to calculate the p-value; default is `auto`.
`axis`	`int or None, optional`	Axis along which to perform the test; default is 0.
`nan_policy`	`{‘propagate’, ‘omit’, ‘raise’}, optional`	How to handle NaN values; default is `propagate`.
`keepdims`	`bool, optional`	Whether reduced axes are retained as singleton dimensions; default is False.

Returns

KstestResult containing statistic (the KS test statistic, D, D+, or D−) and pvalue (a one-tailed or two-tailed p-value).

Key points

Use it for either one-sample goodness-of-fit testing or two-sample distribution comparison.
In one-sample mode, provide observations and a named distribution or CDF representing the reference model.
Two-sample use requires independent samples and tests whether their continuous distributions agree.
The default checks for any difference; less and greater encode directional alternatives.
A string distribution argument refers to a distribution available in scipy.stats.
Pass distribution shape or location parameters through args when using string specifications.
The result includes a p-value whose sidedness follows the selected alternative.

Common mistakes

Do not apply the test directly to discrete distributions; the documented validity assumption is continuity.
An array input for a sample must be one-dimensional.
When supplying a callable as cdf, it must evaluate the hypothesized cumulative distribution function rather than generate observations.

Example: One-sample goodness-of-fit test

from scipy.stats import kstest

sample = [0.12, 0.31, 0.47, 0.66, 0.89]
result = kstest(sample, "uniform")
print(result.statistic, result.pvalue)

Tests whether the sample is consistent with a continuous uniform distribution.

When to use it

One-sample goodness of fit

Validate whether observed continuous measurements are consistent with a named SciPy distribution.

Two-sample comparison

Compare two independent continuous datasets for evidence of different underlying distributions.

Custom CDF validation

Test a custom continuous model by passing its CDF as a callable.

Interview questions

QWhat does kstest test?

The one-sample form compares a sample's underlying distribution with a specified distribution, while the two-sample form compares two independent samples. In both cases, the distributions must be continuous.

Follow-up: What does the null hypothesis assert? It asserts that the compared distributions are identical.

QHow does alternative affect the test?

alternative selects two-sided, less, or greater. The default is two-sided; one-sided alternatives compare the empirical CDF against the hypothesized CDF in the corresponding direction.

Follow-up: How would you choose a directional alternative? Use it only when the direction was specified before examining the data.

QWhat does the returned result contain?

The function returns a KstestResult with the KS statistic and p-value. The statistic is a KS distance, represented as D, D+, or D− depending on the test and alternative.

Follow-up: What does method control? It selects the calculation method used for the p-value, such as the exact, approximate, asymptotic, or automatic strategy documented for the installed SciPy version.

scipy.stats.ks_1samp
scipy.stats.ks_2samp
scipy.stats.kstest

Source: scipy.stats.kstest — SciPy v1.18.0 Manual. Checked 2026-10-15.