Two-Sample Kolmogorov-Smirnov Test

The two-sample Kolmogorov-Smirnov test compares two independent samples by the largest vertical distance D between their empirical cumulative distribution functions.

두 표본 Kolmogorov-Smirnov 검정은 독립된 두 표본의 경험적 누적분포함수 사이의 최대 수직 거리 D 로 두 분포가 같은지 검정하는 방법입니다.

Do the response-time distributions of two independent groups differ in any way, not just in their means?

독립된 두 집단의 반응시간 분포가 평균뿐 아니라 어떤 식으로든 다른지 확인하고 싶어요.

Compute the empirical CDF of each group and take the maximum absolute difference D; its exact null distribution is used for small samples and the asymptotic Kolmogorov distribution for large ones. A small p indicates that the two distributions differ in location, spread or shape.

When to use Two-Sample Kolmogorov-Smirnov Test

• You want to detect any difference between two distributions, not only a shift in location.
• The outcome is continuous and the two samples are independent.
• You need a nonparametric check of whether two samples could come from the same population.

When to use something else

• You only care about a location shift; use the Mann-Whitney U test, which has more power for that.
• Differences are expected mainly in the tails; use the Anderson-Darling k-sample test instead.

Assumptions and requirements

• Two independent random samples.
• A continuous outcome; ties make the p-value conservative.

What the analysis reports

• D statistic with one-sided D+ and D- components
• Exact or asymptotic p-value with the method used
• Location of the maximum distance
• Group sizes, medians, means and SDs

How to report it

A two-sample Kolmogorov-Smirnov test indicated that the distributions of [group 1] (n = [value]) and [group 2] (n = [value]) differed, D = [value], p = [value].

Related methods

• Mann-Whitney U Test
• Kolmogorov-Smirnov Test
• Shift Function (Harrell-Davis Quantile Comparison)

Run Two-Sample Kolmogorov-Smirnov Test on Quorant