Kolmogorov-Smirnov Test
The Kolmogorov-Smirnov test is a nonparametric test that compares a sample's empirical cumulative distribution with a reference distribution, using the largest vertical distance between the two cumulative distribution functions.
콜모고로프-스미르노프 검정은 표본의 경험적 누적분포를 기준 분포와 비교하여 두 누적분포함수 사이의 최대 수직 거리로 적합 여부를 판단하는 비모수 검정입니다.
How do I test whether my data follow a normal or other specified distribution?
내 데이터가 정규분포나 특정 분포를 따르는지 어떻게 검정하나요?
The one-sample Kolmogorov-Smirnov test checks whether a continuous variable is consistent with a fully specified reference distribution, such as a normal distribution with a given mean and standard deviation. When the distribution's parameters are estimated from the same sample, the Lilliefors correction should be used, and for normality checks in small samples the Shapiro-Wilk test usually has greater statistical power.
When to use Kolmogorov-Smirnov Test
- Checking whether a continuous outcome fits a specified theoretical distribution
- Screening a variable for departures from normality before a parametric test
- Comparing the whole shape of a sample distribution, not just its mean, with a reference
When to use something else
- Testing normality in a small sample: use the Shapiro-Wilk test, which has more power
- Discrete or categorical data: use the chi-square goodness-of-fit test
Assumptions and requirements
- Continuous variable
- Independent observations
- Reference distribution fully specified in advance, or the Lilliefors correction when parameters are estimated
What the analysis reports
- D statistic (maximum distance between cumulative distributions)
- p-value
- Empirical versus reference cumulative distribution plot
- Q-Q plot for visual checking
How to report it
A one-sample Kolmogorov-Smirnov test indicated that [variable] did not deviate significantly from a normal distribution, D([n]) = [value], p = [value].
Related methods
- Shapiro-Wilk Test
- Anderson-Darling Test
- Chi-Square Goodness-of-Fit Test
Run Kolmogorov-Smirnov Test on Quorant
- Data you need
- a table (CSV or Excel) with an outcome variable
- Price
- 150 credits for one analysis up to 10,000 rows (complexity level 1); larger or wider data costs more. Optional methodologist review: 900 credits.
- Checking
- Python results are cross-checked against R reference outputs in every deployment
- Before you pay
- A free pre-analysis diagnosis checks your data and gives an exact quote; nothing is deducted until you approve it.