The Kolmogorov-Smirnov Test for Goodness of Fit
Abstract
The test is based on the maximum difference between an empirical and a hypothetical cumulative distribution. Percentage points are tabled, and a lower bound to the power function is charted. Confidence limits for a cumulative distribution are described. Examples are given. Indications that the test is superior to the chi-square test are cited.
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A Kolmogorov-Smirnov test rejected the normality assumption of PHQ-9 scores.
“A Kolmogorov-Smirnov test [42] rejected the normality assumption”
From Mobile Sensing and Support for People With Depression: A Pilot Trial in the Wild (2016) · cites this paper as [42]
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Martis, M. M., Zhou, R., Haseneyer, G., Schmutzer, T., Vrána, J., Kubaláková, M., König, S., Kugler, K., Scholz, U., Hackauf, B., et al. (2013) · The Plant Cell · doi:10.1105/tpc.113.114553 · Cited by 206 · see citing works
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- Authors
- Massey, F. J.
- Affiliations
- University of Oregon (US)
- Corresponding author
- Massey, Frank J.
- Venue
- Journal of the American Statistical Association
- Publisher
- Informa UK Limited
- Published
- 1951-03
- Volume
- 46
- Issue
- 253
- Pages
- 68-78
- ISSN
- 0162-1459 (ISSN-L)
- 1537-274X
- OpenAlex
- W4255375128
- Cited by
- 7,210
- References
- 12
- Citations by year
- 2026: 529 · 2025: 691 · 2024: 580 · 2023: 591 · 2022: 576 · 2021: 562 · 2020: 490 · 2019: 432 · 2018: 369 · 2017: 351 · 2016: 285 · 2015: 273 · 2014: 215 · 2013: 226 · 2012: 181
- FWCI
- 6.34
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of the American Statistical Association (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Distribution Estimation and Applications
- Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Applications
- Keywords
- Kolmogorov-Smirnov test, goodness of fit, empirical distribution function, cumulative distribution function, percentage points, power function, confidence limits
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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