Kolmogorov-Smirnov test

{
  "id": "MLC-T-ENV-015192",
  "term": "Kolmogorov-Smirnov test",
  "field": "Environment",
  "definition": "1. The Kolmogorov-Smirnov (K-S) test is used to decide if a sample comes from a population with a specific distribution. An attractive feature of this test is that the distribution of the K-S test statistic itself does not depend on the underlying cumulative distribution function being tested. Another advantage is that it is an exact test (the chi-square goodness-of-fit test depends on an adequate sample size for the approximations to be valid). Despite these advantages, the K-S test has several important limitations: (1) it only applies to continuous distributions, (2) it tends to be more sensitive near the center of the distribution than at the tails, and (3) perhaps the most serious limitation is that the distribution must be fully specified; that is, if location, scale, and shape parameters are estimated from the data, the critical region of the K-S test is no longer valid. It typically must be determined by simulation. Due to limitations 2 and 3 above, many analysts prefer to use the Anderson-Darling goodness-of-fit test.\n\n2. The Kolmogorov-Smirnov (K-S) test is used to decide if a sample comes from a population with a specific distribution. An attractive feature of this test is that the distribution of the K-S test statistic itself does not depend on the underlying cumulative distribution function being tested. Another advantage is that it is an exact test (the chi-square goodness-of-fit test depends on an adequate sample size for the approximations to be valid). Despite these advantages, the K-S test has several important limitations: (1) it only applies to continuous distributions, (2) it tends to be more sensitive near the center of the distribution than at the tails, and (3) perhaps the most serious limitation is that the distribution must be fully specified; that is, if location, scale, and shape parameters are estimated from the data, the critical region of the K-S test is no longer valid. It typically must be determined by simulation. Due to limitations 2 and 3 above, many analysts prefer to use the Anderson-Darling goodness-of-fit test. (NIST/SEMATECH 2005a)",
  "abbreviation": "K-S test",
  "subject": "Health and safety",
  "references": [
    "NIST/SEMATECH 2005a",
    "Thesaurus of Terms Used in Microbial Risk Assessment"
  ],
  "url": "https://mlchart.com/terminology/environment/kolmogorov-smirnov-test/"
}