Kolmogorov-Smirnov Test Method

{
  "id": "MLC-T-ENV-015193",
  "term": "Kolmogorov-Smirnov Test Method",
  "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that is, if location, scale, and shape parameters are estimated from the data, the critical region of the K-S test is no longer valid.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. (NIST/SEMATECH 2005a)\n\n2. For a single sample of data, the Kolmogorov-Smirnov test is used to test whether or not the sample of data is consistent with a specified distribution function. When there are two samples of data, it is used to test whether or not these two samples may reasonably be assumed to come from the same distribution. The Kolmogorov-Smirnov test does not require the assumption that the population is normally distributed. (STEPS 1997)",
  "abbreviation": "K-S Test Method",
  "references": [
    "EPA Thesaurus of Terms Used in Microbial Risk Assessment: 5.9 Modeling, Statistics, and Math Terms at http://water.epa.gov/scitech/swguidance/standards/criteria/health/microbial/T59.cfm"
  ],
  "url": "https://mlchart.com/terminology/environment/kolmogorov-smirnov-test-method/"
}