Kolmogorov-Smirnov test

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Topic: Kolmogorov-Smirnov test

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	Andrey Kolmogorov - Wikipedia, the free encyclopedia
		The Legacy of Andrei Nikolaevich Kolmogorov Curriculum Vitae and Biography.
		Andrey Nikolaevich Kolmogorov (Андре́й Никола́евич Колмого́ров) (kahl-mah-GAW-raff) (April 25, 1903 in Tambov - October 20, 1987 in Moscow) was a Russian mathematician who made major advances in the fields of probability theory and topology.
		Selected works of A.N. Kolmogorov / edited by V.M. Tikhomirov; translated from the Russian by V.M. Volosov.
	en.wikipedia.org /wiki/Andrey_Nikolaevich_Kolmogorov (179 words)

	1.3.5.16. Kolmogorov-Smirnov Goodness-of-Fit Test
		The Kolmogorov-Smirnov test accepts the normality hypothesis for the case of normal data and rejects it for the double exponential, t, and lognormal data with the exception of the double exponential data being significant at the 0.01 significance level.
		The Kolmogorov-Smirnov test (Chakravart, Laha, and Roy, 1967) is used to decide if a sample comes from a population with a specific distribution.
		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).
	www.itl.nist.gov /div898/handbook/eda/section3/eda35g.htm (859 words)

	SPRNG: Scalable Parallel Pseudo-Random Number Generator Library
		Finally, KS percent is called to determine the percentile of the statistic from the Kolmogorov-Smirnov test.
		We take the chisquare statistics for all the blocks and use the Kolmogorov-Smirnov test to verify that they are distributed according to the chisquare distribution.
		We have provided utilities for others to implement their own tests in C if they are along the pattern of the tests in which we interleave streams and subject them to tests of sequential random number streams.
	archive.ncsa.uiuc.edu /Science/CMP/RNG/www/test-suite.html (2795 words)

	Quantitative Methods in Public Administration, One-Sample K-S Goodness-of-Fit Test
		The Kolmogorov-Smirnov D test is a goodness-of-fit test which tests whether a given distribution is not significantly different from one hypothesized (ex., on the basis of the assumption of a normal distribution).
		From the SPSS menu, select Statistics, Nonparametric Tests, 1-Sample K-S. In the "One-Sample Kolmogorov-Smirnov Test" dialog box which appears, select the desired test distribution (ex., Normal) and select the desired criterion variable(s) from the variable picklist.
		Whereas the chi-square test of goodness-of-fit tests whether in general the observed distribution is not significantly different from the hypothesized one, the K-S test tests whether this is so even for the most deviant values of the criterion variable.
	www2.chass.ncsu.edu /garson/pa765/kolmo.htm (787 words)

	SDL Delphi Component Suite - KolmogSmir1SampleTestStat
		Note that the test statistic is calculated by finding the maximum absolute difference between the cumulative frequency distribution of the samples and the predefined distribution.
		A frequently encountered problem in statistics is to test whether a given number of samples belong to a predefined probability distribution.
		The parameter SampleSize specifies the number samples used for the test, the parameter alpha specifies the level of uncertainty.
	www.lohninger.com /helpcsuite/kolmogsmir1sampleteststat.htm (90 words)

	Evaluation and Analysis of LTPP Pavement Layer Thickness Data FHWA-RD-03-041
		The Kolmogorov-Smirnov test determines whether, for specified level of significance α, the proposed distribution is an acceptable representation of the field data.
		Kolmogorov-Smirnov goodness-of-fit test evaluated for level of significance alpha equal to 1 percent are summarized in table 70.
		A total of 1034 pavement layers were tested to determine how well variability in layer thickness data along the LTPP section could be described using normal distribution.
	www.tfhrc.gov /pavement/ltpp/reports/03041/appc.htm (580 words)

	Cybermetrics. Issues Contents: Vol. 4 (2000): Paper 4. LOTKA: A program to fit a power law distribution to observed frequency data
		This test is based on the maximum absolute deviation between the observed and the theoretical distribution functions.
		Testing (K-S) with these values yields a maximum absolute deviation of 0.135, which is far worse than the ML-estimate.
		One of the main problems being the fact that the data to which we want to apply the test are certainly not random data.
	www.cindoc.csic.es /cybermetrics/articles/v4i1p4.html (1524 words)

	glosi.html
		The Kolmogorov-Smirnov one-sample test for normality is based on the maximum difference between the sample cumulative distribution and the hypothesized cumulative distribution.
		In that case, the test for normality involves a complex conditional hypothesis ("how likely is it to obtain a D statistic of this magnitude or greater, contingent upon the mean and standard deviation computed from the data"), and the Lilliefors probabilities should be interpreted (Lilliefors, 1967).
		Thus, the type of achievement orientation and test difficulty interact in their effect on effort; specifically, this is an example of a two-way interaction between achievement orientation and test difficulty.
	www.statsoft.com /textbook/glosi.html (3481 words)

	GraphPad Library: Normality tests
		Kolmogorov-Smirnov test The KS test is more than just a normality test.
		Possible alternatives if your data violate normality test assumptions If your data are not Gaussian, one possibility is to switch to a nonparametric test.
		Principles of normality tests This article (part of the Engineering Statistics Handbook) explains the basic idea of normality testing, and links to pages describing two particular tests.
	www.graphpad.com /index.cfm?cmd=library.page&pageID=24&categoryID=4 (250 words)

	Kolmogorov-Smirnov Goodness of Fit Test
		The Kolmogorov-Smirnov goodness of fit test is based on the closeness of the empirical and hypothesized distribution functions.
		The Kolmogorov-Smirnov statistic is used to test some simulations from various distributions.
		The distribution of the Kolmogorov-Smirnov statistics is illustrated empirically.
	gateway.cis.ysu.edu /~jholcomb/math743/kolo.htm (247 words)

	Kolmogorov-Smirnov Test
		test is the choice of number and size of the intervals.
		test is designed for discrete distributions, so in continuous case the
		In this sense, KS test makes better use of each sample and is more precise than the
	choices.cs.uiuc.edu /~akapadia/project2/node14.html (117 words)

	IE321 Lab#1
		If the test statistic is less than or equal to the critical value, then the data fits the theoretical distribution.
		Today, we will be testing the goodness of fit for the interarrival time data that we have been modeling.
		If the test statistic is greater than the critical value, then the data does not fit.
	homepages.cae.wisc.edu /~ie321/Lab3_wk4.html (422 words)

	R: Bootstrap Kolmogorov-Smirnov
		The bootstrap p-value of the Kolmogorov-Smirnov test for the hypothesis that the probability densities for both the treated and control groups are the same.
		This function executes a bootstrap version of the univariate Kolmogorov-Smirnov test which provides correct coverage even when the distributions being compared are not entirely continuous.
		Ties are allowed with this test unlike the traditional Kolmogorov-Smirnov test.
	jsekhon.fas.harvard.edu /matching/ks.boot.html (213 words)

	What are the differences amongst the ranking methods for distribution fitting?
		The Kolmogorov-Smirnov test measures the largest vertical distance between the cumulative relative frequency plot of the data and the cumulative distribution function of the distribution under consideration.
		The Chi-Square test is the oldest of the goodness-of-fit tests.
		This test breaks down the distribution into areas of equal probability and compares the data points in each area to the number of expected data points.
	www.decisioneering.com /support/cbtips/cb_tips47.html (252 words)

	NMath Stats User's Guide - 6.7 One Sample Kolmogorov-Smirnov Test
		Class OneSampleKSTest performs a Kolmogorov-Smirnov test of the distribution of one sample.
		For each potential value x, the Kolmogorov-Smirnov test compares the proportion of values less than x with the expected number predicted by the specified CDF.
		The null hypothesis is that the given sample data follow the specified distribution.
	www.centerspace.net /doc/NMath/Stats/user/hypothesistestsa8.html (276 words)

	Math 113: Study Guide - Chapters 7 - 8
		A Kolmogorov Smirnov test was performed with SPSS with several different distributions (normal, uniform, poisson, and exponential) and the resulting p-values are shown.
		Note: the assumption under the Kolmogorov Smirnov test is that the data has the distribution tested.
		An unknown (to you) hypothesis test is performed and the type of test, critical value, and test statistic are given.
	www.richland.edu /james/fall02/m113/m113-s07.html (874 words)

	U.B.C. BIOLOGY 300
		Tests for lower levels of measurement may be applied to higher levels of measurement but these lower level tests generally have less power.
		All parametric tests require normality at the population level in some measure being tested.
		When pooled variances are used in parametric tests, sample variances being pooled must be roughly equal.
	www.zoology.ubc.ca /~mcintyre/bio300/choose.htm (132 words)

	Tests for ordinal series online. Including Mann-Whitney, Wald-Wolfowitz, Wilcoxon, Kolmogorov Smirnov and test for randomness.
		The test can be used to test for trend or seasonality in the data, however, the test is not as powerful as the Durbin-Watson test or some of the techniques used in time series analysis.
		The ordinal tests assess how probable it is that the two groups come from a single ordering and that differences observed are caused by chance fluctuation, or that the two groups come from two different orderings.
		Mann-Whitney U Test or Wilcoxon Two Sample Test studies if the sums of the rankings for two groups are different from an expected number.
	home.clara.net /sisa/ordhlp.htm (1561 words)

	week5.html
		The One-Sample Kolmogorov-Smirnov Test procedure compares the observed cumulative distribution function for a variable with a specified theoretical distribution, which may be normal, uniform, Poisson, or exponential.
		Non-parametric tests are used to test significance in nominal and ordinal variables.
		This goodness-of-fit test compares the observed and expected frequencies in each category to test either that all categories contain the same proportion of values or that each category contains a user-specified proportion of values.
	jan.ucc.nau.edu /~wew/stats/week5.html (351 words)

	The Power of Categorical Goodness-Of-Fit Statistics
		The new test statistic, called the Combined Kolmogorov-Smirnov, is relatively more powerful than Pearson's Chi-Square and the nominal Kolmogorov-Smirnov test statistic for some null and alternative distributions.
		The new and established categorical goodness-of-fit test statistics are demonstrated in the analysis of categorical data with brief applications as diverse as familiarity of defence programs, the number of recruits produced by the Merlin bird, a demographic problem, and DNA profiling of genotypes.
		The continued use of an asymptotic distribution to approximate the exact distribution of categorical goodness-of-fit test statistics is discouraged.
	www4.gu.edu.au:8080 /adt-root/public/adt-QGU20031006.143823 (445 words)

	One-sample Kolmogorov-Smirnov Test
		The Kolmogorov-Smirnov goodness of fit test is used to test whether the empirical distribution of a set of observations is consistent with a random sample drawn from a specific theoretical distribution.
		The Kolmogorov-Smirnov goodness of fit test is generally more powerful than the chi-squared goodness of fit test for continuous variables.
		In this case, the parameters are estimated from the data separately from the test and then entered into the dialog.
	fas.sfu.ca /doc/help/guihelp/__hhelp/one_sample_kolmogorov_smirnov_goodness_of_fit_test.htm (241 words)

	Statistics Glossary - nonparametric methods
		It is used to test the null hypothesis that two populations have identical distribution functions against the alternative hypothesis that the two distribution functions differ only with respect to location (median), if at all.
		It is most often used to test the hypothesis about a population median, and often involves the use of matched pairs, for example, before and after data, in which case it tests for a median difference of zero.
		This test can also be applied when the observations in a sample of data are ranks, that is, ordinal data rather than direct measurements.
	www.stats.gla.ac.uk /steps/glossary/nonparametric.html (744 words)

	Computer Generated Random Numbers
		The spectral test calculates the distances between these parallel planes for a linear congruential random number generator given the modulus M and the multiplier A of the generator.
		To test a sequence of supposedly random numbers, our null hypothesis H0 is that each outcome of the chance experiment is equally likely, and that each trial of the chance experiment is independent of all previous trials.
		Each test used an expected value of 10 balls per bin, and each ball required DIM random numbers per ball, where DIM is the dimension of the chi-square test being performed.
	world.std.com /~franl/crypto/random-numbers.html (10155 words)

	Goodness-of-Fit
		The test presented is a minor variant of the one presented in the previous two references.
		Pearson's chi-square test and the likelihood-ratio test are two well established methods of dealing with this case.
		If these assumptions are significantly violated, the tests may not be valid, and the tests won't necessarily tell you when they are not valid.
	www-cdf.fnal.gov /physics/statistics/recommendations/goodnessoffit.html (934 words)

	Analyzing the Data
		Table 1: Critical values of the Kolmogorov-Smirnov Test Statistic
		We then look for the greatest difference between the two; this is the Kolmogorov-Smirnov statistic, K-S. Table 1 gives critical values for the K-S statistic.
		A sample is selected from an unknown population and its goodness of fit to a hypothetical model of the population must be tested.
	www.cas.usf.edu /~cconnor/colima/Kolmogorov_Smirnov.htm (143 words)

	Prism offers three different normality tests. Which should I choose?
		The Kolmogorov-Smirnov test compares the cumulative distribution of the data with the expected cumulative Gaussian distribution, and bases its P value simply on the largest discrepancy.
		The D'Agostino-Pearson normality test first computes the skewness (how assymetrical is the distribution) and the kurtosis (how far away from a Gaussian shape).
		The one used by Prism is the "omnibus K2" test.
	www.graphpad.com /FAQ/viewfaq.cfm?faq=959 (236 words)

	input.ppt
		Kolmogorov-Smirnov Test The Kolmogorov-Smirnov (K-S) test measures the closeness between a candidate distribution function, and the distribution function, computed from the data.
		Kolmogorov-Smirnov Test In some situations it is not possible to collect data on the random variables of interest.
		The test statistic is where k = Number of intervals Nj = Number of observations in the interval [aj-1, aj) npj = Expected number of observations that would fall in the jth interval if we were sampling from the fitted distribution.
	www.cs.bc.edu /~signoril/mc606/input.ppt (947 words)

	XLStat - Non parametric tests on two independent samples
		Kolmogorov-Smirnov's test: use the Kolmogorov-Smirnov's test to determine if the populations from which the samples were taken have different cumulative distribution functions.
		Note: the Mann-Whitney statistic is related to the Wilcoxon statistic, in that the (unsigned) Wilcoxon test is equivalent to the Mann-Whitney test.
		Mann-Whitney's test: use the Mann-Whitney's test to determine if the samples come from a single population or from two different populations.
	www.kovcomp.co.uk /xlstat/tools/t35.html (118 words)

	Testing random Number Sequences
		For nominal or "binned" measurements, a chi-square test is common.
		In this section we will test three random number generators with uniform outputs [0,1].
		Chi-square test: the best known goodness of fit statistic.
	perso.enstimac.fr /~latailla/cecile/guide/node171.html (275 words)

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