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Topic: Kolmogorov Smirnov test

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In the News (Mon 21 May 18) Kolmogorov-Smirnov Goodness-of-Fit Test   (Site not responding. Last check: 2007-09-19)
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).
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.
www.itl.nist.gov /div898/handbook/eda/section3/eda35g.htm   (859 words)

 SPRNG: Scalable Parallel Pseudo-Random Number Generator Library   (Site not responding. Last check: 2007-09-19)
Passing a test does not imply that the generator is producing a truly random sequence.
Unlike the preceding tests which modify sequential tests to test for correlations between streams, the tests mentioned below are inherently parallel and test for correlations between streams.
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)

 Cybermetrics. Issues Contents: Vol. 4 (2000): Paper 4. LOTKA: A program to fit a power law distribution to observed ...
This test is based on the maximum absolute deviation between the observed and the theoretical distribution functions.
One of the main problems being the fact that the data to which we want to apply the test are certainly not random data.
Testing (K-S) with these values yields a maximum absolute deviation of 0.135, which is far worse than the ML-estimate.
www.cindoc.csic.es /cybermetrics/articles/v4i1p4.html   (1524 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).
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.
SPSS prints the two-tailed significance level, testing the probability that the observed distribution is not significantly deviant from the expected distribution in either direction.
www2.chass.ncsu.edu /garson/pa765/kolmo.htm   (787 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.
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.
Kolmogorov-Smirnov goodness-of-fit test evaluated for level of significance alpha equal to 1 percent are summarized in table 70.
www.tfhrc.gov /pavement/ltpp/reports/03041/appc.htm   (580 words)

 Computer Generated Random Numbers
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.
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.
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)

 [No title]
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.
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).
www.statsoft.com /textbook/glosi.html   (3481 words)

 GraphPad Library: Normality tests   (Site not responding. Last check: 2007-09-19)
Kolmogorov-Smirnov test The KS test is more than just a normality 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.
Possible alternatives if your data violate normality test assumptions If your data are not Gaussian, one possibility is to switch to a nonparametric test.
www.graphpad.com /index.cfm?cmd=library.page&pageID=24&categoryID=4   (250 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.
This test can also be applied when the observations in a sample of data are ranks, that is, ordinal data rather than direct measurements.
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.
www.stats.gla.ac.uk /steps/glossary/nonparametric.html   (744 words)

 Statistics Glossary - Non-parametric Methods
In many applications, this test is used in place of the one sample t-test when the normality assumption is questionable.
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.
It is used to test the null hypothesis that all populations have identical distribution functions against the alternative hypothesis that at least two of the samples differ only with respect to location (median), if at all.
www.cas.lancs.ac.uk /glossary_v1.1/nonparam.html   (744 words)

 [No title]   (Site not responding. Last check: 2007-09-19)
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.
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.
jan.ucc.nau.edu /~wew/stats/week5.html   (351 words)

 SDL Delphi Component Suite - KolmogSmir1SampleTestStat   (Site not responding. Last check: 2007-09-19)
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.
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.
www.lohninger.com /helpcsuite/kolmogsmir1sampleteststat.htm   (90 words)

 IE321 Lab#1   (Site not responding. Last check: 2007-09-19)
Today, we will be testing the goodness of fit for the interarrival time data that we have been modeling.
If the test statistic is less than or equal to the critical value, then the data fits the theoretical distribution.
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)

Pearson's chi-square test and the likelihood-ratio test are two well established methods of dealing with this case.
The test presented is a minor variant of the one presented in the previous two references.
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)

 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)

 Kolmogorov-Smirnov Test   (Site not responding. Last check: 2007-09-19)
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)

 Kolmogorov-Smirnov Goodness of Fit Test   (Site not responding. Last check: 2007-09-19)
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.
Test the hypothesis that these data are values of a random sample from a normal distribution.
gateway.cis.ysu.edu /~jholcomb/math743/kolo.htm   (247 words)

 Andrey Kolmogorov - Wikipedia, the free encyclopedia
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.
The Legacy of Andrei Nikolaevich Kolmogorov Curriculum Vitae and Biography.
en.wikipedia.org /wiki/Andrey_Nikolaevich_Kolmogorov   (179 words)

 The Power of Categorical Goodness-Of-Fit Statistics
Chi-Square type test statistics to determine 'fit' for categorical data are still dominant in the goodness-of-fit arena.
The continued use of an asymptotic distribution to approximate the exact distribution of categorical goodness-of-fit test statistics is discouraged.
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.
www4.gu.edu.au:8080 /adt-root/public/adt-QGU20031006.143823   (445 words)

 What are the differences amongst the ranking methods for distribution fitting?
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.
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.
www.decisioneering.com /support/cbtips/cb_tips47.html   (252 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.
Given the critical value(s) and test statistic, identify the test as left, right, or two-tailed and write the decision (Reject the null hypothesis or Fail to reject the null hypothesis).
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)

 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)

 Tests for ordinal series online. Including Mann-Whitney, Wald-Wolfowitz, Wilcoxon, Kolmogorov Smirnov and test for ...
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.
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.
For example, males might be primarily present in both the higher and the lower ranks while females are particularly present in the middle ranks, in that case the average for the two groups might well be the same, however, the distribution by rank very different.
home.clara.net /sisa/ordhlp.htm   (1561 words)

 [No title]
Also identify whether the test is a left-tailed, right-tailed, or two-tailed test (based on the alternative hypothesis).
Identify the test as about one or two means, proportions, or standard deviations; write the original claim symbolically; write the null and alternative hypotheses; identify as left, right or two-tailed; give the critical value(s), test statistic, and p-value from statdisk; give the decision; give the conclusion.
Note: the assumption under the Kolmogorov Smirnov test is that the data has the distribution tested.
www.richland.edu /james/fall01/m113/m113-s07.html   (763 words)

 [No title]
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.
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.
www.cs.bc.edu /~signoril/mc606/input.ppt   (947 words)

 Kolmogorov-Smirnov 2-Sample Goodness of Fit Test   (Site not responding. Last check: 2007-09-19)
The one sample K-S test is based on the maximum distance between these two curves.
The two sample K-S test is a variation of this.
The word test in the command is optional.
www.itl.nist.gov /div898/software/dataplot/refman1/auxillar/ks2samp.htm   (457 words)

 Analyzing the Data
A sample is selected from an unknown population and its goodness of fit to a hypothetical model of the population must be tested.
Both the sample and and the hypothetical model are plotted together in cumulative form, each scaled so their cumulative sums are 1.0.
If the computed test statistic does not fall into the critical region then we cannot reject the null hypothesis.
www.cas.usf.edu /~cconnor/colima/Kolmogorov_Smirnov.htm   (143 words)

 NMath Stats User's Guide - 6.8 Two Sample Kolmogorov-Smirnov Test
Class TwoSampleKSTest performs a two-sample Kolmogorov-Smirnov test to compare the distributions of values in two data sets.
For each potential value x, the Kolmogorov-Smirnov test compares the proportion of values in the first sample less than x with the proportion of values in the second sample less than x.
Sample data can be passed to the constructor as vectors, numeric columns in a data frame, or arrays of doubles.
www.centerspace.net /doc/NMath/Stats/user/hypothesistestsa9.html   (177 words)

 No Title
This is what we call a 'Load Test' for pseudorandom number generators: as the sample size increases, spectacular breakdowns (i.e.
The rejection area of the KS test with a level of significance of 0.01 is approximated by
Further results of this kind for many linear and inversive congruential generators, a more detailed description of the 'Load Test' and an 'Ultimative Load Test' are given in the pLab-technical reports [6, 1].
random.mat.sbg.ac.at /tests/empirics/mtuple/mtuple.html   (441 words)

 KS-test Data Entry   (Site not responding. Last check: 2007-09-19)
Use the below form to enter your data for a Kolmogorov-Smirnov test.
For each dataset, enter your data into the given box separating each datum from its neighbor with tabs, commas, or spaces.
This KS-test form is designed to handle datasets with between 10 and 1024 items in each dataset.
bardeen.physics.csbsju.edu /stats/KS-test.n.plot_form.html   (133 words)

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