Kolmogorov-Smirnov test

The Kolmogorov Smirnov test Closely related to the visual approach employed in Fig. 42, the KS test evaluates the equality of two distributions. Under the assumption that a saturation parameter has no impact on stability, its distribution within the stable subset is identical (in a statistical sense) to its initial distribution. Deviations between the two distributions, such as those shown in Fig. 42, thus indicate a dependency between the parameter and dynamic stability. 

A basic assumption underlying r-tests and ANOVA (which are parametric tests) is that cost data are normally distributed. Given that the distribution of these data often violates this assumption, a number of analysts have begun using nonparametric tests, such as the Wilcoxon rank-sum test (a test of median costs) and the Kolmogorov-Smirnov test (a test for differences in cost distributions), which make no assumptions about the underlying distribution of costs. The principal problem with these nonparametric approaches is that statistical conclusions about the mean need not translate into statistical conclusions about the median (e.g., the means could differ yet the medians could be identical), nor do conclusions about the median necessarily translate into conclusions about the mean. Similar difficulties arise when - to avoid the problems of nonnormal distribution - one analyzes cost data that have been transformed to be more normal in their distribution (e.g., the log transformation of the square root of costs). The sample mean remains the estimator of choice for the analysis of cost data in economic evaluation. If one is concerned about nonnormal distribution, one should use statistical procedures that do not depend on the assumption of normal distribution of costs (e.g., nonparametric tests of means). 

The normality of the distribution of results is checked by an appropriate test, such as the Kolmogorov-Smirnov test, and outlier tests are performed on... 

Other interesting tests may be undertaken to decide whether the empirical distribution of the measurements obtained from samples follows a certain theoretical distribution, e.g. the normal distribution. In such cases it is quite common to perform the / test of goodness of fit or the KOLMOGOROV-SMIRNOV test. Both tests are based on the evaluation of the cumulative frequency of measured data and are described in detail in [MILLER and MILLER, 1993],... 

For each date, the chlorophyll a distribution and seawater viscosity data were significantly non-normally distributed (Kolmogorov-Smirnov test,... 

The chief non-parametric tests for comparing locations are the Mann-Whitney (7-test and the Kolmogorov-Smirnov test. The former assumes that the frequency distributions of the data sets are similar, whereas the latter makes no such assumption. In the Kolmogorov-Smirnov test, significant differences found with the test may be due to differences in location or shape of the distribution, or both. 

Three tests of shape differences that can be used to evaluate goodness-of-fit are the Kolmogorov-Smirnov test, the Cramer-von Mises test, and the Anderson-Darling Computer programs for aU three... 

Tsvetkov et al. (2001) have shown that surface density distribution of GRBs in their hosts is close to surface brightness distribution in spirals (Kolmogorov-Smirnov test gives the probability Pks = 68%) and to surface brightness of ellipticals (Pks = 40%). The authors did not find significant correlation of GRB distribution and distribution of OB associations (Pks = 4%), also there is no correlation between GRB and supernovae (SN) Ib/c distributions (Pks = 9%). 

The previous tests served the purpose of detecting differences between means or variances. The goodness of fit between an observed and a hypothetical distribution is done by two additional tests, the and the Kolmogorov-Smirnov tests. 

Table A.6 Kolmogorov-Smirnov test statistic d - a, n) to test for a normal distribution at different significance levels a.

Chi-.square. binomial test, runs test, one-sample Kolmogorov Smirnov test. Mann-Whitney U test. Moses test. Wald-Wolfowitz test. Kruskal Wallis te.st, Wilcoxon signed rank test. Friedman s test. Kendall s W test, Cochran s Q test... 

The value of this Kolmogorov-Smirnov test statistic, together with its P-value, can be obtained directly from Minitab in conjunction with a normal probability plot. 

Similar to the CSE method [20], Kolmogorov-Smirnov test (KS) was used to assess the activity of a fragment For this purpose, the activity distribution of compounds belonging to a fragment was compared with the activity distribution... 

Table 3 shows the results of Kolmogorov-Smirnov distances for different equities and states, and the difference in statistical proprieties (Skewness and Kurtosis) of simulated data from the estimated model with respect to those of the real dataset. Note that the Kolmogorov-Smirnov test always leads to the null hypothesis HO which means that the distribution of the simulated data is... 

Comparing Distribution Functions Kolmogorov-Smirnov Test... 

Listing 8.11. Code segments for Kolmogorov-Smirnov Test of two distributions. 

Basic Statistical Properties and Functions. 3 Distributions and More Distributions. 4 Analysis of Mean and Variance. 5 Comparing Distribution Functions - The Kolmogorov-Smirnov Test. 6 Monte Carlo Simulations and Confidence Limits. 7 Non-Gaussian Distributions and Reliability Modeling. 8 Summary... 

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