Kolmogorov Smirnov

The algorithm for estimating the LDC and LDM for teehniques of test analysis with visual indieation is suggested. It ineludes the steps to eheek the suffieieney of experimental material [1]. The hypothesis ehoiee about the type of frequeney distribution in unreliable reaetion (UR) region is based on the ealeulation of eriteria eomplex Kolmogorov-Smirnov eriterion,... 

Frequency domain performance has been analyzed with goodness-of-fit tests such as the Chi-square, Kolmogorov-Smirnov, and Wilcoxon Rank Sum tests. The studies by Young and Alward (14) and Hartigan et. al. (J 3) demonstrate the use of these tests for pesticide runoff and large-scale river basin modeling efforts, respectively, in conjunction with the paired-data tests. James and Burges ( 1 6 ) discuss the use of the above statistics and some additional tests in both the calibration and verification phases of model validation. They also discuss methods of data analysis for detection of errors this last topic needs additional research in order to consider uncertainties in the data which provide both the model input and the output to which model predictions are compared. 

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. 

FIGURE 6.11 Kolmogorov-Smirnov confidence limits (black) acconnting for both mea-snrement uncertainty and sampling uncertainty about the p-box (gray) from Figure 6.9. 

Consider use of Kolmogorov-Smirnov intervals to explicitly calculate uncertainty. 

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... 

Rassokhin, D. N., Agrafiotis, D. K. (2000) Kolmogorov-Smirnov statistic and its applications in library design. J Mol Graph Model 18(4-5), 370-384. 

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%). 

Additional characterisation tests are performed to examine the population of data. They do not lead to decisions on whether or not a parameters should be certified or a set of data should be excluded e.g. normality of distribution of means and individual data (Kolmogorov-Smirnov-Lilliefors), consistency between laboratories of variances (Bartlett), etc. Many other tests could be performed before calculating the certified value. No definitive rules are given in the various guides of ISO [1,7]. The basic principle should remain as follows ... 

Normality of the distribution of the data set of means (Kolmogorov-Smirnov-Lilliefors test)" YES YES YES YES... 

Variations in OC values in soil samples collected along the N-S and W-E transects at the Florida site are shown in Figure 4. Note that for both the transects, OC in soils from the 0-15 cm depth were more variable than in samples collected from the 15-30 cm depth. Variograms ( 14 ) calculated using these data indicated that for the 0-15 cm depth, OC values in soil samples collected within a separation distance (i.e., lag) of 15 m would be spatially correlated. On the other hand, OC values for the 15-30 cm depth are spatially independent. OC data for both depth increments could be fitted to a normal frequency distribution the normality was confirmed by the Kolmogorov- Smirnov D-statistic ( 23 ). The coefficient of variation (CV) in OC data for both depths was less than 20%. 

On the other hand, a number of chemometric procedures are based on the assumption of normality of features. Accordingly, features should be assessed for normality. The well-known Kolmogorov-Smirnov, Shapiro-Wdks and Lilliefors tests are often used (Gonzalez,... 

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. 

Kolmogorov-Smirnov s Test for Small-Sample Collectives In... 

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