Kolmogorov-Smirnov Criterion Research Articles

A substantial psychometric analysis of the scales of the Minnesota Multiphasic Personality Inventory: F. B. Berezin’s version, the MMIL

The MMPI is a test questionnaire that is extremely popular among not only domestic but also foreign experts. The classic version of the MMPI questionnaire was offered by S. Hathaway and J. McKinley in 1940. Since then reworked and reduced versions of the questionnaire have been repeatedly offered. In 1989 the questionnaire was considerably redesigned (the restandardization project began in 1982) and was published under the name MMPI-2 (J. Butcher et al., 1989).Adaptation of the questionnaire in our country began in the 1960s. The first MMIL version consisted of 384 statements by Berezin & Miroshnikov in 1967. Berezin and his colleagues developed an original interpretation of the MMPI scales and carried out a careful standardization and adaptation, taking into account the specifics of sociocultural conditions, the possibilities of applying the test to mentally healthy people, and also the use of the reduced version of the test. As a result, the MMIL was created (Berezin, Miroshnikov, & Rozhanec, 1976, 1994). The MMIL was used in this research.Today there is wide circulation of other domestic versions of the questionnaire: the Standardized Method for the Multivariate Study of Personality (SMIL) (Sobchik, 2007), the Standardized Clinical Personal Questionnaire (SKLO) (M. Bekhterev Psychoneurological Institute in St. Petersburg), and Mini-Mult, which consists of 71 statements selected on the basis of factorial analysis, created by Zaytsev and his colleagues (Zaytsev,1981).Since the standardization and adaptation of the MMIL there have been significant changes in the political, economic, and spiritual spheres of the Russianspeaking culture; these alterations have caused extensive changes in the personal, axiological, semantic, motivational, and behavioral spheres of the Russian people. Therefore, the relevance of the present research is explained by the necessity of reassessing the psychometric indicators of the MMPI to reflect precisely the actual semantic structures of people surveyed in specific sociocultural conditions. The question of how test points are structured is also important as features of this structure reflect the psychological reality that the test is expected to measure. Attempts to apply factor and cluster analyses of MMIL points have been undertaken previously. From our point of view, these methods look most suitable for modeling the psychological reality measured by the MMPI. In particular, one of the most convincing studies was carried out by Shmelev in 2000 (Shmelev, 2002) on a sample of 766 people (students of Moscow colleges and universities). So we were curious to find out what our results in 2009 would be. One of our objectives was to compare the results of the above-mentioned study with those obtained almost 10 years later.Experiment 1. Psychometric analysis of the MMPIIt was necessary to carry out a psychometric analysis of the questionnaire in order to check the reliability, coherence, and internal and external validity of the technique. For that reason we examined the following psychometric indicators of the MMPI test: medians of root-mean-square deviations on each of the test scales and on female and male samples separately, indicators on the one-sample KolmogorovSmirnov criterion, correlations between answers to questions and the total points on a scale, and Cronbach's alpha coefficient values.Methodology1. Creation of linear norms for the test. Medians and root-mean-square deviations were calculated for each of the test scales, for female and male samples separately. Medians and root-mean-square deviations obtained in 1977 for each of the test scales for female and male samples by Berezin, were compared with our 2009 results.2. Check on normality and the assessment of the distribution of points. A check of the sample and the distribution of test points were estimated visually according to the charts of distribution and analytically considering the results of the one-sample Kolmogorov-Smirnov criterion. …

STOCK MARKET FLUCTUATIONS SIMULATION WITHIN LOWLY VOLATILE AND HIGHLY VOLATILE PERIODS

The simulation of stock price fluctuations is analyzed. The statistical criteria application allows drawing the conclusion on the investigated models’ validity. Alongside with well-known Kolmogorov-Smirnov and Anderson-Darling criteria, comparatively new Christoffersen and Berkowitz criteria are used to assess interval predictions. Berkowitz criterion is particularly effective when used to assess extreme price leaps within highly volatile periods, since it gives good results also for a small number of observations. It is shown that the customarily used time-series models with normal distribution and with Student distribution are applicable exclusively during relatively stable periods. Under the unstable conditions at the financial markets, models by means of which it is possible to describe a high probability of great price leaps are required. The time-series model with the heavy tailed distribution is studied. The recommendations on the portfolio management under the crisis time are provided on the basis of the performed calculations.

General nonparametric ROC curve comparison

Although the equality among two or more ROC (receiver operating characteristic) curves is usually contrasted from the respective AUCs (area under the ROC curve), two different ROC curves can share the same AUC and, in order to compare the ROC curves equality, most general criteria must be considered. In this paper, the authors deal with the general ROC curve comparison problem on paired design. They extend the tests for the classical cumulative distribution functions (CDF) comparison to the ROC curves context. To approximate the statistic distribution, two different resampling plans are considered; the usual one based on permutations and a new bootstrap procedure which does not require the exchangeability assumption. As usual, from Monte Carlo simulations, the performance of the proposed methodology is studied for two traditional tests; one based on the Kolmogorov–Smirnov criteria and the other one on the L2-measure. The observed results suggest that the proposed bootstrap provides a good statistic distribution approximation for medium sample size. Therefore the studied methodology allows us to compare the equality of ROC curves by defining a criteria according to the needs of the problem.

Significant Differences in Skin Irritation by Common Suture Materials Assessed by a Comparative Computerized Objective Method

Erythema can be described only through subjective evaluation, except when it is quantified by digital image analysis software. Using such software, the authors performed comparisons of the erythema produced after skin closure of clean surgical wounds. Five suture materials were compared with respect to the local skin irritation that was caused. Different quantities of erythema are produced by suture material after the skin closure of clean surgical wounds. The authors present an objective method of measuring how unreactive a suture material is in comparison with another when applied to the skin. The suture materials polydioxanone, polypropylene blue, polyamide 6, metallic clips, and polyglactin were compared in the present study. Digital photographs of 100 patients were compared by means of software, evaluating red color superiority (mean value of red color) in the region surrounding the wound. The least to most irritation caused to the skin by different suture materials was established for paired data. The Kolmogorov-Smirnov criterion and the Wilcoxon signed rank test were used. Polydioxanone was found to have the best performance, followed in order by polyglactin, polyamide, polypropylene, and metallic clips. Immediately after suture removal, differences between the effects of suture materials were statistically significant on postoperative day 10. Absorbable sutures can be used in skin closure of clean surgical wounds and can produce less erythematous reaction than nonabsorbable ones. Digital image analysis is a reliable method of quantitative evaluation of skin erythema resulting after skin closure of surgical wounds.

Nonparametric algorithms of pattern recognition in the problem of testing a statistical hypothesis on identity of two distribution laws of random variables

The possibility of using nonparametric algorithms of pattern recognition for testing hypotheses on distributions of random variables is discussed. Results of computational experiments are compared with the Kolmogorov-Smirnov criterion.

Estimating the parameters of stochastic differential equations using a criterion function

Estimation of parameters in the drift and diffusion terms of stochastic differential equations involves simulation and generally requires substantial data sets. We examine a method that can be applied when available time series are limited to less than 20 observations per realisation. We compare and contrast parameter estimation for linear and nonlinear first-order stochastic differential equations using two criterion functions: one based on a Chi-square statistic. put forward by Hurn and Lindsay (1997), and one based on the Kolmogorov-Smirnov statistic. The estimates generated reflect the true parameter values well for all models. examined, especially when using the Kolmogorov-smirnov criterion function.

A combined nonparametric approach to feature selection and binary decision tree design

An efficient procedure which integrates feature selection and binary decision tree construction is presented. The nonparametric approach is based on the Kolmogorov-Smirnov criterion which yields an optimal classification decision at each node. By combining the feature selection with the design of the classifier, only the most informative features are retained for classification.

The Smirnov distribution

Adequacy of the Smirnov approximation to P (D mn ≧c/mn), of the exact distribution of the two sample Kolmogorov-Smirnov criterion,D mn ,m<=n is examined. The main finding is that accuracy depends as much on the sample sizes,m andn, as on the ratio, ρ=m/n. The Smirnov approximation is good whenn is an integer multiple ofm, especiallyn=m, 2m; poor otherwise. This contrasts with the Smirnov approximation to P (D mn >c/mn), where this ordering is reversed, the cases forn=m, 2m being poor. The merit of continuity correction, of order ofn −1 in theD mn scale, is demonstrated for the Smirnov approximation, .1≦ρ, as well as for the Kolmogorov approximation, ρ<.1. As an argument for the optimum choice of ρ, the casen=m+1 is shown to have much to recommend it over the casen=m. Finally the usefulness of theχ 2 distribution with 2 degress of freedom is illustrated as an approximation to the Smirnov distribution.

On the Exact and Approximate Sampling Distribution of the Two Sample Kolmogorov-Smirnov Criterion Dmn,m≤n

Abstract The size of errors of the Smirnov approximation to the exact null distribution of the two sample Kolmogorov-Smirnov criterion Dmn, m≤n is investigated. It is shown that a sample size n of 100 is necessary before the overestimating effect of the Smirnov distribution becomes negligible. Several improvements over the Smirnov approximation are considered. With continuity correction of order of , the Smirnov approximation accomplishes for n = 50 about what it does for n = 100 without continuity correction. For n ≥ 25, m/n≥.10, a competitor superior to the Smirnov approximation and having an approximately normal distribution is shown to exist through a logarithmic transformation of Dmn. For n≥50, m/n≤.10, the Kolmogorov one sample results are shown to give a better approximation than the competitor. Numerical results are included to show that the normal approximation is on the average as good as or somewhat better than the Smirnov approximation with continuity correction.