Statnote 34 : the Kolmogorov-Smirnov (KS) test

The Kolmogorov-Smirnov (KS) test is a non-parametric test which can be used in two different circumstances. First, it can be used as an alternative to chi-square (?2) as a ‘goodness-of-fit’ test to compare whether a given ‘observed’ sample of observations conforms to an ‘expected’ distribution of results (KS, one-sample test). An example of the use of the one-sample test to determine whether a sample of observations was normally distributed was described previously. Second, it can be used as an alternative to the Mann-Whitney test to compare two independent samples of observations (KS, two-sample test). Hence, this statnote describes the use of the KS test with reference to two scenarios: (1) to compare the observed frequency (Fo) of soil samples containing cysts of the protozoan Naegleria collected each month for a year with an expected equal frequency (Fe) across months (one-sample test), and (2) to compare the abundance of bacteria on cloths and sponges sampled in a domestic kitchen environment (two-sample test).

Estadística. Problemas resuetos. Contrastes de Bondad de Ajuste para variables continuas, Kolmogorov-Smirnov

Ejercicio resuelto paso a paso sobre el contraste de bondad de ajuste a una distribución normal mediante el método de Kolmogorov-Smirnov.

Exact Nonparametric Two-Sample Homogeneity Tests for Possibly Discrete Distributions.

In this paper, we study several tests for the equality of two unknown distributions. Two are based on empirical distribution functions, three others on nonparametric probability density estimates, and the last ones on differences between sample moments. We suggest controlling the size of such tests (under nonparametric assumptions) by using permutational versions of the tests jointly with the method of Monte Carlo tests properly adjusted to deal with discrete distributions. We also propose a combined test procedure, whose level is again perfectly controlled through the Monte Carlo test technique and has better power properties than the individual tests that are combined. Finally, in a simulation experiment, we show that the technique suggested provides perfect control of test size and that the new tests proposed can yield sizeable power improvements.

Influencia de las asignaturas gráficas sobre el desarrollo de la visión espacial en los alumnos de ETS : estudio monográfico en la ETS de Ingenieros de Caminos, Canales y Puertos de Madrid.

Pretende validar la actividad docente del profesorado mediante la evaluación de las capacidades especiales del alumnado antes y después de la influencia ejercida, a lo largo de un curso, por las labores docentes desarrolladas en la asignatura de dibujo técnico. Los datos se toman durante tres cursos consecutivos, 89-90, 90-91 y 91-92, de 535 estudiantes (398 chicos y 137 chicas) de la asignatura de Dibujo Técnico. Se utiliza los paquetes estadísticos SPSS y BMDP y el test de Kolmogorov-Smirnov. Se aplica a los estudiantes del primer curso el subtest Dat-sr de la batería Dat en el principio y final de curso. Los estadísticos utilizados son: análisis de varianza, distribución de frecuencias, regresión linial. Existe una mejora significativa en la capacidad espacial con el aprendizaje de la signatura. Se observan diferencias en cuanto a la variable sexo. No se encuentran diferencias en las mejoras de la capacidad espacial entre diferentes cursos. Existe una relación directa entre la capacidad espacial, medida por el procedimiento utilizado en el trabajo, y las notas finales obtenidas en clase.

Broiler walking ability and toe asymmetry under harsh rearing conditions

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Determinação de vazões extremas para diversos períodos de retorno para o Rio Paraguai utilizando métodos estatísticos

No presente trabalho foram analisadas as distribuições de probabilidade teórica Normal, Log-Normal, Exponencial, Gama e Weibull, para estimar as vazões máximas e mínimas anuais para o rio Paraguai, utilizando dados de uma estação fluviométrica localizado na cidade de Cáceres-MT. Os testes de Kolmogorov-Smirnov e Qui-Quadrado foram utilizados para verificar a aderência das probabilidades estimadas às freqüências observadas. A série utilizada compreende vazões máximas e mínimas anuais dos anos de 1966 a 2003, excluindo- se dados com falhas. Verificou-se que o melhor ajuste dos valores anuais de vazão máximas e mínimas são referentes a distribuição Gama e Weibull, respectivamente, conforme demonstrado pelo teste de Kolmogorov-Smirnov. Palavras-chave: Previsão de Vazão, teste de aderência.

Stima della fecondità del lotto in una specie ittica a deposizione parziale (Engraulis encrasicolus): due aree a confronto, il Mar Tirreno e lo Stretto di Sicilia.

L'importanza dell'acciuga europea (Engraulis encrasicolus) come risorsa ittica, sia a livello economico che ecologico, nel Mar Mediterraneo, ha portato alla necessità di monitorare la biomassa deponente di questa specie per cercare di dare un limite al suo sovrasfruttamento (rappresentando il 22% delle catture nazionali). Lo studio effettuato riguarda le stime di fecondità dell'acciuga europea tramite l'applicazione di un metodo di analisi d'immagine, Whole Mount, su campioni di gonadi di adulti maturi e pronti alla deposizione. Il campionamento degli esemplari è avvenuto durante due campagne oceanografiche, organizzate dall'U.O.S di Capo Granitola dell'Istituto per l'Ambiente Marino Costiero del CNR, che hanno coperto l'area dello Stretto di Sicilia e del Mar Tirreno, durante i mesi estivi che rappresentano il picco di deposizione della specie. Nel presente lavoro sono stati analizzati in totale 76 ovari di acciuga, provenienti da entrambe le aree di campionamento e che presentassero ovociti maturi e risultassero, quindi, in una fase di deposizione nota come "deposizione imminente". Per entrambe le aree di studio è stata stimata una relazione lunghezza-peso con andamento esponenziale. I test statistici non parametrici di Kolmogorov-Smirnov e di Mann-Whitney hanno permesso di stimare se vi fossero differenze tra la fecondità, l'indice gonadosomatico (IGS) e il fattore di condizione (CF) nelle due aree, Stretto di Sicilia e piattaforma settentrionale siciliana. I valori di CF sono risultati significativamente differenti tra le due aree se valutati con il test di Kolmogorov-Smirnov, tuttavia tale differenza non è stata confermata dal test di Mann-Whitney. L'IGS e la fecondità, invece, sono risultati significativamente diversi nelle due aree per entrambi i test. Si può ipotizzare che valori di fecondità differenti nelle due aree, nonostante in entrambi i casi il campionamento sia avvenuto durante il picco di riproduzione della specie, possono essere dovuti alla variabilità dei fattori abiotici, quali temperature e nutrienti, differenti nello Stretto di Sicilia e nell'area lungo le coste settentrionali siciliane. Temperatura e nutrienti possono essere differenti, poiché vi è un diverso movimento delle masse d'acqua causato da correnti distinte nelle due aree. Conoscere la variabilità dei parametri riproduttivi di una specie di rilevanza commerciale così alta, come l'acciuga, rappresenta uno strumento fondamentale per scegliere le misure di gestione sostenibile degli stock più appropriate per aree differenti.

Integration of Truncated Distributions in Exponential Family with Simulation Models of Logistics and Supply Chain Management

Truncated distributions of the exponential family have great influence in the simulation models. This paper discusses the truncated Weibull distribution specifically. The truncation of the distribution is achieved by the Maximum Likelihood Estimation method or combined with the expectation and variance expressions. After the fitting of distribution, the goodness-of-fit tests (the Chi-Square test and the Kolmogorov-Smirnov test) are executed to rule out the rejected hypotheses. Finally the distributions are integrated in various simulation models, e. g. shipment consolidation model, to compare the influence of truncated and original versions of Weibull distribution on the model.

STATISTICAL TEST FOR GENOTYPE AND ENVIRONMENT CONTRIBUTION IN THE GENOTYPES x ENVIRONMENTS INTERACTION MATRIX

The objective of the present work was to propose a method for testing the contribution of each level of the factors in a genotypes x environments (GxE) interaction using multi-environment trials analyses by means of an F test. The study evaluated a data set, with twenty genotypes and thirty-four environments, in a block design with four replications. The sum of squares within rows (genotypes) and columns (environments) of the GxE matrix was simulated, generating 10000 experiments to verify the empirical distribution. Results indicate a noncentral chi-square distribution for rows and columns of the GxE interaction matrix, which was also verified by the Kolmogorov-Smirnov test and Q-Q plot. Application of the F test identified the genotypes and environments that contributed the most to the GxE interaction. In this way, geneticists can select good genotypes in their studies.

SEM analysis and push-out bond strength of fiberglass posts luted with different cements of glass-ionomer in humid environment: pilot test

The objective of this study was to evaluate the push-out bond strength of fiberglass resin reinforced bonded with five ionomer cements. Also, the interface between cement and dentin was inspected by means of SEM. Fifty human canines were chose after rigorous scrutiny process, endodontically treated and divided randomly into five groups (n = 3) according to cement tested: Group I – Ionoseal (VOCO), Group II – Fugi I (GC), Group III – Fugi II Improved (GC), Group IV – Rely X Luting 2 (3M ESPE), Group V – Ketac Cem (3M ESPE). The post-space was prepared to receive a fiberglass post, which was tried before cementation process. No dentin or post surface pretreatment was carried out. After post bonding, all roots were cross-sectioned to acquire 3 thin-slices (1 mm) from three specific regions of tooth (cervical, medium and apical). A Universal test machine was used to carry out the push-out test with cross-head speed set to 0.5mm/mim. All failed specimens were observed under optical microscope to identify the failure mode. Representative specimens from each group was inspected under SEM. The data were analyzed by Kolmogorov-Smirnov and Levene’s tests and by two-way ANOVA, and Tukey’s port hoc test at a significance level of 5%. It was compared the images obtained for determination of types of failures more occurred in different levels. SEM inspection displayed that all cements filled the space between post and dentin, however, some imperfections such bubles and voids were noticed in all groups in some degree of extension. The push-out bond strength showed that cement Ketac Cem presented significant higher results when compared to the Ionoseal (P = 0.02). There were no statistical significant differences among other cements.

An Alternative Goodness-of-fit Test for Normality with Unknown Parameters

Goodness-of-fit tests have been studied by many researchers. Among them, an alternative statistical test for uniformity was proposed by Chen and Ye (2009). The test was used by Xiong (2010) to test normality for the case that both location parameter and scale parameter of the normal distribution are known. The purpose of the present thesis is to extend the result to the case that the parameters are unknown. A table for the critical values of the test statistic is obtained using Monte Carlo simulation. The performance of the proposed test is compared with the Shapiro-Wilk test and the Kolmogorov-Smirnov test. Monte-Carlo simulation results show that proposed test performs better than the Kolmogorov-Smirnov test in many cases. The Shapiro Wilk test is still the most powerful test although in some cases the test proposed in the present research performs better.

Assessment Of Sleep Bruxism, Orthodontic Treatment Need, Orofacial Dysfunctions And Salivary Biomarkers In Asthmatic Children.

To evaluate the sleep bruxism, malocclusions, orofacial dysfunctions and salivary levels of cortisol and alpha-amylase in asthmatic children. 108 7-9-yr-old children were selected from Policlinic Santa Teresinha Doutor Antonio Haddad Dib (asthmatics, n=53) and from public schools (controls, n=55), Piracicaba, SP, Brazil. Sleep bruxism diagnosis was confirmed by parental report of grinding sounds and the presence of shiny and polish facets on incisors and/or first permanent molars. The index of orthodontic treatment need was used for occlusion evaluation. Orofacial dysfunctions were evaluated using the nordic orofacial test-screening (NOT-S). Salivary cortisol and alpha-amylase were expressed as awakening response (AR), calculated as the difference between levels immediately after awakening and 30min after waking, and diurnal decline (DD), calculated as the difference between levels at 30min after waking and at bedtime. Data were analyzed using Shapiro-Wilk/Kolmogorov-Smirnov, Chi-square, unpaired t test/Mann-Whitney and paired t/Wilcoxon tests. Sleep bruxism was more prevalent in children with asthma than controls (47.2% vs. 27.3%, p<0.05). Asthmatics had higher scores of NOT-S total and interview (p<0.05). Dysfunctions on sensory function and chewing and swallowing were more frequent in asthmatics (p<0.05). Salivary cortisol AR on weekend was significantly higher for asthmatics (p<0.05). Salivary cortisol DD was significantly higher on weekday than weekend for controls (p<0.05). There were no significant differences in alpha-amylase values in and between groups. The presence of asthma in children was associated with sleep bruxism, negative perception of sensory, chewing and swallowing functions, and higher concentrations of salivary cortisol on weekend.

Qualidade de vida e nivel de atividade fisica de funcionarios de empresa de tecnologia da comunicação

Universidade Estadual de Campinas . Faculdade de Educação Física

Newtonian perturbations on models with matter creation

Creation of cold dark matter (CCDM) can macroscopically be described by a negative pressure, and, therefore, the mechanism is capable to accelerate the Universe, without the need of an additional dark energy component. In this framework, we discuss the evolution of perturbations by considering a Neo-Newtonian approach where, unlike in the standard Newtonian cosmology, the fluid pressure is taken into account even in the homogeneous and isotropic background equations (Lima, Zanchin, and Brandenberger, MNRAS 291, L1, 1997). The evolution of the density contrast is calculated in the linear approximation and compared to the one predicted by the Lambda CDM model. The difference between the CCDM and Lambda CDM predictions at the perturbative level is quantified by using three different statistical methods, namely: a simple chi(2)-analysis in the relevant space parameter, a Bayesian statistical inference, and, finally, a Kolmogorov-Smirnov test. We find that under certain circumstances, the CCDM scenario analyzed here predicts an overall dynamics (including Hubble flow and matter fluctuation field) which fully recovers that of the traditional cosmic concordance model. Our basic conclusion is that such a reduction of the dark sector provides a viable alternative description to the accelerating Lambda CDM cosmology.

TESTING STATISTICAL HYPOTHESIS ON RANDOM TREES AND APPLICATIONS TO THE PROTEIN CLASSIFICATION PROBLEM

Efficient automatic protein classification is of central importance in genomic annotation. As an independent way to check the reliability of the classification, we propose a statistical approach to test if two sets of protein domain sequences coming from two families of the Pfam database are significantly different. We model protein sequences as realizations of Variable Length Markov Chains (VLMC) and we use the context trees as a signature of each protein family. Our approach is based on a Kolmogorov-Smirnov-type goodness-of-fit test proposed by Balding et at. [Limit theorems for sequences of random trees (2008), DOI: 10.1007/s11749-008-0092-z]. The test statistic is a supremum over the space of trees of a function of the two samples; its computation grows, in principle, exponentially fast with the maximal number of nodes of the potential trees. We show how to transform this problem into a max-flow over a related graph which can be solved using a Ford-Fulkerson algorithm in polynomial time on that number. We apply the test to 10 randomly chosen protein domain families from the seed of Pfam-A database (high quality, manually curated families). The test shows that the distributions of context trees coming from different families are significantly different. We emphasize that this is a novel mathematical approach to validate the automatic clustering of sequences in any context. We also study the performance of the test via simulations on Galton-Watson related processes.