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.

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).

Incorporating uncertainty in environmental models informed by imagery

In this thesis, the issue of incorporating uncertainty for environmental modelling informed by imagery is explored by considering uncertainty in deterministic modelling, measurement uncertainty and uncertainty in image composition. Incorporating uncertainty in deterministic modelling is extended for use with imagery using the Bayesian melding approach. In the application presented, slope steepness is shown to be the main contributor to total uncertainty in the Revised Universal Soil Loss Equation. A spatial sampling procedure is also proposed to assist in implementing Bayesian melding given the increased data size with models informed by imagery. Measurement error models are another approach to incorporating uncertainty when data is informed by imagery. These models for measurement uncertainty, considered in a Bayesian conditional independence framework, are applied to ecological data generated from imagery. The models are shown to be appropriate and useful in certain situations. Measurement uncertainty is also considered in the context of change detection when two images are not co-registered. An approach for detecting change in two successive images is proposed that is not affected by registration. The procedure uses the Kolmogorov-Smirnov test on homogeneous segments of an image to detect change, with the homogeneous segments determined using a Bayesian mixture model of pixel values. Using the mixture model to segment an image also allows for uncertainty in the composition of an image. This thesis concludes by comparing several different Bayesian image segmentation approaches that allow for uncertainty regarding the allocation of pixels to different ground components. Each segmentation approach is applied to a data set of chlorophyll values and shown to have different benefits and drawbacks depending on the aims of the analysis.

Modeling and multiway analysis of chatroom tensors

This work identifies the limitations of n-way data analysis techniques in multidimensional stream data, such as Internet chat room communications data, and establishes a link between data collection and performance of these techniques. Its contributions are twofold. First, it extends data analysis to multiple dimensions by constructing n-way data arrays known as high order tensors. Chat room tensors are generated by a simulator which collects and models actual communication data. The accuracy of the model is determined by the Kolmogorov-Smirnov goodness-of-fit test which compares the simulation data with the observed (real) data. Second, a detailed computational comparison is performed to test several data analysis techniques including svd [1], and multi-way techniques including Tucker1, Tucker3 [2], and Parafac [3].

Collective sampling and analysis of high order tensors for chatroom communications

This work investigates the accuracy and efficiency tradeoffs between centralized and collective (distributed) algorithms for (i) sampling, and (ii) n-way data analysis techniques in multidimensional stream data, such as Internet chatroom communications. Its contributions are threefold. First, we use the Kolmogorov-Smirnov goodness-of-fit test to show that statistical differences between real data obtained by collective sampling in time dimension from multiple servers and that of obtained from a single server are insignificant. Second, we show using the real data that collective data analysis of 3-way data arrays (users x keywords x time) known as high order tensors is more efficient than centralized algorithms with respect to both space and computational cost. Furthermore, we show that this gain is obtained without loss of accuracy. Third, we examine the sensitivity of collective constructions and analysis of high order data tensors to the choice of server selection and sampling window size. We construct 4-way tensors (users x keywords x time x servers) and analyze them to show the impact of server and window size selections on the results.

Establishing definitions and modeling public transport travel time variability

Public transport travel time variability (PTTV) is essential for understanding deteriorations in the reliability of travel time, optimizing transit schedules and route choices. This paper establishes key definitions of PTTV in which firstly include all buses, and secondly include only a single service from a bus route. The paper then analyses the day-to-day distribution of public transport travel time by using Transit Signal Priority data. A comprehensive approach using both parametric bootstrapping Kolmogorov-Smirnov test and Bayesian Information Creation technique is developed, recommends Lognormal distribution as the best descriptor of bus travel time on urban corridors. The probability density function of Lognormal distribution is finally used for calculating probability indicators of PTTV. The findings of this study are useful for both traffic managers and statisticians for planning and researching the transit systems.

Public transport travel time variability definitions and monitoring

Public Transport Travel Time Variability (PTTV) is essential for understanding the deteriorations in the reliability of travel time, optimizing transit schedules and route choices. This paper establishes the key definitions of PTTV in which firstly include all buses, and secondly include only a single service from a bus route. The paper then analyzes the day-to-day distribution of public transport travel time by using Transit Signal Priority data. A comprehensive approach, using both parametric bootstrapping Kolmogorov-Smirnov test and Bayesian Information Creation technique is developed, recommends Lognormal distribution as the best descriptor of bus travel time on urban corridors. The probability density function of Lognormal distribution is finally used for calculating probability indicators of PTTV. The findings of this study are useful for both traffic managers and statisticians for planning and analyzing the transit systems.

Inferential, non-parametric statistics to assess quality of probabilistic forecast systems

Many statistical forecast systems are available to interested users. In order to be useful for decision-making, these systems must be based on evidence of underlying mechanisms. Once causal connections between the mechanism and their statistical manifestation have been firmly established, the forecasts must also provide some quantitative evidence of `quality’. However, the quality of statistical climate forecast systems (forecast quality) is an ill-defined and frequently misunderstood property. Often, providers and users of such forecast systems are unclear about what ‘quality’ entails and how to measure it, leading to confusion and misinformation. Here we present a generic framework to quantify aspects of forecast quality using an inferential approach to calculate nominal significance levels (p-values) that can be obtained either by directly applying non-parametric statistical tests such as Kruskal-Wallis (KW) or Kolmogorov-Smirnov (KS) or by using Monte-Carlo methods (in the case of forecast skill scores). Once converted to p-values, these forecast quality measures provide a means to objectively evaluate and compare temporal and spatial patterns of forecast quality across datasets and forecast systems. Our analysis demonstrates the importance of providing p-values rather than adopting some arbitrarily chosen significance levels such as p < 0.05 or p < 0.01, which is still common practice. This is illustrated by applying non-parametric tests (such as KW and KS) and skill scoring methods (LEPS and RPSS) to the 5-phase Southern Oscillation Index classification system using historical rainfall data from Australia, The Republic of South Africa and India. The selection of quality measures is solely based on their common use and does not constitute endorsement. We found that non-parametric statistical tests can be adequate proxies for skill measures such as LEPS or RPSS. The framework can be implemented anywhere, regardless of dataset, forecast system or quality measure. Eventually such inferential evidence should be complimented by descriptive statistical methods in order to fully assist in operational risk management.

Korpien ennallistamisen lyhyen aikavälin vaikutukset puustorakenteeseen

Korpien puustorakenteen palautumisen nopeus ja ennallistettujen kohteiden kehitys on huonosti tunnettua. Monet tutkimukset ovat osoittaneet, että korvet ovat lajistollisen monimuotoisuuden keskittymiä boreaalisessa vyöhykkeessä. Korvet ovat usein merkittäviä lahopuukeskittymiä, joten niillä on iso vaikutus lahottajalajistolle. Valtaosa suojelualu- eiden korvista Etelä-Suomessa on ojitettu ja korpien puustorakenne on metsätalouden muovaamaa ja yksipuolistamaa. Korpien puustorakennetta tutkittiin kahdella erillisellä tutkimusalueella, jotka sijaitsevat Etelä-Suomessa. Työn tavoit- teena oli selvittää luonnontilaisten ja ennallistettujen korpien puuston rakenteellista monimuotoisuutta sekä ennallista- mistoimien vaikutuksia Evon suojelumetsässä ja Liesjärven kansallispuistossa. Molemmat alueet ovat olleet aikaisem- min metsänhoidon piirissä. Evolta valittiin tarkasteluun ennallistettuja ja luonnontilaisen kaltaisia korpia: 12 ennallis- tettua koealaa ja 16 luonnontilaisen kaltaista koealaa. Liesjärveltä valittiin tarkasteluun ennallistettu Soukonkorpi, jossa oli 15 koealaa. Koealat olivat pinta-alaltaan neljä aaria. Evon tutkimusalueella maastomittaukset on tehty kesällä 2002 ja 2010. Liesjärven tutkimusalueella maastomittaukset on tehty vuosina 1995–2010. Tarkastellut muuttujat olivat elävän puuston määrä ja puulajisuhteet, lahopuun määrä ja laatu (lahopuutyyppi, läpimittaluokka, lahoaste ja puulaji). Lahopuuston määrää ja laatua sekä lahopuuston ja elävän puuston suhdetta kuvaavien muuttujien välisiä eroja testattiin ei-parametrisellä Kolmogorov-Smirnov-testillä. Evon ja Liesjärven tutkimusalueiden ennallistamistoimien yhtenä tavoitteena oli lahopuumäärien lisääminen ja laho- puun monipuolistaminen. Lahopuun lisäämisessä on onnistuttu molemmilla tutkimusalueilla. Ennallistamisen jälkeen lahopuumäärä kasvoi Evolla kolminkertaiseksi 8 vuodessa. Lahopuuta oli ennallistamisen jälkeen keskimäärin 71 m³/ha. Sen sijaan Evon luonnontilaisen kaltaisissa korvissa lahopuumäärä pysyi keskimäärin samana (28 m³/ha) tar- kastelujakson aikana. Liesjärvellä lahopuumäärä kasvoi ennallistamisen jälkeen noin kuusinkertaiseksi 15 vuodessa. Lahopuuta oli ennallistamisen jälkeen keskimäärin 124 m³/ha. Suuriläpimittaisen (? 30 cm) lahopuun määrä kasvoi huomattavasti ennallistamisen jälkeen molemmilla tutkimusalueilla. Suuriläpimittaisen lahopuun määrä kasvoi Evolla noin 12-kertaiseksi ja Liesjärvellä noin 9-kertaiseksi. Lahopuun määrä ja laatu vaihtelivat suuresti ennallistettujen ja luonnontilaisen kaltaisten korpien välillä. Evolta löytyi lahopuustoltaan runsaita ja monipuolisia korpia, mutta myös korpia, joiden lahopuusto on luonnontilaisiin korpiin ver- rattuna määrältään vähäistä ja laadultaan yksipuolista. Liesjärvellä koealojen lahopuumäärät poikkesivat suuresti toisis- taan. Valtaosalla koealoista lahopuusto oli kuitenkin runsaampaa ja monimuotoisempaa kuin talousmetsissä yleensä. Molemmilla tutkimusalueilla ennallistetut korvet muistuttavat nyt puustorakenteeltaan lahopuun osalta enemmän luon- nontilaisia korpia kuin ennen ennallistamista. Ilman ennallistamistoimia lahopuumäärän kasvu olisi todennäköisesti ollut hidasta. Evolla ennallistettujen ja luonnontilaisen kaltaisten korpien välillä oli tilastollisesti merkitseviä eroja suuriläpimittaisen lahopuun ja tuoreimpien lahoasteiden (1 ja 2) määrässä. Valtaosalla korvista oli lahopuuta vähintään 20 m³/ha. Metsäaluetasolla keskimäärin 20–30 m³/ha järeää, vaihtelevanlaatuista lahopuuta näyttäisi aikaisempien tutkimusten mukaan täyttävän useimpien saproksyylilajien elinympäristövaatimukset Etelä-Suomessa.

Formação in vitro de biofilme de Candida albicans em materiais usados no preenchimento dos acessos aos parafusos das próteses sobre implantes

Os orifícios de acesso aos parafusos de retenção devem ser preenchidos para que o parafuso não seja danificado caso seja necessária a remoção da prótese. Dentre os materiais mais utilizados estão o algodão, a fita de politetrafluoretileno e a guta percha. O objetivo deste estudo é avaliar a formação de biofilme de Candida albicans nos materiais anteriormente descritos, buscando estabelecer um parâmetro que contribua para a escolha do tipo de material mais adequado a ser utilizado clinicamente. Foram utilizados UCLAs, análogos e parafusos sextavados, todos de titânio. Os conjuntos foram montados com torque de 32N. Os materiais foram condensados no interior dos UCLAs e colocados em meio de cultura com uma suspensão de 3x106 células/ml de Candida albicans. O sistema foi armazenado à 37C com agitação, por 15 dias e o meio foi renovado a cada 48 horas. A quantificação de biofilme foi realizada pelo ensaio de MTT e leitura à 490nm, resultando em diferentes valores de densidade óptica. A normalidade (p=0,304 - Kolmogorov-Smirnov) e a igualdade de variâncias (p=0,721 - Scheffe) foram testadas primeiramente. O teste de análise de variância demonstrou diferença significativa entre os grupos (p<0,001) e com o Holm-Sidak foi observada diferença significativa entre os grupos algodão e guta (p<0,05) e algodão e fita de politetrafluoetileno (p<0,05); não houve diferença significativa entre os grupos guta e fita de politatrafluoretileno (p>0,05), apesar dos valores da fita de politetrafluoetileno terem sido maiores. Considerando-se as limitações deste estudo in vitro, podemos concluir que tanto a guta-percha quanto a fita de politetrafluoretileno apresentaram menor formação de biofilme, não havendo diferença estatisticamente significativa entre os materiais. O algodão apresentou um nível de formação de biofilme significativamente maior que a fita de politetrafluoretileno e a guta percha. Diante disso, serão necessários novos estudos para confirmar as limitações que este tipo de material pode apresentar quando usado como material de preenchimento do acesso do parafuso da prótese sobre implante.

Postrelease survival, vertical and horizontal movements, and thermal habitats of five species of pelagic sharks in the central Pacific Ocean

From 2001 to 2006, 71 pop-up satellite archival tags (PSATs) were deployed on five species of pelagic shark (blue shark [Prionace glauca]; shortfin mako [Isurus oxyrinchus]; silky shark [Carcharhinus falciformis]; oceanic whitetip shark [C. longimanus]; and bigeye thresher [Alopias superciliosus]) in the central Pacific Ocean to determine species-specific movement patterns and survival rates after release from longline fishing gear. Only a single postrelease mortality could be unequivocally documented: a male blue shark which succumbed seven days after release. Meta-analysis of published reports and the current study (n=78 reporting PSATs) indicated that the summary effect of postrelease mortality for blue sharks was 15% (95% CI, 8.5–25.1%) and suggested that catch-and-release in longline fisheries can be a viable management tool to protect parental biomass in shark populations. Pelagic sharks displayed species-specific depth and temperature ranges, although with significant individual temporal and spatial variability in vertical movement patterns, which were also punctuated by stochastic events (e.g., El Niño-Southern Oscillation). Pelagic species can be separated into three broad groups based on daytime temperature preferences by using the unweighted pair-group method with arithmetic averaging clustering on a Kolmogorov-Smirnov Dmax distance matrix: 1) epipelagic species (silky and oceanic whitetip sharks), which spent >95% of their time at temperatures within 2°C of sea surface temperature; 2) mesopelagic-I species (blue sharks and shortfin makos, which spent 95% of their time at temperatures from 9.7° to 26.9°C and from 9.4° to 25.0°C, respectively; and 3) mesopelagic-II species (bigeye threshers), which spent 95% of their time at temperatures from 6.7° to 21.2°C. Distinct thermal niche partitioning based on body size and latitude was also evident within epipelagic species.

Evaluation of a Pound Net Leader Designed to Reduce Sea Turtle Bycatch

Offshore pound net leaders in the southern portion of Chesapeake Bay in Virginia waters were documented to incidentally take protected loggerhead, Caretta caretta, and Kemp’s ridley, Lepidochelys kempii, sea turtles. Because of these losses, NOAA’s National Marine Fisheries Service (NMFS) in 2004 closed the area to offshore pound net leaders annually from 6 May to 15 July and initiated a study of an experimental leader design that replaced the top two-thirds of the traditional mesh panel leader with vertical ropes (0.95 cm) spaced 61 cm apart. This experimental leader was tested on four pound net sites on the eastern shore of Chesapeake Bay in 2004 and 2005. During the 2 trial periods, 21 loggerhead and Kemp’s ridley sea turtles were found interacting with the control leader and 1 leatherback turtle, Dermochelys coriacea, was found interacting with the experimental leader. Results of a negative binomial regression analysis comparing the two leader designs found the experimental leader significantly reduced sea turtle interactions (p=0.03). Finfish were sampled from the pound nets in the study to assess finfish catch performance differences between the two leader designs. Although the conclusions from this element of the experiment are not robust, paired t-test and Wilcoxon signed rank test results determined no significant harvest weight difference between the two leaders. Kolmogorov-Smirnov tests did not reveal any substantive size selectivity differences between the two leaders.

Qualidade do debridamento obtido pela técnica de instrumentação da lima única de NiTi em canais ovais e circulares

O presente avalia a qualidade da remoção de tecido pulpar após o preparo químico-cirúrgico realizado com a técnica da lima única, descrita por Ghassan Yared. Ainda não há publicado pesquisa sobre os resultados desta técnica. Este estudo compara o percentual de tecido pulpar remanescente em canais radiculares ovais e circulares de incisivos inferiores recém-extraídos que possuíssem polpa viva e armazenados em formol a 10%. Foram comparadas duas técnicas: ProTaper Universal e a técnica da lima única F2. Após uma rigorosa seleção, quarenta e oito dentes com polpa viva que possuíam indicação de extração, foram preparados, classificados em canais ovais e circulares, separados aleatoriamente em 4 grupos e instrumentados com as duas técnicas. O grupo controle, com 12 espécimes, não recebeu nenhum tipo de intervenção. G1 (n=12), canais ovais, instrumentados com a técnica ProTaper Universal; G2 (n=12), canais ovais instrumentados com a técnica da lima única F2; G3 (n=12), canais circulares instrumentados com a técnica ProTaper Universal; G4 (n=12), canais circulares instrumentados com a técnica da lima única F2. Então, seções transversais foram preparadas para avaliação histológica. A análise da quantidade de tecido pulpar remanescente foi avaliada digitalmente. A análise preliminar dos dados brutos em conjunto de todos os grupos experimentais revelou um padrão de distribuição normal por meio do uso do teste Kolmogorov-Smirnov. A análise foi realizada, e os dados brutos foram avaliados através de métodos não-paramétricos: Teste H Kruskal-Wallis. O valor percentual mínimo de tecido remanescente foi de 0% e o máximo de 37,78% entre todos os grupos. Os valores relativos a quantidade de tecido pulpar remanescente variaram entre 0 a 43.47% m2. Os resultados do Teste H Kruskal-Wallis não revelaram diferenças entre as seções mais apicais (p > 0.05). Entretanto, foi encontrada diferença significante entre as seções mais apicais e a seção do terço médio (p < 0.05). Também foram encontradas diferenças significantes quando canais circulares foram comparados com canais ovais independente da técnica de instrumentação utilizada (p < 0.05). Porém, entre as duas técnicas de instrumentação estudadas, tanto nos canais ovais quanto para os os canais circulares, não houve diferença estatística significante (p > 0.05). A proposta deste estudo é a de fazer uma reflexão sobre a real necessidade de um grande número de instrumentos para o total preparo de canais radiculares, uma vez que nenhuma das técnicas foi capaz de debridar por completo o espaço do canal radicular.

杂谷脑河流域河网统计自相似性

河网自相似性是水文尺度研究的重要方向,统计自相似研究不同尺度下河网参数概率分布函数的相似性.从统计自相似的角度,推导出河网参数、全河网分布和单级河道分布的关系,并用杂谷脑河DEM进行验证;对所得数据进行Kolmogorov-Smirnov双样本检验,结果显示,推导结论与实际数据吻合,说明整个河网和单级河道之间是复杂的层叠关系,而不是简单的比例关系.

Chuvas intensas em Mato Grosso do Sul.

O objetivo deste trabalho foi determinar as chuvas intensas para o Estado de Mato Grosso do Sul. Séries com os valores máximos anuais da precipitação de um dia de 106 postos pluviométricos, localizados em 54 municípios de Mato Grosso do Sul foram ajustadas à Distribuição de Gumbel. Os parâmetros da distribuição foram estimados pelo método de máxima verossimilhança. Houve ajuste de todas as séries de intensidade máxima anual à distribuição Gumbel, de acordo com o teste Kolmogorov-Smirnov. Através das distribuições ajustadas foram calculados os valores de precipitação máxima de um dia para períodos de retorno de 2, 3, 4, 5, 10, 15, 20 e 50 anos. Utilizando o método de desagregação de chuvas, estimou-se a precipitação máxima com duração de 5, 10, 15, 20, 25, 30 minutos e 1, 6, 8, 10, 12 e 24 horas. Foram confeccionados mapas de isolinhas com os dados de chuva intensa com duração de 5, 10, e 30 minutos e 1, 6 e 24 horas para períodos de retorno de 4, 10, 15, 20 anos.