scholarly journals A Cautionary Note on the Use of the Kolmogorov–Smirnov Test for Normality

2007 ◽  
Vol 135 (3) ◽  
pp. 1151-1157 ◽  
Author(s):  
Dag J. Steinskog ◽  
Dag B. Tjøstheim ◽  
Nils G. Kvamstø
Keyword(s):  
Goodness Of Fit ◽  
Small Sample ◽  
Power Comparison ◽  
Goodness Of Fit Test ◽  
Kolmogorov Smirnov ◽  
The Mean ◽  
Small Sample Problem ◽  
Tests For Normality ◽  
Test For Normality ◽  
Smirnov Test

Abstract The Kolmogorov–Smirnov goodness-of-fit test is used in many applications for testing normality in climate research. This note shows that the test usually leads to systematic and drastic errors. When the mean and the standard deviation are estimated, it is much too conservative in the sense that its p values are strongly biased upward. One may think that this is a small sample problem, but it is not. There is a correction of the Kolmogorov–Smirnov test by Lilliefors, which is in fact sometimes confused with the original Kolmogorov–Smirnov test. Both the Jarque–Bera and the Shapiro–Wilk tests for normality are good alternatives to the Kolmogorov–Smirnov test. A power comparison of eight different tests has been undertaken, favoring the Jarque–Bera and the Shapiro–Wilk tests. The Jarque–Bera and the Kolmogorov–Smirnov tests are also applied to a monthly mean dataset of geopotential height at 500 hPa. The two tests give very different results and illustrate the danger of using the Kolmogorov–Smirnov test.

scholarly journals El entrenamiento de la resistencia y sus efectos en la competición en la altura en el fútbol ecuatoriano (Endurance training and its effects in competition at altitude in the Ecuadorian soccer)

Retos ◽  
2017 ◽  
pp. 221-227
Author(s):  
Manuel Gutierrez Cruz ◽  
Lisbet Guillen Pereira ◽  
Flavio Antonio Perlaza ◽  
José Ramón Guerra Santiesteban ◽  
Giovanny Capote Lavandero ◽  
...  
Keyword(s):  
Endurance Training ◽  
Goodness Of Fit ◽  
Technical Skills ◽  
Three Dimensions ◽  
Maximum Volume ◽  
Goodness Of Fit Test ◽  
Four Dimensions ◽  
Kolmogorov Smirnov ◽  
Student’S T ◽  
Smirnov Test

La investigación se realizó en el equipo de la reserva del Barcelona Sporting Club del fútbol ecuatoriano de primera división, cuyo objetivo se enfocó en validar una alternativa metodológica para el entrenamiento de la resistencia con vista a la competición en la altura, para ello se asumió un pre-experimento el cual permitió evaluar cuatro dimensiones, la primera relacionada con el conocimiento sobre el entrenamiento de resistencia para la competición en la altura; en este aspecto se trabajó con el cuerpo técnico del equipo. De igual forma intervino una muestra de 12 futbolistas seleccionados mediante un muestreo intencional, en esta se evaluaron tres dimensiones: la efectividad de las acciones ofensivas y defensivas, la segunda  analiza la cantidad de metros recorridos (Test de Cooper) y la tercera el VO2. Para el análisis estadístico de los datos se utilizó un test de bondad de ajustes (test de Kolmogorov-Smirnov: KS), los resultados permitieron aplicar un test paramétrico (T de Student). En cada una de las dimensiones analizadas los resultados arrojados fueron significativos siendo p=.000. Para el análisis estadístico se empleó el paquete SPSS 23.0. Los resultados del estudio demostraron como resultado de la aplicación de la propuesta un incremento en la efectividad en la utilización de la técnica para  crear y solucionar situaciones en los últimos 15 minutos de juego, en concordancia se observó  un mejor estado de las manifestaciones externas de la carga física y la capacidad de resistencia aerobia a partir del incremento del VO2.Summary: The research was carried out with the reserve team of Barcelona Sporting Club from the Ecuadorian soccer first division. The objective was to validate a methodological alternative for endurance training focused on competitions at altitude. The pre-experimental design of the study was directed to evaluating four dimensions. The first one concerned developing knowledge about endurance training for competitions at altitude; in this aspect, we worked with the technical staff of the team. In the same way, a sample of 12 players was selected using intentional sampling, three dimensions being evaluated: effectiveness of offensive and defensive actions; meters covered (Cooper test); and maximum volume of oxygen (VO2). Data analysis was based on goodness of fit test (Kolmogorov-Smirnov test [KS]). Data normality allowed to apply parametric tests (Student's T). Results were significant in each of the analyzed dimensions, being p = .000. SPSS 23.0 package was used for statistical analysis. Results of the implementation of the method demonstrated an increased effectiveness in using technical skills to create and solve situations in the last 15 minutes of the matches, at the same time as we could observe a better state of the external manifestations of physical load as well as improved capacity of aerobic endurance derived from the increase in VO2.

A New Goodness-of-Fit Test for Grouped Data

2012 ◽  
Vol 569 ◽  
pp. 455-460
Author(s):  
Jin Qin ◽  
Jun Yang
Keyword(s):  
Goodness Of Fit ◽  
Test Method ◽  
Ratio Method ◽  
Grouped Data ◽  
Survival Ratio ◽  
Goodness Of Fit Test ◽  
Goodness Of Fit Tests ◽  
Kolmogorov Smirnov ◽  
Distribution Type ◽  
Smirnov Test

In data analysis of reliability, the traditional goodness-of-fit test is not applicable for grouped data under some circumstances. In this paper, a Kolmogorov-Smirnov test based on survival ratio method is proposed to determine the distribution type of grouped data. The power of the proposed test and other well-known goodness-of-fit tests are compared by Monte Carlo simulation, and the results show that the proposed test method is more powerful.

scholarly journals PEMODELAN DISTRIBUSI FREKWENSI TIME HEADWAY LALU LINTAS DI WILAYAH JALAN BERBUKIT

2016 ◽  
Vol 12 (2) ◽  
pp. 71
Author(s):  
Rizky Indra Utama ◽  
Purnawan Purnawan ◽  
Hendra Gunawan
Keyword(s):  
Goodness Of Fit ◽  
Traffic Simulation ◽  
Test Model ◽  
Goodness Of Fit Test ◽  
Microscopic Traffic Simulation ◽  
Time Headway ◽  
Kolmogorov Smirnov ◽  
Data Program ◽  
Smirnov Test

Time headway merupakan besaran mikroskopik arus lalu lintas yang sangat penting kegunaannya dalam analisis dan perencanaan suatu sistem transportasi. Pentingnya time headway, khususnya dalam microscopic traffic simulation, mendorong perlunya penentuan standar nilai yang dapat digunakan untuk keperluan praktis. Penelitian ini bertujuan untuk mengetahui model distribusi time headway yang sesuai untuk data hasil penelitian di wilayah jalan berbukit. Penelitian mengambil data arus lalu lintas pada ruas jalan Padang Panjang– Bukittinggi Km. 5. Pengumpulan data primer dilakukan dengan menggunakan handycam. Pengolahan data pengamatan menggunakan Software Stop Data Program. Untuk mendapatkan goodness of fit dari model distribusi data pengamatan yang cocok dengan distribusi teoritis, maka dilakukan Kolmogorov Smirnov Test (K-S Test) dengan menggunakan Software EasyFit, sehingga dihasilkan model yang cocok dengan kondisi wilayah jalan berbukit. Dari analisis didapatkan hasil sebagai berikut: model distribusi terbaik hasil uji time headway individual Hari Sabtu pada jalur tanjakan didapatkan model hasil uji yang terbaik adalah model Beta dengan nilai α1=2,290 ,α2=7,668 , 􀜽 =4,615 􀵈10􀬿􀬵􀬻, 􀜾 =16,809, pada jalur turunan didapatkan model hasil uji yang terbaik adalah model Weibull dengan nilai α= 1,546 ,β=3,551 ,γ = 0. Model distribusi terbaik hasil uji time headway individual Hari Minggu pada jalur tanjakan didapatkan model hasil uji yang terbaik adalah model Beta dengan nilai α1=2,217 ,α2=6,626 ,􀜽=2,895􀵈10􀬿􀬵􀬺 ,􀜾 =15,046, untuk jalur turunan didapatkan model hasil uji yang terbaik adalah model Cauchy dengan nilai σ=0,703 dan μ=2,937.Time headway rata-rata Hari Sabtu pada jalur tanjakan diperoleh 3,86 detik, pada jalur turunan didapatkan 3,17 detik. Selanjutnya time headway rata-rata Hari Minggu pada jalur tanjakan didapatkan 3,77 detik, pada jalur turunan diperoleh 3,21 detik.Kata kunci : Time Headway, Goodness Of Fit Test, Model Distribusi

AN ALTERNATIVE TEST FOR UNIFORMITY

2009 ◽  
Vol 16 (04) ◽  
pp. 343-356 ◽  
Author(s):  
ZHENMIN CHEN ◽  
CHUNMIAO YE
Keyword(s):  
Probability Distribution ◽  
Goodness Of Fit ◽  
Integral Transformation ◽  
Test Statistic ◽  
Goodness Of Fit Test ◽  
Underlying Distribution ◽  
Goodness Of Fit Tests ◽  
Kolmogorov Smirnov ◽  
Alternative Test ◽  
Smirnov Test

Improving power of goodness-of-fit tests is an important research topic in statistics. The goal of the goodness-of-fit test is to check whether the underlying probability distribution, from which a sample is drawn, differs from a hypothesized distribution. Numerous research papers have been published in this area. It has been shown that the power of the existing goodness-of-fit tests in the literature is unsatisfactory when the alternative distributions are of V-shape or when the sample sizes are small. This motivates the development of more powerful test statistics. In this research, a new test statistic is proposed. The result can be used to test whether the underlying probability distribution differs from a uniform distribution. By applying the probability integral transformation, the proposed test statistic can be used to check whether the underlying distribution differs from any hypothesized distribution. The performance of the method proposed in this research is compared with the Kolmogorov–Smirnov test, which is a widely adopted statistical test in the literature. It has been shown that the test proposed in this proposal is more powerful than the Kolmogorov–Smirnov test in some cases.

scholarly journals Consistency Bands for the Mean Excess Function and Application to Graphical Goodness-of-fit Test for Financial Data

2016 ◽  
Vol 8 (1) ◽  
pp. 42
Author(s):  
Amadou Diadie Ba ◽  
El Hadj Deme ◽  
Cheikh Tidiane Seck ◽  
Gane Samb Lo
Keyword(s):  
Goodness Of Fit ◽  
Empirical Processes ◽  
Financial Data ◽  
Generalized Hyperbolic Distribution ◽  
Goodness Of Fit Test ◽  
Excess Function ◽  
Monthly Data ◽  
Hyperbolic Distribution ◽  
Mean Excess Function ◽  
The Mean

<p>In this paper, we use the modern setting of functional empirical processes and recent techniques on uniform estimation for non parametric objects to derive consistency bands for the mean excess function in the i.i.d. case. We apply our results for modelling Dow Jones data to see how good the Generalized hyperbolic distribution fits monthly data.</p>

scholarly journals AJUSTE DA FUNÇÃO DE DISTRIBUIÇÃO DIAMÉTRICA WEIBULL POR PLANILHA ELETRÔNICA

FLORESTA ◽  
2011 ◽  
Vol 41 (2) ◽  
Author(s):  
William Thomaz Wendling ◽  
Dartagnan Baggio Emerenciano ◽  
Roberto Tuyoshi Hosokawa
Keyword(s):  
Distribution Function ◽  
Goodness Of Fit ◽  
Diameter Distribution ◽  
Goodness Of Fit Test ◽  
Function Model ◽  
Helpful Tool ◽  
Test Efficiency ◽  
Kolmogorov Smirnov ◽  
Electronic Spreadsheet ◽  
Main Model

Desenvolve-se uma metodologia traçada por um roteiro em algoritmo factível e amigável para efetivação em planilhas eletrônicas, reconhecidas como uma interface popular para cálculos. Busca-se, assim, apresentar uma ferramenta útil para alunos de graduação e recém-graduados em engenharia florestal, ou engenheiros mais experientes que ainda não dominem a técnica, para ajuste de um modelo de função densidade de probabilidade, com o objetivo de descrever a estrutura da distribuição diamétrica de populações florestais. O modelo adotado é o da função de Weibull, e o método de ajuste é o do percentis, com simulações comparadas por teste de aderência de Kolmogorov-Smirnov. A eficiência do método apresentado é testada por comparação a outro método alternativo.Palavras-chave:  Manejo florestal; florestas - modelos matemáticos; florestas - simulação por computador. AbstractWeibull diameter distribution function adjusts for electronic spreadsheet. This research develops a methodology based on easy and friendly algorithm for spreadsheets, a well known interface for calculus. It aims to present a helpful tool for forestry students, as well as for newly or experienced engineers who haven’t already known adjustment techniques for a density function model of probability, which is useful into diametric distribution structure descriptions of forest population. It has Weibull’s function as main model, percentile as adjustment method, and comparing simulations by Kolmogorov-Smirnov goodness-of-fit test. Efficiency of the presented method was tested by comparison to another method.Keywords: Forest management; forest - mathematical models; forest - computer simulator.

On the use of chi-square analyses in studies of resource utilization

1991 ◽  
Vol 21 (1) ◽  
pp. 58-65 ◽  
Author(s):  
Dennis E. Jelinski
Keyword(s):  
Resource Utilization ◽  
Goodness Of Fit ◽  
Small Sample ◽  
Homogeneity Test ◽  
Type I ◽  
Sample Sizes ◽  
Goodness Of Fit Test ◽  
Chi Square ◽  
Test Of Homogeneity ◽  
Small Sample Sizes

Chi-square (χ2) tests are analytic procedures that are often used to test the hypothesis that animals use a particular food item or habitat in proportion to its availability. Unfortunately, several sources of error are common to the use of χ2 analysis in studies of resource utilization. Both the goodness-of-fit and homogeneity tests have been incorrectly used interchangeably when resource availabilities are estimated or known apriori. An empirical comparison of the two methods demonstrates that the χ2 test of homogeneity may generate results contrary to the χ2 goodness-of-fit test. Failure to recognize the conservative nature of the χ2 homogeneity test, when "expected" values are known apriori, may lead to erroneous conclusions owing to the increased possibility of committing a type II error. Conversely, proper use of the goodness-of-fit method is predicated on the availability of accurate maps of resource abundance, or on estimates of resource availability based on very large sample sizes. Where resource availabilities have been estimated from small sample sizes, the use of the χ2 goodness-of-fit test may lead to type I errors beyond the nominal level of α. Both tests require adherence to specific critical assumptions that often have been violated, and accordingly, these assumptions are reviewed here. Alternatives to the Pearson χ2 statistic are also discussed.

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