Utilização dos testes estatísticos de Kolmogorov-Smirnov e Shapiro-Wilk para verificação da normalidade para materiais de pavimentação

Abstract

Resumo: Na pavimentação, é comum tratar os dados obtidos em ensaios à luz de conceitos da estatística clássica, que consideram que um conjunto de dados possui distribuição Normal e utilizam os parâmetros média e desvio padrão na análise dos dados. O presente trabalho se propõe a verificar a aderência à distribuição Normal de dados oriundos de alguns ensaios de materiais para pavimentação: densidades aparente e real e absorção do agregado graúdo, densidade aparente e volume de vazios de corpos de prova de mistura asfál-tica. Utilizaram-se os testes de Kolmogorov-Smirnov (K-S) e Shapiro-Wilk (S-W), por meio do pacote estatístico SPSS. Cada ensaio foi realizado pelo menos 30 vezes por um mesmo operador, utilizando os mesmos equipamentos. Observou-se convergência entre os testes K-S e S-W para cinco dos seis ensaios avaliados. Os mesmos ensaios também foram realizados por nove laboratórios, em amostras semelhantes; e foi utilizado apenas o teste S-W. Os resultados do teste S-W com relação ao conjunto de dados obtidos por um mesmo operador e por nove operadores foram semelhantes. Estas análises estatísticas contribuíram para a decisão com relação à escolha das ferramentas estatísticas utilizadas no Programa Interlaboratorial de Agregados e Misturas Asfálticas da Rede Asfalto N/E. DOI:10.4237/transportes.v21i1.566.Palavras-chave: normalidade; análise estatística; materiais para pavimentação.Abstract: For pavement materials evaluation, it is common to treat laboratorial test data with classical statistical concepts, considering that a data set has a normal distribution, and therefore using the parameters average and standard deviation. The present work aims to verify if the normal distribution can be applied for the results of some tests, such as bulk specific gravity, apparent specific gravity and absorption for coarse aggregates, bulk specific gravity and air voids for hot mixture asphalt samples. The Kolmogorov-Smirnov (K-S) e Shapiro-Wilk (S-W) tests were used with the SPSS. Each test was carried out at least 30 times by the same operator using the same equipment. There was convergence between the two normality tests for five of the six parameters. Then, the tests were also performed by nine different laboratories using similar samples; and only S-W test was used. These statistical analyses support the decision about the statistical tools used in the Interlaboratory Program of Aggregates and Asphalt Mixtures of the North-Northeast Asphalt Network.

Estimation of Fuel Consumption in Agricultural Mechanized Operations Using Artificial Neural Networks

“…According to Table 4, only the residues of the neural network 3 (MLP 12: 12-21-1: 1) showed normality. Taking as reference the studies of TORMAN et al (2012) and LOPES et al (2013), the non-significance in normality tests gives it greater reliability to this network. However, the t-test indicated that there are no differences between the measured fuel consumption values and the estimated by the four networks (Table 5).These results allow to affirm that the four networks are appropriate, although the third formed by a single hidden layer with twenty-one neuron is presented as the most suitable for predicting this consumption, depending on the variables that characterize the soil, the implement type in combination with the tillage system and operating conditions for mechanized set.…”

Influence of particulate matter and meteorological conditions on multiple sclerosis relapse: a preliminary study in São Paulo, Brazil

“…The exponential smoothing method of HoltWinters was used to smooth and eliminate any noise of the time series 13 . After the Kolmogorov-Smirnov test indicated normal distribution of data, the variables PM 10 , relative humidity, air temperature, and hospital admissions due to MS were correlated using Pearson's model 14,15 . Although many studies that correlate air pollution and meteorological variables with diseases use the Poisson family of generalized linear models (MLG), in this study we used multiple linear regression 3,16,17 .…”

Study on concrete through its hardened state properties

“…Afterwards, the statistical assumptions of Independence, Normality and Homoscedasticity were checked [37]. In order to assess if the data were normally distributed, the test of Shapiro-Wilk (1965) [39] was used. The theory of Shapiro-Wilk (1965) is based on two hypotheses: Ho the variable's data follow normal distribution and H1 the variable's data do not follow normal distribution.…”