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Nanomaterials in the Work Environment
Published in Małgorzata Pośniak, Emerging Chemical Risks in the Work Environment, 2020
Lidia Zapór, Przemysław Oberbek
From the point of view of statistical analysis, the NOAA concentrations determined during the measurements are a time series. Statistically significant differences in size distributions of “background” nanoparticles and NOAA emitted during processes can be determined using appropriate descriptive statistics methods, including geometric mean and deviation from number concentration geometric mean, particle surface area, and mass concentration. Parametric statistics is mainly used for testing the dependence between concentration levels and other factors, and the variance analysis (ANOVA) with Bonferroni post hoc test and Student t-test is used to determine the level of significance of the differences in concentration levels between given events/stages of the studied processes [Ham et al. 2012]. As the standard t-test is not the perfect choice for NOAA concentration time series analysis, Annex D to EN standard 17058:2019 recommends the use of the autoregressive integrated moving average (ARIMA) model [Klein Entink et al. 2011]. Measurement results from different real-time concentration assessment devices are compared using Pearson’s correlation analysis [Ham et al. 2016].
Distributions
Published in Robert M. Bethea, R. Russell Rhinehart, Applied Engineering Statistics, 2019
Robert M. Bethea, R. Russell Rhinehart
Most of you will use the techniques in this book to assist you with the organization, interpretation, and presentation of data. For this reason, the methods presented here are all intended to help you determine the implications of the data you plan to collect or already have in hand. The primary characteristics that will interest you are the average value (mean) and a measure of the variability of results due to errors (variance). Most statistical methods are based on theoretical distributions, described by parameters (mean, variance), that approximate the actual distributions. Parameters, then, are descriptors of a theoretical distribution. Statistical procedures that state conclusions about such parameters using sample data are parametric statistics. Statistical procedures that state conclusions about populations for which the theoretical distribution has not been assumed are termed nonparametric statistics. Before you can appreciate and effectively utilize such methods, you must become familiar with theoretical distributions and the characteristics of the populations involved.
Fundamental Relationships for Flow and Transport
Published in James L. Martin, Steven C. McCutcheon, Robert W. Schottman, Hydrodynamics and Transport for Water Quality Modeling, 2018
James L. Martin, Steven C. McCutcheon, Robert W. Schottman
Many statistical tests require that the observed and simulated data sets be normally distributed. Parametric statistics are those based on the assumption that samples are drawn from a population with a known distribution, like the normal distribution. Nonparametric statistics are distribution free; no underlying distribution is assumed. For those parametric statistics like the Student’s t that depend on the normal distribution, tests for normality are required. These tests include plotting on normal probability paper, the chi-square test, and the Kolmogorov-Smimov test. However, many statistical tests are not affected by mild nonnormality. When a distribution lacks normality, a series of transformations (Kennedy and Neville 1976) can be attempted, starting with the log transformation. These log-transformed data are then tested to determine if the residuals or errors are normally distributed. Since water quality concentrations cannot be negative, many distributions of natural parameters are log-normal (Reckhow et al. 1990). Finally, if the distribution cannot be transformed to achieve normality, nonparametric tests like the sign test and the Wilcoxon ranked test can be used.
BEPU Method Applied to CFD Simulation of Mixing Flows
Published in Nuclear Technology, 2019
Andrej Prošek, Boštjan Končar, Matjaž Leskovar
When applying computational fluid dynamics (CFD) to nuclear reactor safety problems, the uncertainty methodologies accepted by the regulatory bodies should be understood.1 Different techniques for the uncertainty propagation in the system thermal-hydraulic code calculations were identified in the past, including Monte Carlo analysis, response surface (RS) methods, and statistical tolerance limits.2 Other methods have also been developed [e.g., Code with capability of Internal Assessment of Uncertainty3 (CIAU)]. Due to demanding calculation requirements the Monte Carlo method is currently not applicable to the complex thermal-hydraulic codes. In the RS methods the RS replaces the code calculation in the Monte Carlo analysis. Statistical tolerance limits is the approach, which applies random sampling (N times) of input parameters in the computer code calculations used for direct generation of N output results for estimation of actual uncertainty. Parametric statistics are based on parameters that describe the population from which the sample is taken. Nonparametric statistics are not based on a specific distribution. The consideration of nonparametric tolerance limits was originally presented by Wilks.4 In this case the tolerance limit is given by the order of statistics (highest, second highest, etc.).
Sprinting and dribbling differences in young soccer players: a kinematic approach
Published in Research in Sports Medicine, 2022
Aristotelis Gioldasis, Apostolos Theodorou, Evangelos Bekris, Athanasios Katis, Athanasia Smirniotou
All results are presented as mean ± SD. Descriptive statistics were used in order to present the participants’ characteristics. Before the parametric statistics the researchers conducted tests of normality and homogeneity (Histograms, Shapiro-Wilks W and Levene’s tests) to ensure that data meet these assumptions. T-tests for dependent samples were conducted to establish whether any significant differences existed among the variables. Pearson’s (r) correlations were calculated to examine the relationships among sprinting and dribbling tests while the norms of Evans (1996) were used for correlation coefficients. The criterion level for significance was set at P < 0.05. Statistical analysis was performed in SPSS version 23.0 (SPSS, Inc., Chicago, IL).
A prospective study of risk factors for hamstring injury in Australian football league players
Published in Journal of Sports Sciences, 2021
Nigel A. Smith, Melinda M. Franettovich Smith, Matthew N. Bourne, Rod S. Barrett, Julie A. Hides
All statistical analyses were conducted using the Statistical Package for Social Sciences (version 25, IBM, USA). Data were checked for normality and assumptions were adhered to; therefore, parametric statistics were used. Independent samples t-test was used to assess the effect of group (season hamstring injury/no hamstring injury) on participant characteristics (age, height, mass, AFL playing experience, professional AFL playing experience, Nordic strength and torque). Paired samples t-tests were used to assess differences in Nordic strength and torque between subsequently injured and uninjured limbs, and between previously injured (less than 1-year and greater than 1-year) and uninjured limbs. Nordic strength and torque (both using the injured limb versus dominant limb for the uninjured group) were dichotomized using a receiver operator characteristic (ROC) curve to identify the value that maximized specificity and minimized sensitivity. Age was dichotomized using a cut-off value equal to or greater than 25 years, consistent with previous literature (Gabbe et al., 2006). Injury history was already dichotomized with responses of yes/no. The association of Nordic strength, torque, age and injury history with prospective hamstring injury during the AFL season was assessed using chi-square analysis and reported as Odds Ratios (ORs). Finally, an analysis of variance with Bonferroni post hoc was used to assess the effect of team on demographic, Nordic strength and hamstring injury information. Significance was accepted as p < 0.05. Data are presented as means (one SD) or mean difference (95% confidence interval, CI).