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Evaluation and Incorporation of Uncertainties in Geotechnical Engineering
Published in Chong Tang, Kok-Kwang Phoon, Model Uncertainties in Foundation Design, 2021
Two main statistical methods can be used to analyse the population: descriptive and inferential. Descriptive statistics are summary statistics that quantitatively describe the features of the population. Univariate analysis aims to describe the distribution of a single variable, including its central tendency or location (e.g. mean, median and mode) and variability or dispersion (e.g. range, coefficient of variation (COV), skewness and kurtosis). Unlike descriptive statistics that are solely concerned with properties of the population, inferential statistics make propositions about the population based on a study of a sample taken from the population. There are two main methods of inferential statistics: (1) estimation of the parameters (e.g. mean and COV) that can be done by constructing confidence interval – range of values in which the true population parameters are likely to fall and (2) hypothesis testing (also known as significance testing) that involves determining whether the difference in the means of two samples is statistically significant. Verification of randomness and identification of the probability distribution of a model factor are usually implemented by hypothesis testing. Details on descriptive and inferential statistics can be found in Bernstein and Bernstein (1999a, b).
Applied Statistics
Published in Vinayak Bairagi, Mousami V. Munot, Research Methodology, 2019
Varsha K. Harpale, Vinayak K. Bairagi
Univariate analysis is method of analyzing data using one variable. It describes or summarizes the data and also states patterns of the data. A variable in univariate analysis states about the behavior of data or it states category of the data. Level of measurements also plays a very important role to find best fit analysis. These levels are Nominal, Ordinal, Interval, and Ratio. Data are classified according to the highest level that it fits.
Data Science with Semantic Technologies: Application to Information Systems Development
Published in Journal of Computer Information Systems, 2023
The process makes use of one or several data science techniques. These latter may be classified into the following categories:90Techniques based on mathematics and statistics encompassing those related to regression, dispersion, density estimation, central tendency, discriminant, and time-series analysis.Techniques based on artificial intelligence and machine learning including neural networks, decision trees, evolutionary programming, and fuzzy logic.Techniques based on visualization and graphs are suitable for univariate analysis such as distribution and box plots, for bivariate analysis such as line, bar, and scatter plots and for multivariate analysis such as star plots and pixel-oriented representations.
Latent variable dose–response modelling of external training load measures and musculoskeletal responses in elite rugby league players
Published in Journal of Sports Sciences, 2021
Dan Weaving, Nicholas Dalton Barron, Jeremy A. Hickmans, Clive Beggs, Ben Jones, Tannath J. Scott
Another broader consideration is that due to the multidimensional aspects of both the training load and fatigue measurements (e.g. cardiovascular, neuromuscular, musculoskeletal) it can be hard to provide a parsimonious model of their dose–response relationship (Ryan et al., 2020). This is because the variables used to represent different dimensions of the training load and fatigue constructs frequently exhibit considerable multicollinearity (McLaren et al., 2017; Weaving et al., 2019). Consequently, a common approach is to conduct multiple univariate models involving each of the individual measurements (e.g. correlation between total distance and adductor squeeze strength, total distance and ankle dorsiflexion). However, univariate analysis is limited as it assumes that each of the variables are independent and also does not “capture” any information that may be included within the covariance of the datasets. As a result, those models are evaluating the relationships between individual dimensions of the construct, rather than the multidimensional construct as a whole. This can be problematic with training load and fatigue measurements, as the magnitude of covariance differs depending on the training modes prescribed over a training period (McLaren et al., 2017; Weaving et al., 2020). However, orthogonal data analysis approaches, such as singular value decomposition (SVD) (Till et al., 2016) or partial least squares correlation analysis can overcome this issue (PLSCA) (Abdi & Williams, 2013; Weaving et al., 2019). PLSCA has potential to dose–response analyses, as key relationships between datasets that both include multiple variables can be evaluated together within a single analysis. This can enable complex load and response constructs to be evaluated more effectively and visualised more simply (Krishnan et al., 2011; Weaving et al., 2019). Whilst these techniques are regularly utilised in other fields such as chemometrics and genomics (Barker & Rayens, 2003; Liquet et al., 2012), their application has been limited in sports science. Therefore, the primary aim of the current study was to evaluate the relative importance of external load variables to relate to measures of musculoskeletal fatigue response in elite rugby league players through PLSCA. A secondary aim was to assess the extent to which group level (i.e. between-subject) variable importance was applicable to each individual players own dose–response relationship.