Nabil Semmar
Institut Supérieur des Sciences Appliquées de Tunis (ISSBAT). University of Tunis El Manar, Tunis, Tunisia and Institut Méditerranéen de Biodiversité et d’Ecologie Marine et Continentale (IMBE), Aix-Marseille Université, Marseilles, France

Series: Mathematics Research Developments
BISAC: MAT027000

“Native Statistics for Natural Sciences” is a book which presents step-by-step several complementary and chained statistical tools. These tools are applied to analyze structures and variability of natural systems helping to gradually understand and control their complexity. The book is organized into a serial of chapters which are extensively illustrated by intuitive figures and simple numerical examples.

Statistics represent a large field of applied mathematics aiming to extract and analyze information from sampled data issued from complex systems or populations. Extraction of reliable information on systems requires a priori the application of strategic rules by which intrinsic variability and extrinsic limits are considered. Such strategic rules are given by sampling designs and experimental designs which are applied for open and close systems, respectively. Sampling designs presented in this book include simple random, systematic and stratified designs which are applied to estimate and control variability in open systems having different organizations or distributions. Moreover, sampling designs are appropriate tools for later biodiversity and spatiotemporal analyzes of natural systems. Experimental designs include factorial, response surface and mixture designs which are specifically applied to control systems defined by different geometrical structures. Such geometrical structures have different dimension defined by strategic values of experimental factors which could have potential effects on the studied system.

After collect of reliable experimental data by means of sampling or experimental designs, population structures, variability and working will be analyzed in different methodological steps aiming at description, comparison and prediction of quantitative or qualitative states of the studied system. Descriptive statistics aim at estimation of the unknown central and peripheral characteristics of studied system. This is carried out by means of several calculated parameters including position, dispersion, precision and shape parameters. In addition to the numerical parameters, complex system structure can be described by means of different types of graphics helping to visualize the distribution shape of the whole population. Graphical representations of sampled data include histogram, box-plot, bar, pie and stacked columns charts.

After the descriptive step, the summarized information of studied system can be compared to some reference values or to other systems. For statistical comparisons, hypothesis tests are applied using theoretical probability distributions from which the states of sampled data are concluded to be original or ordinary with well-defined error risks (or doubt levels). Hypothesis tests can be of parametric or nonparametric type and give conclusions about significant and not significant differences by reference to cut-off values provided by appropriate probability distributions. Theoretical probability distributions presented in this book include the normal, Student, Chi-2, Fisher, binomial, Poisson, hypergeometric and Pascal laws. These reference laws are used according to the quantitative or qualitative types of the sample data.

In a next statistical step, system controllability can be reached by applying link analysis between different descriptive variables. Such analyzes help to (i) detect significant factor(s) influencing system states, and (ii) formulate relationships predicting system variables in relation to intrinsic or extrinsic factors. Link analyses presented in this book include analysis of variance, linear regression and independency Chi-2 test. (Imprint: Nova)