Mathematical and Statistical Tools for Data Analysis: A Practical Guide to Descriptive, Inferential, and Multivariate Methods for Environmental Analysis

This work presents an in-depth exploration of the essential statistical methods and techniques for data analysis. It covers the fundamental concepts necessary for understanding statistics, as well as the mathematical parameters underlying these tools.Statistical tests form a central focus, including methods for assessing data normality and techniques for comparing populations. Classical tests such as the t-test and the Wilcoxon test are discussed, along with approaches for comparing two independent populations.Multivariate analysis is also addressed, with concepts such as the Divergence Coefficient, Enrichment Factor, and Pearson Correlation. Advanced techniques, including Principal Component Analysis (PCA) and Hierarchical Cluster Analysis (HCA), are explored, providing powerful tools for interpreting complex datasets.In sum, this work serves as a valuable resource for anyone seeking to master statistical tools and apply this knowledge across various fields of study.