A Mathematical Primer for Social Statistics (Quantitative Applications in the Social Sciences) 1st Edition

This gem of a book provides a concise and quite readable overview of important mathematical concepts that are important for understanding both basic and advanced statistical methods, not only for sociologists, but any practitioner of applied statistics. John Fox has successfully pulled together and integrated into a 166 page primer mathematical concepts that often appear scattered in more advanced mathematics courses, including advanced calculus courses that many users of applied statistical methods might not have taken. The book starts with an introduction and overview of matrices, linear algebra, and vector geometry. The material in this chapter is absolutely essential to anyone who wishes to use multivariate methods such as principle components analysis and should be mastered even if the reader chooses not to finish the book. The following chapter provides a practical review of differential and intgeral calculus concepts important to statistics; after a brief review of planes, functions, and limits of functions, Dr. Fox quickly reviews differentiation of functions,optimization problems involving derivatives, multivariate and matrix differential calculus, Taylor's theorem, and finally an overview of integral calculus whose concepts are important in understanding probability distributions. Chapter 3 provides an excellent introduction to mathematical statistics to include properties of various distributions and estimators, maximum-likelihood estimation, and an introduction to Bayesian inference. Chapter 4 entitled "Putting the Math to Work: Linear Least Squares Regression" closes out this primer and shows how the method of least squares and the Gauss-Markov Theorem is used to estimate regression parameters and associated statistics. All in all, this is an excellent and highly readable overview of mathematics concepts that can function to fill the "math gap" that many users of statistical methods often have due to inadequate math preparation. At ~$16, the book is a smashing bargain. Very highly recommended!

An introduction that is easy to read and understand

Has saved me from reading countless hours of linear algebra and calculus texts. A real must-have if you want to know more about what goes on "under the hood" of statistical analyses, but don't want to become a mathematician.