Bernard W. Lindgren’s Statistical Theory is an important primer in the application of statistical methods to exploratory data analysis and decision making. This comprehensive text is a comprehensive guide to the theory and techniques of professional statistical practice.
Rather than focusing on the details of technical operations, Lindgren concentrates on the conceptual framework of statistics and its role in scientific inquiry and decision making. The text is broken into eight detailed parts, each pertaining to a specific aspect of statistical theory. Each part delves into a topic using vivid examples and practical exercises, building a strong foundation in both the application of statistics and an appreciation for its abstract properties.
The book begins with an introduction to the language of statistics, which includes the basic concepts of data, probability, and random variables. This foundation is further elaborated upon in Part II, which presents the core techniques used in descriptive and inferential statistics. Among these techniques are descriptive measures such as the mean, median, and quartiles as well as methods of measurement such as hypothesis testing and correlation. The main areas of inference are outlined in Part III, with discussions of linear models, random effects, and nonlinear relationships.
Part IV discusses the application of probability theory to the design and analysis of experiments. This includes instructions on the design of studies, the extraction of useful information on variation sources, and the estimation of parameters. The core topics of probability distributions and sampling methods are explored in Part V. Part VI covers the fundamentals of statistical computing, emphasizing the use of simulation, Monte Carlo procedures, and statistical programming.
Topics from Part VII encompass the use of statistical models in everyday decision making. This section covers the concepts of risk and utility, as well as Bayesian approaches to hypothesis testing and linear programming. The final part concludes with a survey of selected topics in advanced statistics, such as the Gibbs sampler, nonparametric methods, and the analysis of variance.
Throughout the text, Lindgren’s keen insights and apt examples ensure that each topic is delivered with a free and easy accessibility. While the topics are explained in a manner that will empower even the most novice of students, the detail used throughout the book will leave readers with an admiration of the intricate beauty of statistics. From the basics of sampling to the mysteries of predictive modeling, Bernard W. Lindgren’s Statistical Theory provides a valuable guide to the world of applied statistics.
