This book aims to be a relatively non-technical guide to statistical reasoning and techniques, setting out the basic ideas underlying most of the major areas of statistics and surveying the most popular statistical techniques, all this without becoming bogged down in computational or mathematical technicalities. The intended readership is graduates and researchers in the Sciences and Social Sciences that want to increase their understanding of the statistical tool that they use. In particular, the author mentions two kinds of readers that he has in mind: The diehard skeptic, who distrusts all kinds of statistical analyses, and the self-appointed expert, who often has not progressed beyond some fairly basic ideas and techniques. The mathematical prerequisite is only a reasonable knowledge of elementary algebra.

The book consists of ten chapters, with the first five chapters focusing mainly on the underlying logic of statistical reasoning and less on specific statistical techniques. The first chapter discusses the basic concepts of probability, including conditional probability, the addition and multiplication rules, and Bayes’ theorem. This is illustrated with real-life examples and the usual dice, coin and playing card examples. The second chapter is concerned with populations, samples and data summary, discussing e.g. levels of measurement, sampling techniques, and summary statistics.

Population models are the topic of the third chapter, with a focus on describing the most common probability distributions and methods for estimating the parameters of these, especially the maximum likelihood method. Chapter 4 is devoted to the frequentist approach to statistical inference, especially discussing confidence intervals and hypothesis tests, while Chapter 5 discusses Bayesian and other approaches to statistical inference.

The remaining five chapters of the book provide a closer look at specific statistical techniques, but still with a focus on the rationale and objectives of the techniques rather than on technical details. Chapter 6 discusses linear models and least squares, including correlation, simple and multiple linear regression models, model building, ANOVA, and the general linear model, as well as discussing observational versus experimental data and the design of experiments. Chapter 7 considers the assumptions of the linear regression model and how to check and remedy these, while Chapter 8 is concerned with association between variables, including partial correlations, latent variable models, and factor analysis methodology. The exploration of complex data sets is the topic of Chapter 9, using principal component analysis, canonical variate analysis, canonical correlation analysis, cluster analysis, and discriminant analysis. Chapter 10, finally, is devoted to miscellaneous special topics, such as repeated measurements, time series, extreme values, and survival data analysis.

The book is well-written, easy to read, and gives a good non-technical overview of both statistical reasoning and most of the important statistical techniques in use today, with mathematical formulas used only when necessary. It would be valuable reading for any non-statistician that wants to get deeper insights into what statistics is all about.

I have some minor complaints about the author’s discussion of frequentist versus Bayesian inference, where the author argues that Bayesian methods are today (almost) universally accepted. On the contrary, Bayesian methods are rarely used in applied statistics, due to the inherent subjectivity of Bayesian inference, which many scientists feel uncomfortable with. Since the book is aimed at scientists and social scientists, this subject should have been given a deeper discussion.

Apart from this minor complaint, this book should serve as a useful non-technical guide to statistical reasoning and techniques.

Andreas Rosenblad (andreas.rosenblad@ltv.se) is a Ph. D. in statistics graduated from the Division of Statistics, Department of Information Science, Uppsala University (http://www.dis.uu.se/Statistik/). He is currently working as a biostatistician at the Västerås Center for Clinical Research (part of Uppsala University) at Central Hospital in Västerås, Sweden. His primary research interest is in bootstrap methods and quantile regression with applications in biostatistics.