Statistics for linguistics with R: A practical introduction by Stefan Th. Gries is a revised version of Gries (Reference Gries2009). This work is one of a considerable number of introductory statistics books that have been published recently. This one, however, differs from the others in some important ways. First of all, it is one of the few books on statistics that is written by a linguist for linguists; another publication of this kind is Baayen (Reference Baayen2008), cited by Gries. Therefore, general principles of quantitative research discussed in it are related to aims and goals relevant to linguistic studies and supported by examples from real linguistic research. Practical guidelines referring to various aspects and stages of data analysis are illustrated with examples adapted from various sets of real (or simulated but realistic) linguistic data, which is why the surrounding explanations sound relevant and comprehensible for linguists, and the guidelines themselves can, to a large extent, be applied in a variety of linguistic studies almost as ready-to-use recipes. Having said this, I must point out that the book under review is designed more as a textbook for those who would like to learn to do statistical analysis rather than as a reference book, unlike Baayen (Reference Baayen2008) mentioned above.

Statistics for linguistics with R provides a comprehensive step-by-step guide into (i) statistical analysis of linguistic data, and (ii) using the R software package for statistical analysis (R Core Team 2014). R is a programming language and environment which is becoming more and more widely used for data analysis. Its benefits include that it is open-source (and therefore free), cross-platform, and supported by a worldwide community of users and experts which enhances its stability and steady development. One of the disadvantages of R for an inexperienced user is, however, its steep learning curve, and this is why books like the one under review here are especially useful for those who are unfamiliar with this software. Addressing readers who have little or no experience either in R or in statistics, Gries walks them (Chapter 1) through the essential steps of a quantitative study: formulating hypotheses, operationalizing variables, collecting data, determining which types of statistical analysis to apply for which hypotheses, and acquiring the necessary statistics. The mathematical background to the statistical procedures is described in enough detail to enhance the understanding of key statistical notions by a reader with little or no knowledge in this field, but briefly enough not to make the discussion overly cumbersome. Various statistical procedures relevant for each step of data analysis are then discussed and accompanied by examples of reproducible R code and supportive graphs. In Chapters 3–5 of the book the procedures mentioned in Chapter 1 are considered in more detail, with specific examples and even sample descriptions of statistic results formulated in accordance with widely accepted conventions of linguistic publications.

Chapter 2, ‘Fundamentals of R’, provides a brief instruction on how to install R and load data into it, and a concise introduction to the functions of R. The information provided should be sufficient for even a reader with no experience in R to be able to download the data referred to in the book and to run the suggested code. The introduction is, however, very succinct and covers only some of the aspects of R; other features are briefly mentioned in passing or omitted altogether. The choice of what to cover is, of course, determined by the author's preferences. Thus, for example, the function merge which is essential for combining several sets of data into one, as can often be necessary for various experimental designs, is left out from the discussion and mentioned in recommendations for further study, while some programming features of R (such as looping) are discussed rather extensively. In this sense, the chapter provides enough introductory information for the reader to comprehend the rest of the book, but with regard to R and its functionality can be used only as a starting point rather than as a reference guide: Crawley (Reference Crawley2007) or Kabacoff (Reference Kabacoff2011), for example, can be used for this purpose, the former being recommended by Gries for further study of R.

Another important aspect of Gries' book related to the above is that it works in tandem with the companion website which contains data files referred to in the book, as well as a reproducible code file from which the code examples are taken, and additional exercises for each chapter. Although one can fully understand the main content of the book without referring to the website, the code file and other files available there contain a lot of additional information such as variants of tests or plots (including three-dimensional plots which are useful for data exploration but not reproducible in print), as well as a number of examples of statistical models which are not included in the main text. In some cases, though, the main text would be clearer if it relied less on the files from the website. For example, when fundamentals of analytical statistics are introduced (Chapter 4), a whole page (161) of the discussion of which tests to use for which types of data refers to a graph that is not present in the book. In some instances, on the other hand, a more precise reference to the code file would make the text easier to follow. For example, no code is provided for generating the graph in Figure 68, to which the discussion (284–285) refers, so it is only by searching in the online code file that the reader can find the appropriate code. Chapter 5 is where the code provided in the file becomes an indispensable part of the discussion. This means, on the one hand, that much more information is packed in the chapter than its 102 printed pages would allow, but, on the other hand, that this chapter is much harder to follow than the rest of the book.

Chapters 3–5 cover three aspects (which can also be temporal stages) of quantitative research: descriptive statistics, analytical statistics, and multivariate data analysis. Chapter 3, ‘Descriptive statistics’, discusses the ways of estimating and visualising the distributions of variables of different types and measures of central tendency of different kinds of data. As in Chapter 1, relevant statistical notions such as median, quartiles, standard deviation and variance are first explained in a mathematical sense (with minimal use of jargon, though), and then the appropriate R code is discussed. Gries shows how to compute many statistical functions (for example, standard deviation) semi-manually, that is, by using a mathematical formula as R input, in addition to simply providing the name of the R function (in this case, sd). The benefits of this approach are twofold. First, it can enhance the readers' understanding of the mathematical background of statistical analysis; second, it is a convincing demonstration of powerful functionality and flexibility of R.

Chapter 4, ‘Analytical statistics’, provides an overview of hypothesis-testing methods applicable to various kinds of data. First, theoretical aspects of inferential statistics are explained and supported with relevant examples of linguistic research questions and studies. The introductory section of Chapter 4 aims to explain which statistical tests are to be used for which combinations of independent and dependent variables, although this is done, again, with reference to a visualisation that is available online only. The subsequent sections cover a number of examples of data analysis using various statistical tests many of which, as above, can be computed semi-manually in R as well as by the use of the appropriate functions.

The discussion in Chapter 4 is restricted to cases where the relations between a dependent variable and ‘maximally one independent variable’ (247) are estimated. ‘Selected multifactorial and multivariate methods’ are covered in Chapter 5. This chapter in the second edition is completely different from the corresponding chapter in Gries (Reference Gries2009). Firstly, the chapter includes a detailed discussion of theoretical aspects of regression modelling, types of models and approaches to model selection (it has to be noted here that only one of these approaches, backward selection, is considered in any detail and applied in the subsequent sections). Then, compared to the first edition, many more regression models are discussed (such as ordinal, multinomial, and Poisson regression), although the majority of the models referred to in the chapter are provided in the code file only. This seems to cover a wide variety of situations that can arise in different linguistic studies with various types of data. Realistically, however, the chapter only scratches the surface of multivariate analysis, and such crucial aspects of it as, for example, mixed effects modelling (that is, building regression models including both fixed and random effects) are barely mentioned. Some reasons for this given by the author (335–336) are that the field is not well-developed yet, and therefore there are many contradictory points of view on model selection, handling problems such as intercorrelation of random intercepts, multiple ways of centering variables, etc. To this I would add that to provide a description of mixed effects modelling at the level of comprehensibility of the rest of the book would require a whole chapter, if not a whole volume. Even restricted to a selection of methods of multivariate analysis, as it is, Chapter 5 feels much more packed with information than the previous chapters; in particular, each method is discussed in less detail in comparison to the rest of the book. The same is true of methods of hypothesis-generating statistics such as cluster analysis, which are barely skimmed over in Chapter 5.

In sum, Gries' book provides no more and no less than its title states, that is, a practical introduction into the statistical analysis of linguistic data with R. Using only the code that is provided in the book (and especially on the companion website), it is possible to solve many practical problems in various fields of linguistics, but in terms of expertise in statistical analysis the book merely cracks the door open, leaving a purposeful researcher to further study both the functionality of R and the methods of statistical analysis with a guidance of Crawley (Reference Crawley2007), Baayen (Reference Baayen2008) and many other sources mentioned by Gries. Some guidelines for further study are also outlined in Chapter 6, ‘Epilog’.

Despite the complexity of the material covered, the book is generally easy to read. In terms of navigation, though, it may be confusing because the section numbers do not include the number of the chapter, while it is included in cross-references (for example, Section 2.6.1 mentioned in the text (94), is numbered 6.1, being part of Chapter 2). This, as well as a notable number of typographical errors (especially in Chapter 5), slightly overshadow the overall very positive impression of the book. Notwithstanding this, I can hardly overestimate the importance of this publication for both novice and experienced researchers in linguistics.