**Statistics for Archaeologists: A Commonsense Approach**. Robert D. Drennan. Plenum Press, New York and London, 1996. 278 pp. $42.50 (cloth), ISBN 0-306-45327-4; $24.50 (paper), ISBN 0-306-45326-6.

Reviewed by Robert E. Dewar, Department of Anthropology, University of Connecticut, Storrs, CT 06269 USA

Introductions to statistics for archaeologists are quite varied in their style, the topics they cover, the order of presentation of material, the extent to which they detail the mathematical underpinnings of the statistical tools they present, and in the fundamental philosophy of their authors. Drennan’s book is quite explicitly shaped both by his experience teaching statistics to undergraduate and graduate students interested in archaeology, and by his approach to statistics in general. Its attractiveness to other instructors will depend in part on their reaction to Drennan’s approach to statistics, and how readily they can adapt this book to their own courses. Apart from these issues, however, there is a great deal to recommend this book. It is written in an engaging style by an author who does not hide his prejudices or his opinions, and it is consistently focused on the practical problems of archaeological analysis. Drennan assumes, for the most part, that students will be using statistics software in the course, and makes efforts to make the output of most packages comprehensible. The book’s price strikes me as low enough that I could envision asking students to purchase both it and an instructional statistics package like *Student Systat*.

The most important issue for most archaeologists selecting a text will be the extent to which it conforms to their taste in statistical approaches, and Drennan’s approach will not have universal appeal, though I am happy to say that I find it very congenial. First, his approach is explicitly and strongly influenced by John Tukey’s *Exploratory Data Analysis* (1977). Thus, he considers early in the text differing ways of describing the location of a distribution (means and modes), its spread (standard deviation and midspread), examines shapes of distributions with box and stem-and-leaf plots, and emphasizes the robustness of different ways of examining data when there are outliers. He discusses methods of standardizing data and controlling the shape of distributions with transformations. Second, and before we ever meet a "p value" , Drennan carefully discusses the nature of samples, the utility of a random sample, and the difficulties archaeologists must often face in determining just exactly what populations they are sampling, how they may be biased, and what substantively can be done about it. Finally, he emphasizes the concept of the standard error, the construction of confidence intervals, and their use in interpretation. He builds a case against reliance on tests of null hypotheses, arguing that an all-or-nothing approach to significance should be replaced with scales of increasing confidence of significance, both statistical and substantive.

The introduction discusses the problems that we all face in teaching statistics to students who are often poorly prepared in mathematics, and frequently without confidence in their abilities. He avoids presenting mathematical proofs and derivations for the statistical tools he discusses, primarily because "the language of abstract mathematics...remains utterly impenetrable to many archaeologists" (p. ix). On the other hand, he attempts to avoid presenting the tools in a "cookbook" approach. Thus, each chapter attempts to explain the basic logic of the methods presented, and always links the analysis to data through developed examples. For simpler techniques, he moves step-by-step through the calculations involved, but for more complex techniques, like the calculation of confidence intervals around regression lines, he assumes that the calculations themselves will be done by computer, and that the formulae involved are essentially irrelevant to his students. Throughout, he avoids using arcane terms derived from classical usage in statistics.

In comparison with most competing texts, Drennan presents a unique range of statistical tools - many classical tools are ignored, while others, particularly with regard to dealing with different kinds of sampling, are presented in greater detail here than in competing books. The tools are all limited to those concerned with one variable, or the relation between two variables; there are no multivariate statistics presented. Among commonly encountered techniques, he presents one and two-sample t-tests, chi-square, linear regression and Spearman’s rank correlation in detail and has a more limited discussion of ANOVA. There are briefer discussions of measures of association and the analysis of residuals. Throughout he considers the question of the robustness of the techniques to ill-shaped distributions and outliers, and offers alternatives, like analyses based on trimmed means and standard deviations, and the careful examination of bivariate plots when interpreting regressions. Unusual, but welcome, are his discussions of techniques for dealing with stratified and cluster samples.

Probably every instructor will want to supplement Drennan’s coverage, and present additional statistics or techniques. What I find tremendously appealing is the consistency of discussion throughout the volume. All of the examples link the analysis performed to the interpretations that can be made, in the context of sample size, potential bias, and substantive significance. Drennan assumes that instructors will be teaching a particular statistical software package to students in the same course that they are using this book. Depending upon the package employed, the manuals may be of great value in teaching other techniques, but standard statistics packages can give no coverage to the peculiar aspects of archaeological data, and the ways that archaeological inference and research are constrained. This is the greatest value of this book.

There are problem sets for each chapter, but there are no correct answers given, in keeping with its design for use in the classroom rather than as a stand-alone introduction. The book concludes with suggestions for further reading that reflect the tenor and some of the sources for Drennan’s approaches. There are brief reviews of texts in statistics, primarily those that focus on the EDA approach or on the details of sampling. He comments on other available introductions to statistics for archaeologists, with particular attention to the ways that they differ from his book. He concludes by saluting seven papers about statistics by archaeologists that have clearly influenced his thinking.

I am sure that none of us will ever be completely satisfied with any textbook that is not our own product, but Drennan’s text is certainly a better choice for the course I would like to teach than any of its competitors. For instructors who find exploratory data analysis and a reasoned approach to confirmatory statistics attractive, this text is certainly worth a careful review. I, at least, will be using it next semester.

Reference

Tukey, John W. 1977. *Exploratory Data Analysis*. Reading, MA: Addison-Wesley.