Abstract
For many students of archaeology, part of the appeal of the social sciences may be to avoid math. Those of us who employ quantitative approaches within our research are often used to seeing eyes glaze when we explain our research to students and colleagues. Despite these reservations, quantitative techniques have become an essential part of archaeological research. Even those who do not employ quantitative approaches have an increasing need for math competency in order to assess the work of fellow scholars. Strategies for Quantitative Research not only acknowledges these facts, but it also embraces and makes light of them. McCall seeks to fill a void within the statistical literature. Instead of spending time showing how to solve statistical formulas, McCall wants to focus on how to apply these tests and the questions they can help us answer. In his introduction, he points out that in the modern era, none of us need break out pen and paper to calculate statistics. Yet, the majority of quantitative textbooks for archaeologists assume exactly that (Drennan, 2010; Kachigan, 1986; Thomas, 1986). For most of us, working statistics involves logging into our computers and hitting a few quick buttons. Calculations which for previous scholars were tedious and laborious (or involved the use of the dreaded “cards” in early computing) can be completed in seconds. This book has no calculations to solve or sample problems to work through, as it says in the title, this book provides strategies to approach quantitative research confidently and competently.
This book consists of 10 chapters plus a brief preface and totals 224 pages. It is designed to be read cover-to-cover, straight through, as there are frequent callbacks to previous examples, techniques, and terms. Picking out a chapter from the middle to investigate a particular concept is only recommended for those with some statistics background. From the perspective of a professor, this book has a major advantage over others, it is short. Chapters are rarely over 30 pages, which I appreciated, as getting undergraduates to read chapters much longer than this, is a challenge. However, with this brevity comes a tradeoff, it covers A LOT, very quickly.
The author begins with a short preface that explains why this book was needed, much of which I discussed in the previous paragraphs. McCall argues that the hard part of archaeological statistics is not the math but choosing the right test; modern technology has made the calculations easy. However, an unfortunate side effect of the fast-computing approach to statistics has been a compounding of the black-box or cookbook approach to statistics, as students (and professionals as well) can run a huge array of tests without asking if we should. McCall’s book seeks to address this issue.
Chapter 1 is an Introduction which expands on the themes of the preface. In addition, it gives what those who have taught statistics before may recognize as, the “don’t panic we are going to ease into the math slowly” lecture. He begins by reinforcing the fact that this book is not about doing math, that’s what computers are for, this book is about “finding patterns by making comparisons,” using statistics to help (p. 5). He reassures the reader that humans are innately good at identifying patterns, statistics just help us to make sure they are significant. The chapter gradually pivots to define basic terms of the trade: population, sample, distribution, variance, null hypothesis, and so on and does so in plain terms that are clear and concise. The chapter concludes with the core theme, how do we choose what we want to test? The remainder of the book is dedicated to providing enough knowledge to make us confident in our choices.
Chapter 2 is where the book really dives in to its instruction, what McCall calls “knowing your data” (p. 15). This chapter covers standard ways of describing data form (nominal, ordinal, interval, ratio, and count data) and probability distributions. There is a particularly amusing aside to explain the Poisson distribution as it relates to mule kick deaths in the Prussian Army (pp. 31–32). This chapter goes further, than many introductory statistics books, by emphasizing that the way we collect and organize our data determines the kinds of questions we can answer with it. There are two handy charts in this chapter which students will be sure to appreciate. The first lists common archaeological data types by their levels of measurement (Table 2.1, pp. 21–22), while the second is flow chart to help identify the kinds of statistics you can use with your data type (Figure 2.11, p. 39).
Building off what was learned in Chapter 2, Chapters 3 and 4 cover data transformations, standardizations, and descriptive statistics. In Chapter 3, the coverage of transformation and standardizations receives more coverage than one often sees in archaeological textbooks and drives home the limitations associated with each data type. This chapter provides helpful techniques for how we can answer the questions we want while respecting the limits of our data. In Chapter 4, coverage of descriptive statistics is brief, but covers the essentials, and uses terminology that will allow students to easily transition to creating graphs in a statistical software packages.
Chapter 5 is intense. McCall calls this chapter hypothesis testing using univariate data. In the span of 30 pages (including a works cited and an enjoyable aside about William S Gosset), it covers what many archaeological stats courses cover in nearly a semester (pp. 70–100). Within this chapter is all the instruction this book provides for chi-square, Fisher’s exact, Phi, Cramer’s V, t-tests, analysis of variance, Mann–Whitney U, Kolmogorov–Smirnov, Kruskall–Wallis, eta-squared statistic, and the difference between one- and two-tailed statistical tests. Although the introduction thoroughly warns that this book will not spend time on how to calculate statistics, I was still shocked by how fast McCall moves through this information. In particular, the coverage of the limitations associated with these basic tests seemed thin.
In contrast to Chapter 5, Chapter 6 is the longest chapter in the book and covers only two core topics: linear regression and correlation or bivariate analysis. This chapter slowly and carefully moves through these techniques providing in-depth information as to the kinds of questions we can explore with these methods. It provides many visualizations of data distributions and does an excellent job of addressing solutions for common problems in the use of these techniques.
Chapters 7 and 8 cover multivariate analysis including data reduction, pattern recognition (Chapter 7), and hypothesis testing (Chapter 8). McCall notes that univariate and bivariate statistical analyses are problematic, as rarely are human activities explained well using only one or two variables. These chapters are where the book moves beyond your introductory level archaeological statistics course and into material not often covered in a standard course (or covered only at the very end). McCall assures us that multivariate analysis is not necessarily more complex or more difficult to complete and can be a powerful method of understanding complex datasets. Chapter 7 covers factor analysis and principle component analysis (and their variants) in excellent detail, with strong examples and clear diagrams. Chapter 8 covers multiple regression and partial correlation. McCall jokes many archaeologists may never have a need of these techniques, which is likely why this chapter is less than 20 pages. Although brief, this chapter is well written and full of clear, helpful examples that illustrate when we should consider applying these techniques or at the very least why it’s important to understand what they do.
Chapter 9 is the final, of what I would call, the core-content chapters. It covers cluster analysis and discriminate function analysis. However, many archaeological students are not inclined to dive into the previously discussed multivariate analyses cluster and discriminate function analysis seem to have particular allure. The ability to test our classificatory schemes, create new ones, or identify how we should group the things we want grouped is an ongoing area of concern. McCall does a solid job of explaining what each of these techniques is doing and why they are different. His clear language approach and the examples in this chapter do a very nice job of demystifying this topic. I appreciated his emphasis on applying too much meaning to classificatory schemes. Techniques, like discriminate function analysis, are only as powerful as the researchers who use them. McCall reminds readers that multivariate analyses must be paired with a “robust body of referential knowledge” in order to have value (p. 208).
Chapter 10 is a 10-page conclusion. This is very much a statistics book with a point of view and nowhere is that more obvious then in this conclusion. Most statistical textbooks do not have conclusion chapters, something the author acknowledges. McCall takes an almost philosophical tone as he reflects upon the growth of statistical methods in the social sciences, our fits and starts, and shames. He states that while anthropologists rarely agree on what our data mean, the ability to have some concrete way of describing what we see is still important (p. 212). He notes that growths in technology and open source computing have helped democratize statistics. Thirty years ago, the ability to do a complex model was reserved for the elite few who had access to the expensive hardware and software that could complete the task. Today open source software is becoming more powerful, and more anthropologists will be able to experiment with these methods. He closes with this idea, statistics are not perfect, and they cannot help us answer all of your questions, but they can provide a powerful tool for our research.
There are a few areas in which I think this volume could be improved. Chapter 5 is simply too short. Although the brevity of this volume is mostly a positive trait, some key concepts and limitations of the tests in this chapter receive less attention then they deserve. However, by no means, the most exciting or cutting-edge techniques are still widely used in the current publications and are often a go-to for students.
The box in Chapter 10 discussing the author’s suspicion around Bayesian statistics is well taken, but I think overstated. Bayesian models are currently a hot trend in quantitative archaeology circles (Alberti, 2015; Burley and Edinborough, 2014; Feranec and Kozlowski, 2016; Otárola-Castillo and Torquato, 2018; Rieth and Athens, 2017), and the author is correct that any new tool will have those who use it poorly. However, rather than blame our tools, I think that we should acknowledge that any statistical technique, in the wrong hands, can be abused (Huff, 1993). Any new application of a technique should be utilized with caution but I think Bayesian models can offer us an alternative to null hypothesis testing that is worth pursuing (Otárola-Castillo and Torquato, 2018).
My overall impression of this book is positive. It provides a refreshing approach to an often-boring subject and does it with clear concise language. It uses terminology that will make opening a statistical programming package less intimidating even for the most rudimentary of students. This acknowledgement of the language divide between archaeologists and statistics programs will lead to fewer students running out the door when they open the software.
This book’s largest strength is in its general mirth for the subject. McCall provides numerous, easy to understand examples addressing archaeologists love of beer, mule kick deaths in the Prussian army, and calculating the volume of coffee cups based off rim size. Although he has many archaeological examples as well, these injected points of silliness help to keep the book moving. Statistics books will never be enjoyable to read for any but the most diehard math nerds, but McCall has certainly done his best to make this one just a little more fun.