Strategies for Quantitative Research begins with a discussion of data and transformations, moves to univariate and bivariate statistics, and ends with multivariate methods. It is highly readable with welcome humor and whimsical examples, as well as some interesting history. The text is evidently meant to be read through rather than worked through: it contains not a single exercise for the reader/student—a disadvantage for one attempting to put the recommended approaches into practice.
Grant McCall admirably strives to appeal to “math phobes,” and he peppers the text with apologies—using words such as “frightening” and “painful”—when he finds it necessary to delve gently into mathematics or probability. However, an unfortunate result of this accommodation is downplaying essential issues demanding such engagement.
For McCall, the goal of quantitative analysis in archaeology is to identify patterning in the archaeological record, ensure that it could not have occurred by chance, and understand how that patterning of our samples relates to the population characteristics. To these ends, he promotes classical statistical inference as the route to gaining secure knowledge, but without adequately describing the logic of the significance testing approach—perhaps for fear of alarming the math averse. Given this focus, it is inexcusable that McCall devotes only 15 words to Type I (rejection of a true null hypothesis) and Type II (accepting a false null hypothesis) errors, presents no serious discussion of statistical independence, says regression's R2 explains “variation” (an everyday term) rather than “variance” (a mathematically defined term), altogether ignores the power of the tests, and worst, fails to make clear precisely what a significance test result does and does not tell us. An α level cannot be directly converted into the probability of the validity of an hypothesis, as the book sometimes seems to suggest.
As a partial antidote to these issues, McCall's readers should be required to study George Cowgill's article, “The Trouble with Significance Tests and What We Can Do About It” (American Antiquity 42:350–368, 1977) carefully. There is insufficient room to summarize Cowgill's technical argument here, but his larger point is that it is more useful to evaluate the strength of the quantitative evidence with respect to a proposition (e.g., using estimation procedures) than to rely slavishly on significance tests that are highly influenced by sample size, especially when there is no need to make a yes or no decision (as there is usually not). As an aside, Cowgill would have strenuously objected to being labeled a processualist, as McCall does.
Insofar as it can be done with less-than-minimal mathematics, the book presents lucid discussions of both common and little-used significance tests. Unfortunately, they are accompanied by formulae that are mostly unusable because the ubiquitous Σ's never include the limits (e.g., i = 1 to n) indicating what is being summed. To its credit, the text will serve to condition readers to consider carefully whether data are normal or poisson-distributed and to choose parametric or nonparametric tests appropriately. Its extensive treatment of the underappreciated complexities of analyzing count data is a valuable contribution.
McCall's discussions of more complex methods occasionally slip into descriptions that will be opaque, especially to his math-averse audience. The Mann-Whitney U test, a nonparametric test that compares the distributions of two samples, requires calculation of a “sum of ranks” of the samples, but how one ranks and sums them is not described. With regression, one is left to wonder how one finds the standard deviation of a deleted residual value. He introduces ternary plots, which graphically depict the values of three variables that sum to a constant (typically three percentages that sum to 100), but he never describes how one reads them (which is not self-evident).
The author's treatment of multivariate methods is generally clear, and it is particularly strong with respect to factor analysis. However, his conclusion that the choice of agglomeration methods does not much matter in hierarchical cluster analysis does not align with my experience, nor does his preference for single linkage clustering. His facile put-down of Bayesian approaches does not give them nearly the credit they deserve. There is little discussion of graphics and no mention whatsoever of exploratory data analysis or Monte Carlo methods that are useful in dealing with unusual data distributions with which McCall is otherwise concerned.
In his examples, McCall's point of departure is a statistical question to be answered, not an archaeological problem to be solved. He explicitly declines to discuss interpretations of the statistical results with respect to the archaeological questions, although he apologetically offers interpretive comments on specific examples. To this reviewer, this seems most unfortunate. In my decades of teaching quantitative methods, successfully addressing an actual archaeological problem with real data using a relevant quantitative method is what has most effectively engaged both my quantitatively sophisticated and my initially math-phobic students.
