Introduction
If you are reading this book, it is a pretty good bet that it is not because you really want to be. It is little secret that many – perhaps most – archaeologists are phobic about statistics. Most people did not go into the field of archaeology with the goal of becoming an expert in statistics or quantitative methods. We became archaeologists because we want to know about the lifeways of past people, to understand human diversity as it has played out over time, and to develop ways of making sense of the causes of this diversity. Most archaeologists, therefore, view statistics as either a necessary evil or a roadblock in the way of doing more interesting things. If conducting statistical research were really our passion, we would all be better off going into the field of statistics and not archaeology. Statistics certainly pays better, anyhow.
The goal of this book is to help archaeologists conduct quantitative analysis appropriately and to do so with a minimum of unpleasantness. Given this objective, a few things are on my side in the modern world. Above all, statistical software is now ubiquitous and is increasingly accessible to all who want it. Even in the last two decades, computers have grown almost unimaginably in both their power and affordability. Statistical software packages are now sublimely user-friendly, and market prices have dropped to near affordability for regular everyday people. Perhaps most importantly, open-source software seems poised to revolutionize our tools for quantitative analysis in terms of both the development of improved statistical models and universal availability.
The good news is that the actual mathematical calculations involved in statistical research are a thing of the past. While there are likely forlorned, undergraduate statistics students out there somewhere laboring over the calculation of a Chi-square test by hand, no one really does this sort of thing outside of the classroom setting any longer – and good riddance. Instead, virtually all calculating is now done by our statistical software packages. Obviously, this makes doing statistical research infinitely easier, faster, and more accurate. There are also many statistical tests, which are fairly commonplace today, that are so complex that they simply could not be done by hand with a dataset of any real size. Computers and statistical software packages have fundamentally reshaped the cultural disposition of the field of archaeology when it comes to our approaches to quantitative analysis. V. Gordon Childe (1944) would be proud when I say that technological determinism is alive and well in the twenty-first century.
Yet, with statistical calculation now simplified to the checking of boxes and the pushing of buttons in the graphical user interfaces of software packages, many daunting problems present themselves. Researchers must correctly choose the appropriate tests to use to accomplish a given research goal. They must know the assumptions of the statistical tests that they wish to use and ensure that their data do not violate these assumptions. And, of course, they must be able to make sense of the results! Failure on any one of these requisites of computer-aided statistical calculation would lead to meaningless findings. Picking the wrong test, checking the wrong boxes, or pressing the wrong buttons can easily lead to generation of numerical gibberish. Furthermore, statistical software packages are not capable of telling anyone that they are doing the wrong test or that they are making a mistake in how they go about using it. As smart as statistical software may be, it is currently incapable of speaking up when something is going off the rails.
This book is meant to help fill this gap in knowledge and understanding. As a disclaimer, this book provides only a relatively superficial explanation of how to calculate the statistical tests discussed in it. Instead, this book is a handbook of strategies for quantitative research in archaeology, and it is designed to help readers do the following: (1) establish ways of recognizing what their research questions and goals really are; (2) organize their data and select the statistical approaches they should consider using given their goals; (3) understand the assumptions of these statistical tests and know if one’s data are suitable for these tests given their assumptions; and (4) be aware of common problems and mistakes that occur when conducting various kinds of quantitative analysis, as well as how to recognize problematic results when they happen. As such, this book is organized around the kinds of questions that archaeologists ask and not the mathematics of statistical models.
In addition, this book is designed to be readable and, whenever possible, to keep a sense of humor. As a sophomore in college, I remember sitting in my dorm room reading my statistics textbook (I won’t say which one, but it’s still in print). It was a rare, nice spring day in central Iowa. Outside the sun was shining, birds were chirping, and happy people were playing Frisbee. Looking down at the pages of my textbook, the mathematical formulae and impenetrable blocks of text might as well have been written in Sanskrit. Now, I make no pretense that anyone really wants to read this book. I do hope, however, that it will be less unpleasant within the ecosystem of statistics manuals than was, let’s say, my undergraduate textbook. Whether or not my jokes are funny is a separate issue, but I have worked hard to make this book as free from jargon as possible and to be simple in my explanations without being simplistic.
This chapter lays out some of logical and philosophical underpinnings of this book. First, I discuss the distinction between statistics as a logical approach to thinking about quantitative observations and the mathematics that are used in the calculations of statistics: while we need math for calculation, statistics is not math. Next, I offer some basic thoughts on how the field of archaeology works in terms of quantification and statistical analysis. Finally, I consider how the field of archaeology uses quantitative analysis in approaching its research problems, and I use this discussion as a way of structuring the remainder of this book.
The distinction between statistics and mathematics
I believe that much of the math anxiety in the field of archaeology when it comes to the use of statistics may be misplaced. Of course, there is math involved in the calculation of statistics, as well as their interpretation and representation. Similarly, mathematical proofs form the foundations of the sophisticated statistical models that are in wide use today. However, statistics is really more of a logical approach to making inferences about the nature of a whole population based on a sample of that population, which (generally speaking) involves the analysis of numerical facts. While it never hurts to know some math, one need not be a math genius to do consequential statistical research.
Already, some terms warrant definition before we go further. The term population refers to the entirety of what we are interested in; in more technical terms, all individual members of a particular class phenomenon that we choose to study. In the field of biology, for example, a population might be all of the individuals belonging to a species of fish living in a pond. In the field of archaeology, populations may be many different things, though they always include all of the things belonging to a particular class of phenomenon present within some bounded context: all of the artifacts present at a site or within a stratum or feature; all of the sites in a region; all the artifacts belonging to a particular type; and other examples too numerous to list here.
While we want to know about the characteristics of the whole population, it is impractical – often impossible – and methodologically problematic to try to collect information about all individual members of the whole population. A biologist cannot catch and observe every single fish in our imaginary pond. An archaeologist cannot find and observe every single artifact at our imaginary site or, worse yet, collect information on every single artifact belonging to a type that exists on planet Earth. The term sample refers to the smaller subset of the whole population upon which we actually make observations. The biologist catches some number of fish from the pond as a sample in order to make inferences about the whole population. The archaeologist collects the artifacts from some bounded part of a site (an excavation unit, for example) in order to understand the populations of artifacts present at the site as a whole.
The issue of sampling, or how we make decisions about where we excavate, collect artifacts, and so forth, is crucially important for the field of archaeology as it is for all of the observational sciences. Unfortunately, it is beyond the scope this book to consider problems of sampling thoroughly (here Orton, 2000, provides a strong reference on this subject; see also papers in Flannery, 1976, for a classic discussion). Sampling procedures are designed to ensure that our excavations and our artifact collections accurately represent the whole populations in which we are interested. Archaeological sampling often uses some form of randomization in order to prevent the introduction of systematic bias. Thus, sampling procedures are a key element of our research designs aimed at ensuring that our samples represent our populations of interest accurately and without bias.
We collect quantitative data on the individual members of our samples through a process of systematic and repeatable observation. We do so in order to characterize the whole population by identifying patterns within the data collected on the sample. As archaeologists, we have two ways of quantifying things in our research: (1) counting objects classified as belonging to particular “types,” or other such classes of phenomena; and (2) measuring objects in standardized ways (linear measurement, mass, composition, etc.). In gross simplification, therefore, archaeology is the subfield of anthropology in which we (sometimes) dig stuff up, count it, and measure it. The fundamental purpose of these quantification procedures is to be able to make systematic comparisons between the populations of objects in different contexts, such as populations of artifacts at different sites or in different strata. And, of course, we do so by making inferences about the characteristics of populations based on our quantitative analysis of samples of those populations.
This exposition of the goals of archaeology frames the main purposes of statistics and its distinction from the broader field of mathematics: we need tools for recognizing patterns within our samples of quantitative data and to use our sample data to characterize populations. The question of what our sample data can tell us about the nature of broader populations is extremely complex and problematic. Put simply, how do we recognize patterns within our sample data? And then, how do we know that our data are not simply the result of chance? From there, how do we know if the patterning we have identified within our sample relates to the characteristics of the whole population when we can never actually observe the whole population directly? These are fundamental logical questions having to do with the characterization of a part and its relation to the whole, which involves basic questions of composition and comparability.
The great leap forward in statistical thinking occurred in the late nineteenth and early twentieth centuries when scientists such as Karl Pearson and Ronald Fisher began to think about how researchers could assess the relationships between samples and populations through the development of a better mathematical understanding of issues such as distribution, variance, and probability. How can we characterize the arrangements of values within our sample data? How variable are our data? How likely is it that the patterning evident in our sample data reflects real relationships within the population of interest and is not simply the result of chance? The field of mathematics obviously offered solutions to these problems for the likes of Pearson and Fisher in providing ways of modeling distributions and calculating numerical values for the assessment of variance and probability.
Some of these calculations, such as the calculation of standard deviations for the assessment of variance, are actually fairly simple. Others, such as the modeling of statistical distributions using mathematical functions, are quite complex. The point here is that questions about the relationship between samples and populations are really questions of logic, and math only comes into play when we undertake calculations in order to evaluate these logical questions.
So take heart if you are among the many in the field of archaeology who fear statistical research because of some deep-seated math phobia. I won’t go so far as to say that you can become a competent statistical researcher without any knowledge of math. However, I would say that you can do strong statistical research using the sophisticated software that is widely available today without understanding all of the math involved in the statistical calculations you choose. As an analogy, it is a bit like driving a car without understanding all of the details of how the internal combustion engine works.
With that said, there is still a lot that can go wrong given this situation and, as with driving a car, there are still many skills that are needed in order to achieve good results. Above all, archaeological statisticians still need to know the circumstances under which to use certain models and approaches, and this requires a working knowledge of the different kinds of data we might collect. As this book will explain in the next chapter, archaeological statisticians must know how to deal with different levels of measurement and to be able to assess some basic things about the nature of the distribution of their data.
I grant that this sounds complicated but, as with many skills, it really involves the ability to differentiate between a handful of different potential characteristics of your data and to be able to correctly pick from among a few different statistical test options. These choices also require researchers to be familiar with the underlying assumptions of the models that they use, which is again mostly a question of knowing some basic things about the level and distribution of their data. And again, while phrases like “the assumptions of statistical models” may sound intimidating, it really boils down to developing an understanding of a manageable number of relatively simple things.
This book is aimed at providing archaeologists doing statistical research with a guide to choosing which statistical approaches are appropriate given certain kinds of questions and various types of data. It also offers an overview of the assumptions behind various statistical tests and provides tips on how to avoid common errors in statistical research. Some math will come up here and there, but this is not a math book. Instead, this book is a handbook of strategies for quantitative research in the field of archaeology that focuses much more on the logical questions behind statistical inference, which is actually a simpler task than it may sound.
The role of quantitative analysis in archaeology
It is perhaps an unhappy truth for many of us that the field of archaeology relies heavily on quantification and therefore quantitative analysis. Why is this the case? Part of it has to do with the limited range of things archaeologists have access to in making observations. We conduct field research in which we document the spatial distribution of artifacts and features. We then make observations on those artifacts and features, which usually amounts to counting and measuring them in various ways. Unlike cultural anthropologists, who are able to make direct observations on the vast and complex milieu of social interactions in the human world, most archaeological research reduces to the study of the relationships between certain things and certain other things. Quantification and quantitative analysis offer ways of characterizing these relationships in systematic fashion and in ways that allow us to evaluate their significance.
To be a little more dogmatic about it, the field of archaeology is aimed at making inferences about the cultural or behavioral phenomena that happened in the past based on the relationships between things we find in the archaeological record in the present (Binford, 1983; O’Connell, 1995; Shennan, 1997; Gamble, 2015; cf. Hodder, 1991; Johnson, 2010). The first step in this process is the identification of patterning in terms of the artifacts and features we find in the archaeological record. Generally speaking, this is a two-part process: first, we seek to systematically describe or characterize the artifacts and features within some discrete units of archaeological context (sites, excavation units, strata, etc.); next, we look for patterns by making comparisons between our units of context, which hopefully hold significance for understanding variation over space and/or time. Based on the patterns we find in terms of the inter-contextual variability of the archaeological record, we generate ideas about what was going on in the past and how it changed over time.
We could be a bit simpler in our understanding of all this: as archaeologists, we find stuff at archaeo-logical sites; based on patterning among the stuff we find, we come up with explanations of the human cultural activity that went on in the past and which accounts for the patterning we have found in our stuff. By comparing patterns between different contexts, we make inferences about how these cultural activities differed between places and how they changed over time. This is, of course, a damn sight harder than it...
