Quantitative Analysis in Archaeology E-Book

Todd L. VanPool

• Herausgeber: John Wiley & Sons
• Kategorie: Geisteswissenschaft
• Sprache: Englisch

Seitenzahl: 605

Veröffentlichungsjahr: 2011

Beschreibung

Quantitative Analysis in Archaeology introduces the application of quantitative methods in archaeology. It outlines conceptual and statistical principles, illustrates their application, and provides problem sets for practice. 

• Discusses both methodological frameworks and quantitative methods of archaeological analysis
• Presents statistical material in a clear and straightforward manner ideal for students and professionals in the field
• Includes illustrative problem sets and practice exercises in each chapter that reinforce practical application of quantitative analysis

Leseprobe

Table of Contents

Cover

Table of Contents

Half title page

Title page

Copyright page

Dedication

Tables

Figures

Equations

Acknowledgments

1 Quantifying Archaeology

2 Data

Scales of Measurement

Validity

Accuracy and Precision

Populations and Samples

3 Characterizing Data Visually

Frequency Distributions

Histograms

Stem and Leaf Diagrams

Ogives (Cumulative Frequency Distributions)

Describing a Distribution

Bar Charts

Displaying Data like a Pro

Archaeology and Exploratory Data Analysis

4 Characterizing Data Numerically: Descriptive Statistics

Measures of Central Tendency

Measures of Dispersion

Calculating Estimates of the Mean and Standard Deviation

Coefficients of Variation

Box Plots

Characterizing Nominal and Ordinal Scale Data

5 An Introduction to Probability

Theoretical Determinations of Probability

Empirical Determinations of Probability

Complex Events

Using Probability to Determine Likelihood

The Binomial Distribution

Probability in Archaeological Contexts

6 Putting Statistics to Work: The Normal Distribution

7 Hypothesis Testing I: An Introduction

Hypotheses of Interest

Formal Hypothesis Testing and the Null Hypothesis

Errors in Hypothesis Testing

8 Hypothesis Testing II: Confidence Limits, the t-Distribution, and One-Tailed Tests

Standard Error

Comparing Sample Means to µ

Statistical Inference and Confidence Limits

The t-Distribution

Hypothesis Testing Using the t-Distribution

Testing One-Tailed Null Hypotheses

9 Hypothesis Testing III: Power

Calculating β

Statistical Power

Calculating Power: An Archaeological Example

Power Curves

Putting It All Together: A Final Overview of Hypothesis Testing

10 Analysis of Variance and the F-Distribution

Model II ANOVA: Identifying the Impacts of Random Effects

Model I ANOVA: The Analysis of Treatment Effects

A Final Summary of Model I and Model II ANOVA

ANOVA Calculation Procedure

Identifying the Sources of Significant Variation in Model I and Model II ANOVA

Comparing Variances

11 Linear Regression and Multivariate Analysis

Constructing a Regression Equation

Evaluating the Statistical Significance of Regression

Using Regression Analysis to Predict Values

Confidence Limits around Yˆ for a Given Xi

Estimating X from Y

The Analysis of Residuals

Some Final Thoughts about Regression

12 Correlation

Pearson’s Product-Moment Correlation Coefficient

Spearman’s Rank Order Correlation Coefficient

Some Final Thoughts (and Warnings) about Correlation

13 Analysis of Frequencies

Determining the Source of Variation in a Chi-Square Matrix

Assumptions of Chi-Square Analysis

The Analysis of Small Samples Using Fisher’s Exact Test and Yate’s Continuity Correction

The Median Test

14 An Abbreviated Introduction to Nonparametric and Multivariate Analysis

Nonparametric Tests Comparing Groups

Multivariate Analysis and the Comparison of Means

15 Factor Analysis and Principal Component Analysis

Objectives of Principal Component and Factor Analysis

Designing the Principal Component/Factor Analysis

Assumptions and Conceptual Considerations of Factor Analysis

An Example of Factor Analysis

Factor Analysis vs. Principal Component Analysis

16 Sampling, Research Designs, and the Archaeological Record

How to Select a Sample

How Big a Sample is Necessary?

Some Concluding Thoughts

References

Appendix A  Areas under a Standardized Normal Distribution

Appendix B  Critical Values for the Student’s t-Distribution

Appendix C  Critical Values for the F-distribution

Appendix D  Critical Values for the Chi-Square Distribution

Appendix E  Critical Values for the Wilcoxon Two-Sample U-Test

Index

QUANTITATIVE ANALYSIS IN ARCHAEOLOGY

This edition first published 2011

© 2011 Todd L. VanPool and Robert D. Leonard

Blackwell Publishing was acquired by John Wiley & Sons in February 2007. Blackwell’s publishing program has been merged with Wiley’s global Scientific, Technical, and Medical business to form Wiley-Blackwell.

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Library of Congress Cataloging-in-Publication Data

VanPool, Todd L., 1968-

 Quantitative analysis in archaeology Todd L. VanPool, Robert D. Leonard.

p. cm.

 ISBN 978-1-4051-8951-4 (hardback : alk. paper) – ISBN 978-1-4051-8950-7 (pbk. : alk. paper) – ISBN 978-1-4443-9017-9 (ebk)

 1. Archaeology–Methodology. 2. Quantitative research. 3. Archaeology–Research. I. Leonard, Robert D. II. Title.

 CC75.7.V36 2010

 930.1072–dc22

2010030199

A catalogue record for this book is available from the British Library.

To Connie Woebke and Glenn McCoy, two teachers who taught TVP what counts

To Grandmas Maggie and Ferne, for helping RDL learn his numbers

Acknowledgments

First and foremost, we express our gratitude to the many students who have contributed to this volume through their participation in our Quantitative Methods in Anthropology classes. Our interaction with them has been the inspiration for both the structure and contents of this book. Robert R. Sokal’s and F. James Rohlf’s excellent text Biometry, has, no doubt, influenced this volume, given that we have taught from it for years. We also gratefully acknowledge the helpful comments of Drs. R. Lee Lyman and Gordon F.M. Rakita, as well as two anonymous reviewers. They read drafts of this volume and helped strengthen it tremendously. We thank Drs. Christine S. VanPool and Marcus Hamilton for their useful comments and suggestions through the years. Finally, Robert Leonard thanks Drs. Donald Grayson and Loveday Conquest, and Todd VanPool thanks Dr. Stephen R. Durand for introducing us to quantitative methods. Thank you all so very much!

1

Quantifying Archaeology

If archaeologists do anything, it is count. We count stones, bones, potsherds, seeds, buildings, settlements, and even particles of earth – virtually everything that constitutes the archaeological record. We also measure essentially everything that we touch. Length, weight, thickness, depth, volume, area, color, and height are only some of the simplest measurements taken. We are exaggerating only slightly when we state that our predilection for counting and measuring ensures fame (if not fortune) to anyone who brings to our attention some forgotten or never known aspect of the archaeological record that archaeologists should be counting and/or measuring.

Most archaeologists are in the counting and measuring business not for its own sake, but to help us fashion a meaningful perspective on the past. Quantification isn’t required to back up every proposition that is made about the archaeological record, but for some propositions it is absolutely essential. For example, suppose we proposed an idea about differences in Hallstatt assemblages in Central Europe that could be evaluated by examining ceramic variation. Having observed hundreds of the pots, we could merely assert what we felt the major differences and similarities to be, and draw our conclusions about the validity of our original idea based upon our simple observations. We might be correct, but no one would take our conclusions seriously unless we actually took the relevant measurements and demonstrated that the differences and/or similarities were meaningful in a way that everyone agreed upon and understood. Quantification and statistics serve this end, providing us with a common language and set of instructions about how to make meaningful observations of the world, how to reduce our infinite database to an accurate and understandable set of characterizations, and how to evaluate differences and similarities. Importantly, statistics do this by using a framework that allows us to specify the ways in which we can be wrong, and the likelihood that we are mistaken. Statistics consequently provide archaeologists with a means to make arguments about cause that will ultimately help us construct explanations.

Statistical thinking plays an important role in archaeological analysis because archaeologists rely so heavily on samples. The archaeological record contains only the material remains of human activity that time and the vagaries of the environment (including human activity) have allowed to be preserved. The artifacts, features, and other material manifestations of human behavior that enter the archaeological record are only a small subset of those originally produced. Funding constraints, time limits, and our emphasis on conserving the archaeological record further dictate that archaeologists generally recover only a small subset of those materials that have been preserved. Thus, we have a sample of the material remains that have been preserved, which is only a sample of all of the materials that entered the archaeological record, which is only a sample of all of the materials that humans have produced.

Archaeologists are consequently forced to understand and explain the past using imperfect and limited data. Connecting our sample to a meaningful understanding of the past necessitates the application of a statistical framework, even when quantitative methods are avoided as part of a purportedly humanistic approach. It is only through statistical reasoning, no matter how implicit, that any form of general conclusion can be formed from the specifics of the archaeological record. Regardless of whether an archaeologist studies the social differentiation of Cahokia’s residents, subsistence shifts during the Mexican colonial occupation of New Mexico, or the religious systems of Upper Paleolithic cave dwellers, they are going to employ a statistical approach, even if they don’t acknowledge it. Quantitative methods allow us to make this approach explicit and make our arguments logically coherent and thereby facilitate their evaluation. Even the most ardent humanist should appreciate this.

As important as statistics are, we must remember that they are only tools, and subservient to theory. Our theoretical perspectives tell us which observations are important to make and how explanations are constructed. Statistics are useful only within this larger context, and it is important to remember their appropriate role. It is also important to recognize that the use of statistics does not equal science. The historical confluence of events that brought statistics, computers, the hypothetico-deductive method, and the theoretical advances of the New Archaeology to our discipline in a relatively brief span of time in the 1960s make it appear that they are inseparable. Nothing could be farther from the truth. While this might seem self-evident, at least one quite popular introductory archaeology textbook overstates the relationship, as a discussion of the role of science in archaeology begins with a brief discussion of statistics. Not the role of theory, not the scientific method, but statistics! Statistics do not a science make, and statistical analyses conducted in the absence of theory are merely vacuous description.

This book approaches quantification and statistics from the perspective that they are a simple set of tools that all competent archaeologists must know. Most readers will use statistics innumerable times throughout their career. Others may never calculate a mean or standard deviation willingly, but at least they will know the basics of the statistical tool kit. Choosing not to use a tool is fine. Remaining ignorant is unfortunate and unnecessary. At the very least, knowledge of statistics is needed to evaluate the work of others who do use them.

So, why should two archaeologists write a book about statistics when there are thousands of excellent statistics books in existence? Here are our reasons in no particular order. First, few of us entered archaeology because we wanted to be mathematicians. In fact, many archaeologists became interested in archaeology for very humanistic (or even romantic) reasons, and many avoided math in school like the plague. There definitely needs to be a book that is sympathetic to those coming from a non-quantitative background. We seek to achieve this goal by presenting the clearest description of techniques possible, with math no more complicated than simple algebra, but with enough detail that the reader will be able to actually understand how each technique operates.

Second, most statistics textbooks use examples that are not anthropological, and are very hard to relate to the archaeological record. While knowledge of dice examples is useful when playing craps in Las Vegas, the implications of these examples for archaeological studies are often difficult to decipher. Our examples are almost exclusively archaeological, and we hope that they provide good illustrations of how you might approach various archaeological data sets from a statistical perspective.

Third, archaeologists do not always need the standard set of statistics that are presented in popular textbooks. Some techniques of limited importance to archaeology are overemphasized in these texts, while other extremely important statistical methods are underemphasized or do not appear at all.

Fourth, it is our observation that many degree-granting programs in archaeology focus solely on computer instruction in quantitative methods rather than on the tried and true pencil and paper method. We have nothing against the use of computers and statistical software, as long as it is done by people who first learn statistical techniques by putting pencil to paper. However, our experience has shown us that when all training is focused on using a statistical package instead of learning a statistical method, the computer becomes a magic black box that produces “results” that students who don’t know what actually happened inside the box are (hopefully) trained to interpret. This lack of understanding causes confusion and, more importantly, embarrassment when insupportable or erroneous conclusions are drawn. These students need a friendly text to which they can refer to help clarify how the quantitative methods work and how their results should be understood.

Finally, many disciplines use samples, but few are as wholly reliant on them as is archaeology. This in turn means that the application of quantitative reasoning has special significance in archaeological research that needs to be explored if we are to produce the best archaeological analyses we can. This consideration is absent from statistical texts written for general audiences, but should be central to those specifically for archaeologists. It certainly will be central to the discussions that follow this chapter.

Ultimately, our goal is to illustrate the utility and structure of a quantitative framework to the reader (i.e., you), and to provide a full understanding of each statistical method so that you will understand how to calculate a statistical measure, why you would want to do so, and how the statistical method works mathematically. If you understand these issues, you will find each method to be intuitively meaningful and will appreciate the significance of its assumptions, limitations, and strengths. If you don’t understand these factors, your applications will be prone to error and misinterpretations, and, as a result, archaeology as a discipline will suffer. Hopefully, this text will serve to aid you, gentle reader, as we all work to accomplish our collective goals as a discipline.

Practice Exercises

1 Identify five attributes of artifacts or features that archaeologists routinely measure. Why do archaeologists find these attributes important? What information do they hope to gain from them?

2 Identify an archaeological problem that might interest you. What attributes of archaeological materials might be useful for your research problem? Why would you select these attributes as opposed to any others that might be possible?

2

Data

Quantitative methods and statistics are applied to data. Data are observations, not things. Data are not artifacts. They are not pots or stones or bones or any other component of the phenomenological world. We build data by making systematic observations on pots and stones and bones. What constitutes data is determined by our research questions and theoretical perspective. We create data to serve a purpose defined by a pre-existing intellectual framework. Most certainly, the real world exists in terms of various arrangements of matter and energy, but that real world is not to be confused with the observations that we make about it.

In addition to the theoretical perspective that we bring to bear and the research question we address, the tools with which we look at the world also influence what our data look like. As Gulliver’s travels taught us, the world looks very different to Lilliputians and Brobdingnags, and the view is very different when the instrument we hold to our eye switches from a telescope to a microscope. There is no “high court” of archaeologists that makes the rules about what kind of observations we are restricted to make or what tools we use to make them. Data are what we determine them to be. Certainly, there is a range of observations that many archaeologists agree are useful for addressing particular problems. Michael Shott (1994: 79–81), for example, outlines a “minimum attribute set” for flaked stone debitage that archaeologists have found to be consistently useful for answering the questions they frequently ask. His list includes the “usual suspects” of weight, cortex, platform angle and raw material, among others. Despite the utility of these attributes for addressing certain questions, we, as archaeologists, are by no means restricted to looking at the world from a single perspective or using only these attributes. Shott (1994) in fact discusses how scholars have employed these and other attributes using a variety of perspectives to answer many different questions.