Suggested Reading

Bibliographic citations have been avoided in this book in order to streamline the presentation and because careful tracing of the intellectual pedigree of many of the ideas and techniques discussed here is a scholarly endeavor in itself, and one not comfortably combined with an introduction to their appli-cation in archaeology. The books and articles listed below, however, are places to go for further information on statistics in archaeology. The litera-ture on statistics in archaeology has become very large, and the list below is both very short and slanted toward statistics in general more than toward statistics specifically in archaeology. Consequently, a large number of per-fectly relevant references have not been included-the selection is idiosyn-cratic rather than comprehensive. Some of the items included are relatively new; some are not so new. Some are included because they share the general outlook of this book (and indeed in some cases are the specific inspiration for it); some, because they complement it (which is to say they take a different perspective).

GENERAL STATISTICS BOOKS

Exploratory Data Analysis, by John W Tukey (Reading, MA: Addison-Wesley, 1977, 688 pages), is one of the classic presentations of an approach to statis-tics from which much in this book is derived, and its author is the father of the approach. Not surprisingly, there is a great deal more to exploratory data analysiS (EDA) than has been presented in this volume, and readers who would like to go directly to the source to find out about it should read Tukey's book, which is a full-scale introductory text in EDA. Although EDA is now more than 20 years old, only parts of the prescription Tukey laid out for EDA have been much applied in archaeology (and even those parts that have been do not yet constitute the "standard" statistical approach in the archaeological literature). Many of the techniques Tukey discusses in his

269

270 SUGGESTED READING

book were intended to be easily accomplished with pencil and paper or, at most, with a calculator, but more widespread availability in the most com-monly used computer statpacks would undoubtedly encourage greater use of EDA techniques in archaeology and in other fields.

Exploratory Data Analysis, by Frederick Hartwig and Brian E. Dearing (Bev-erly Hills, CA: Sage Publications, 1979, 83 pages), is a brief presentation of the basic techniques of EDA. It nevertheless includes a number of EDA topics not covered in this volume.

Applications, Basics, and Computing of Exploratory Data Analysis, by Paul F. Velleman and David C. Hoaglin (Boston: Duxbury Press, 1981,354 pages), is yet another introduction to EDA techniques, less formidable than Tukey's and more comprehensive than Hartwig and Dearing's.

Understanding Data, by Bonnie H. Erikson and 1. A. Nosanchuk (Toronto: McGraw-Hill Ryerson, 1977, 388 pages), is an introductory statistics text that combines EDA with more traditional statistical approaches. It advocates two different and complementary kinds of work with numbers (exploratory and confirmatory), keeping the two strongly separated and emphasizing the differences between their goals. The presentation is especially accessible and free of jargon and abstract mathematics.

Introduction to Contemporary Statistical Methods, by Lambert H. Koopmans (Boston: Duxbury Press, 1987, 683 pages), also combines EDA with more traditional statistics. A very wide range of methods is covered, and the logic behind the methods is presented in more abstract mathematical terms than in most of the other books listed here. Instead of focusing on the difference between exploration and confirmation throughout the book, Koopmans con-siders statistical exploration at the beginning, and then complements the discussion of the usual significance testing techniques with a wide array of robust techniques suitable for use on data that present problems for the usual techniques.

Nonparametric Statistics for the Behavioral Sciences, by Sidney Siegel (New York: McGraw-Hill, 1956, 312 pages), is a classic presentation of a full array of robust techniques for evaluating Significance, that is, ones that are not much affected by things like very asymmetrically shaped batches for which means and standard deviations are not useful. Many of these techniques require special tables in which to look up the results, and Siegel provides them.

Sampling Techniques, by William G. Cochran (New York: John Wiley &: Sons, 1977, 428 pages), describes itself (quite accurately) as "a comprehensive account of sampling theory." It is, perhaps, the ultimate source on this sub-ject. Estimating means and proportions, sample selection, stratified sam-

SUGGESTED READING 271

pling, cluster sampling, sampling with and without replacement, determining necessary sample size, and many other topics are covered in detail. The full logic behind the techniques presented is given in mathematical terms.

Elementary Survey Sampling, by Richard L. Scheaffer, William Mendenhall, and Lyman Ott (Boston: Duxbury Press, 1986, 324 pages), covers much of the same ground that Cochran does. The presentation is largely in terms of abstract mathematics, but it is considerably less detailed and formidable than Cochran's.

INTRODUCTIONS TO STATISTICS FOR (AND OFTEN BY) ARCHAEOLOGISTS

Refiguring Anthropology: First Principles of Probability and Statistics, by David Hurst Thomas (Prospect Heights, IL: Waveland Press, 1986,532 pages), is an introductory statistics text speCifically for anthropologists (including archae-ologists). The approach is purely traditional (that is, it does not incorporate an EDA perspective or techniques), and some rules are laid down that this volume has argued against, but numerous robust methods are discussed. There are abundant examples of the application of all the techniques pre-sented to real data from archaeology, cultural anthropology, and biological anthropology.

Digging Numbers: Elementary Statistics for Archaeologists, by Mike Fletcher and Gary R. Lock (Oxford: Oxford University Committee for Archaeology, 1991, 187 pages), applies basic statistical techniques (both traditional and EDA) specifically to archaeology. The presentation is informal, avoids jargon, and is designed to be very accessible, especially to those suffering math anxiety.

"Regional Sampling in Archaeological Survey: The Statistical Perspective," by Jack D. Nance (Advances in Archaeological Method and Theory 6:289-356, New York: Academic Press, 1983), attempts a comprehensive discussion of spatially-based sampling in the context of regional survey, although many of the same issues arise at smaller spatial scales as well. The statistical tech-niques involved in sample selection and in making estimates about the popu-lation are described, with special emphasis on cluster sampling. Numerous concrete and practical problems in archaeology are discussed with both hy-pothetical and real examples.

Quantifying Archaeology, by Stephen Shennan (Edinburgh: Edinburgh Uni-versity Press and San Diego, CA: Academic Press, 1988, 364 pages), is an introductory statistics text (and more) specifically for archaeologists. Mostly

272 SUGGESTED READING

traditional statistical methods are covered, but some EDA techniques are also included. Shennan goes beyond basic statistical principles to deal with multi-variate analysis (with emphasis on multiple regression, clustering, and prin-cipal components and factor analysis). Methods for estimating population means and proportions are presented (not usual in introductory statistics books) and the special issues that sampling raises in archaeology are dis-cussed.

Exploratory Multivariate Analysis in Archaeology, by M. J. Baxter (Edinburgh: Edinburgh University Press, 1994, 307 pages), contains only a very brief review of basic statistical techniques (including the fundamental ones from EDA). Its aim is to consider more advanced topics in multivariate analysis-techniques that can deal Simultaneously with the patterns of relationships among numerous variables. Extended treatment is given to principal compo-nent analysis, correspondence analysis, cluster analysis, and discriminant analysis, and numerous examples of multivariate analyses of real archaeologi-cal data are woven into the explanations.

ARCHAEOLOGISTS CONSIDER STATISTICS IN OUR DISCIPLINE

"The Trouble with Significance Tests and What We Can Do about It," by George L Cowgill (American Antiquity 42:350-368, 1977), makes the case for an attitude about significance testing that has inspired much in the per-spective taken on this subject in this volume. It is a distinctly different view than is often adopted in introductory statistics texts-indeed it is branded as heresy by the rules often found in introductory statistics texts. This article is fundamental for those interested in a fuller presentation of the arguments that archaeologists will often find it useful to use samples directly to make estimates about populations and that it is usually a mistake for archaeologists to force significance tests into the mold of a yes-or-no decision. Cowgill's suggestions about the most useful ways to approach these issues in archaeol-ogy go well beyond what is presented in this volume, which has stopped at the point where the information commonly provided by computer statpacks imposes a limitation.

"A Selection of Samplers: Comments on Archaeo-statistics," by George L Cowgill [In Sampling in Archaeology, edited by James W Mueller (Tucson: University of Arizona Press, 1975, pp. 258-274)], prefigures some of the issues Cowgill argues more fully in his later paper (above), and focuses especially on sampling, criticizing many of what he sees as erroneous notions that appear in other papers in the same volume.

SUGGESTED READING 273

"On the Structure of Archaeological Data," by Mark S. Aldenderfer [In Quanti-tative Research in Archaeology: Progress and Prospects, edited by Mark S. Aldenderfer (Newbury Park, CA: Sage Publications, 1987, pp. 89-113) 1, is a discussion of the fundamental nature of data in archaeology, the position that numbers occupy in such data, and the implications that this has for how we think about and analyze data. The other articles listed below (and other interesting ones as well) all appear in this same volume.

"Quantitative Methods Designed for Archaeological Problems," by Keith W Kintigh (in Aldenderfer, pp. 126-134), discusses the issue of the extent to which standard statistical techniques and those borrowed directly from other disciplines are suited to the particular needs of archaeology.

"Simple Statistics," by Robert Whallon (in Aldenderfer, pp. 135-150), stresses the importance of exploring the patterns in numbers in batches before pro-ceeding to more complicated analyses.

"Archaeological Theory and Statistical Methods: Discordance, Resolution, and New Directions," by Dwight W Read, and "Removing Discordance from Quantitative Analysis," by Christopher Carr (in Aldenderfer, pp. 151-243), try to place archaeological data analysis firmly in a broader context. Both authors are concerned that data analysis is too often conceived and carried out in isolation from the theoretical questions that analysis aims to help answer. As a consequence, "discordance" between data, analysis, and theory arises and seriously impedes the archaeological endeavor.

Adjacent values, 42 Amounts, 66 Analysis of variance, 171-177 ANOVA,I71-177 Associated probability; 158 Assumptions and robust methods

analysis of variance, 181-182 chi-square 196-198 error ranges, 134-137, 181-182 rank correlation, 233 regression, 222-225 t test, 164-165

Asymmetry: see Symmetry Average, 17-19

Balances, 66 Bar graph, 71 Batches, 3-4

center of: see Level of a batch level of: see Level of a batch multiple peaked, 13-15,24-26 shape of: see Shape of a batch spread of: see Spread of a batch two-peaked,13-15,24-26

Be Careful How You Say It analysis of variance, 180 chi-square, 192 error ranges, 128 regression, 218 t test, 158 trimmed mean, 137

Best-fit straight line, 209-212 Bias, 88-93,112-114,261-267 Bimodality: see Peaks, multiple Box-and-dot plot, 39-44

Index

Bullet graph, 150-154, 169-171, 185-187 Bunches: see Peaks

Categories, 65-73, 139-144 Center of a batch: see Level of a batch Central limit theorem, 109 Central tendency: see Level of a batch Chi-square, 187-192, 197-198

one-sample 198-201 table of, 190

Cluster sampling, 86, 243-254 Coefficient of X, 206 Computers, x; see also Statpacks Confidence, 120-123, 154-155,216-217 Confidence interval: see Error range Confidence level, 123-132, 141-142 Correlation, 214-218 Counts, 66 Cowgill, George, vii Cramer's V, 193-194 Cross tabulation, 67-69, 187-188, 197

Degrees of freedom, 124, 191 Densities, 254 Dependent variable, 176, 179-181,208 Dispersion of a batch: see Spread of a batch Distribution of a batch: see Shape of a batch

Equations for straight lines, 206-208 Error range, 123-132, 140-142, 150-154, 169-

171,185-187,238-241,247-251 Expected values, 187-188 Explaining variability in regression, 214-218,

220 Exploratory Data AnalYSiS, vi

275

276

F distribution, 176-177,216-218 Fmite populations. 129-130 Frequencies, 67-73

Grab sampling. 87-93 Grouping variable. 176

Haphazard sampling, 87-93 Hinges, 29 Histograms, 10-13

Independent variable, 176, 179-181,208 Index of center: see Level of a batch Index of level: see Level of a batch Interpretation of results, 163-164,261-267 Interquartile range: see Midspread Interval scale, 66

Judgmental sampling, 87-93

Kinds of data, 66-67

Least-squares regression, 209-225 Level of a batch

average, 17-19 indexes compared, 23-24 mean, 17-19

outliers, 20 resistance, 20 trimmed, 21-23 See also Mean

median, 19-20,23,46-49 outliers, 20 resistance, 20

midmean,22 mode, 26 removing, 44-46

Level of confidence: see Confidence level Linear regression, 209-225 Linear relationships, 206-208 Logarithms, 57

Marginal totals, 188 Mean, 17-19

comparing for more than two samples, 167-181

comparing for two samples, 149-165 estimating from a sample, 111-137,238-

241,251-253 resistance, 20 trimmed, 21-23, 136-137

INDEX

Measure of central tendency: see Level of a batch

Measurements. 66 Median, 19-20,23.39,46-49

resistance, 20 Midmean,22 Midspread, 28-29. 39, 46-49 Mode. 26 Mutually exclusive and exhaustive categories,

66

Nominal data, 67 Nonrandom samples, 89-93, 112-114, 261-

267 Normal distribution, 63-64 Null hypothesis, vii, 160-163

Observed values, 187-188 Ordinal data, 67 Outliers, 4,19-20,32,39-43,46-49

eliminating, 20-21

Peaks, multiple, 13-15,24-26 Pearson's r, 214-217 Percentages: see Proportions Percentiles, 50 Phi, 193-194 Pie chan, 71 Point sampling, 244 Pooling estimates in stratified sampling, 238-

241 Population, 81,112-114,261-267

finite, 129-130 Precision, 114-115, 120-123 Prediction, 212-214 Probability, 161-163

associated, 158 See also Confidence, Significance

Proportions, 67-73 comparing, 185-194 estimating from a sample. 139-144, 238-

241,247-251 row and column, 69-73

Purposive sampling, 87-93

Quadrat sampling, 244-247 Quartiles, 29, 39

r,214-217 r,,227-233

table for small samples, 232

INDEX

Random numbers, 82-85 table of, 83-84

Random sampling: see Sampling Range, 27-28 Rank correlation, 227-233 Ranks, 67, 227-233 Ra tio scale, 66 Regression, 209-225 Removing the level, 44-46 Removing the spread, 46-49 Replacement in sample selection, 85, 247 Representativeness, 85-89, 112-114, 261-

267 Residuals, 210-211, 214-217, 219-222 Resistance, 20, 28,32, 134-137 Robust methods

analysis of variance, 181-182 chi-square. 196-198 error ranges, 134-137, 181-182 rank correlation, 233 regression, 222-225 t test, 164-165

Rounding error. 70-71, 176 Rules of thumb, vi, 41, 134

Sample size, 102-106, 132-134, 142-144, 194-195

Samples: see Sampling Sampling

bias, 88-93, 112-114,261-267 cluster, 86, 243-254 general principles, 79-82, 261-267 grab, 87-93 haphazard, 87-93 judgmental, 87-93 nonrandom samples, 89-93, 112-114, 261-

267 population, 81, 261-267

target, 93-96,112-114,261-267 purposive, 87-93 replacement, 85, 247 representativeness, 85-89,105,112-114,

261-267 sample selection, 82-93, 244-247 sample size, 102-106, 132-134 simple random, 85 spatial, 243-254 special batch, 106-109 standard error, 107-109 stratified, 86, 237-241 systematic, 245-247

277

Sampling (cont.) variation between samples, 99-109 without finding anything, 255-259

Sampling distribution of the mean, 106-109 Sampling fraction, 134 Scatter plot, 204-206, 222-225 Shape of a batch

correcting asymmetry, 59-63 normal distribution, 63-64 single-peaked and symmetrical, 63-64 symmetry, 53-56 transformations, 56-59

Significance, vii, 154-155, 158, 160-163, 177-179,187-192,194-195,197, 216-218, 231-232

Simple random sampling, 85 Single-peaked and symmetrical shape, 63-

64 Skewed distributions: see Symmetry Slope of a line, 206-207 Software: see Statpacks Spatial sampling, 243-254 Spearman's rank correlation, 227-233

table for small samples, 232 SpeCial batch, 106-109 Spread of a batch

indexes compared, 35-36 interquartile range, 28-29 midspread,28-29,46-49 range, 27-28 removing, 46-49 standard deviation, 29-32

outliers, 32 resistance, 32 trimmed, 33-35

statpacks, 35 variance, 29-32

outliers, 32 resistance, 32

Standard deviation, 29-32 outliers, 32 resistance, 32, 134-13 7 trimmed, 33-35, 136-137

Standard error, 107-109, 115-120,247-253 of a proportion, 140-144,247-251

Standard scores, 51 Standardizing, 49-51 Statpacks, x

analysis of variance, 176 box-and-dot plots, 47 chi-square, 197

278

Statpacks (conI.) cluster sampling, 251 histograms, 13 level of a batch 23 manuals, x rank correlation, 233 regression, 221 removing level and spread, 47 spread of a batch 35 stem-and-Ieaf plots, 13 transformations, 47

Stem-and-Ieaf plot, 4-13 back-to-back, 10, 18-19 computer drawn, 13 conventions, 9 intervals, 9 orientation, 9 scale, 5-9

Stratified sampling, 86, 237-241 Strength, 154-155, 158, 177-179, 191-194,

214-218 Student's t: see t Subjective judgments, vi Sum of squares, 30 Symmetry, 53-56

correcting asymmetry, 59-63 Systematic sampling, 245-247

and degrees of freedom, 124 and error ranges, 123-132 and rank correlation, 231-232 and sample size, 132 table of, 125

t test one-sample, 159-160 two-sample, 155-159

Tabulation, 67-69, 187-188 Target population, 93-96, 261-267 Terminology, vi Tools, viii-x

INDEX

Total number, estimating f;om a sample, 254 Transect sampling, 244 Transformations, 56-59, 164-165, 181-182,

222-225 Trimmed mean, 21-23, 136-137 Trimmed standard deviation, 33-35, 136-137 Tukey,John W, vi Two-way table, 67-69 Types, 65

Unusualness, 49-51

V, 193-194 Vagaries of sampling, 151, 158 Variable

dependent, 176, 179-181,208 grouping, 176 independent, 176, 179-181,208

Variance, 29-32 outliers, 32 resistance, 32, 134-137

Winsorized batch, 33

Y intercept, 207-208

Z scores, 51

INTERDISCIPLINARY CONTRIBUTIONS TO ARCHAEOLOGY Chronological Listing of Volumes

THE PLEISTOCENE OLD WORLD Regional Perspectives Edited by Olga Soffer

HOLOCENE HUMAN ECOLOGY IN NORTHEASTERN NORTH AMERICA Edited by George P. Nicholas

ECOLOGY AND HUMAN ORGANIZATION ON THE GREAT PLAINS Douglas B. Bamforth

THE INTERPRETATION OF ARCHAEOLOGICAL SPATIAL PATTERNING Edited by Ellen M. Kroll and T. Douglas Price

HUNTER-GATHERERS Archaeological and Evolutionary Theory Robert L. Bettinger

RESOURCES, POWER, AND INTERREGIONAL INTERACTION Edited by Edward M. Schortman and Patricia A. Urban

POTTERY FUN CTION A Use-Alteration Perspective James M. Skibo

SPACE, TIME, AND ARCHAEOLOGICAL LANDSCAPES Edited by Jacqueline ROSSignol and LuAnn Wandsnider

ETHNOHISTORY AND ARCHAEOLOGY Approaches to Postcontact Change in the Americas Edited by J. Daniel Rogers and Samuel M. Wilson

THE AMERICAN SOUTHWEST AND MESOAMERICA Systems of Prehistoric Exchange Edited by Jonathon E. Ericson and Timothy G. Baugh

FROM KOSTENKI TO CLOVIS Upper Paleolithic-Paleo-Indian Adaptations Edited by Olga Soffer and N. D. Praslov

EARLY HUNTER-GATHERERS OF THE CALIFORNIA COAST Jon M. Erlandson

HOUSES AND HOUSEHOLDS A Comparative Study Richard E. Blanton

THE ARCHAEOLOGY OF GENDER Separating the Spheres in Urban America Diana diZerega Wall

ORIGINS OF ANATOMICALLY MODERN HUMANS Edited by Matthew H. Nitecki and Doris V. Nitecki

PREHISTORIC EXCHANGE SYSTEMS IN NORTH AMERICA Edited by Timothy G. Baugh and Jonathon E. Ericson

STYLE, SOCIETY, AND PERSON Archaeological and Ethnological Perspectives Edited by Christopher Carr and Jill E. Neitzel

REGIONAL APPROACHES TO MORTUARY ANALYSIS Edited by Lane Anderson Beck

DIVERSITY AND COMPLEXITY IN PREHISTORIC MARITIME SOCIETIES A Gulf of Maine Perspective Bruce J. Bourque

CHESAPEAKE PREHISTORY Old Traditions, New Directions Richard J. Dent, jr.

PREHISTORIC CULTURAL ECOLOGY AND EVOLUTION InSights from Southern Jordan Donald O. Henry

STONE TOOLS Theoretical InSights into Human Prehistory Edited by George H. Odell

THE ARCHAEOLOGY OF WEALTH Consumer Behavior in English America James G. Gibb

STATISTICS FOR ARCHAEOLOGISTS A Commonsense Approach Robert D. Drennan

DARWINIAN ARCHAEOLOGIES Edited by Herbert Donald Graham Maschner

CASE STUDIES IN ENVIRONMENTAL ARCHAEOLOGY Edited by Elizabeth J. Reitz, Lee A. Newsom, and Sylvia J. Scudder

HUMANS AT THE END OF THE ICE AGE The Archaeology of the Pleistocene-Holocene Transition Edited by Lawrence Guy Straus, Berit Valentin Eriksen, Jon M. Erlandson, and David R. Yesner