ebook THE GUILFORD PRESS Elementary Statistics for Geographers Elementary Statistics for Geographers Third Edition JAMES E BURT GERALD M BARBER DAVID L RIGBY THE GUILFORD PRESS New York London © 2009 The Guilford Press A Division of Guilford Publications, Inc 72 Spring Street, New York, NY 10012 www.guilford.com All rights reserved No part of this book may be reproduced, translated, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming, recording, or otherwise, without written permission from the Publisher Printed in the United States of America This book is printed on acid-free paper Last digit is print number: Library of Congress Cataloging-in-Publication Data Burt, James E Elementary statistics for geographers / James E Burt, Gerald M Barber, David L Rigby — 3rd ed p cm Includes bibliographical references and index ISBN 978-1-57230-484-0 (hardcover) Geography—Statistical methods I Barber, Gerald M II Rigby, David L III Title G70.3.B37 2009 519.5024′91—dc22 2008043409 Preface Readers who know our book will quickly see that this edition represents a significant revision, containing both a substantial amount of new material and extensive reorganization of topics carried over from the second edition However, our purpose remains unchanged: to provide an accessible algebra-based text with explanations that rely on fundamentals and theoretical underpinnings Such an emphasis is essential if we expect students to utilize statistical methods in their own research or if we expect them to evaluate critically the work of others who employ statistical methods In addition, when students understand the foundation of the methods that are covered in a first course, they are far better equipped to handle new concepts, whether they encounter those concepts in a more advanced class or through reading on their own We acknowledge that undergraduates often have a limited mathematical background, but we not believe this justifies a simplified approach to the subject, nor we think that students are well served by learning what is an inherently quantitative subject area without reference to proofs and quantitative arguments It is often said that today’s entering students are less numerate than previous generations That may be However, in our 20-plus years of teaching undergraduates we have seen no decrease in their ability or in their propensity to rise to an intellectual challenge Like earlier versions, this edition of Elementary Statistics for Geographers is meant for instructors who share this outlook, and for their students, who—we trust—will benefit from that point of view The Descriptive Statistics section of this edition greatly expands the coverage of graphical methods, which now comprise a full chapter (Chapter 2) This reflects new developments in computer-generated displays in statistics and their growing use; also, students increasingly seem oriented toward visual learning It is likely, for example, that a student who obtains a good mental image of skewness from Chapter can use that visual understanding to grasp more readily the quantitative measures presented in Chapter A second new chapter appearing in the descriptive section is Chapter 4, Statistical Relationships It introduces both concepts of and measures for correlation and regression This is somewhat nonstandard, in that most books postpone these topics until after the discussion of univariate methods We have found that earlier v vi PREFACE introduction of this material has several advantages First, correlation and regression are large topics, and some students better learning them in two parts Second, the concept of association is useful when explaining certain aspects of probability theory such as independence, conditional probability, and joint probability Finally, it is easier to discuss nonparametric tests such as chi-square when the idea of statistical association has already been presented Of course, instructors who prefer to cover correlation and regression in one section of their course can postpone Chapter and cover it as part of a package with Chapters 12 and 13 The Inferential Statistics section has also been heavily revised We merged basic probability theory with the treatment of random variables to create more streamlined coverage in a single chapter (Chapter 5, Random Variables and Probability Distributions) Gone is the Computer-Intensive Methods chapter, with much of that material incorporated into the Nonparametric Methods chapter As bootstrapping and related techniques have become mainstream, it is appropriate to locate them in their natural home with other nonparametric methods Chapter 11, Analysis of Variance, is a new chapter, which covers both single- and two-factor designs Also new is Chapter 13, Extending Regression Analysis, which treats diagnostics as well as transformations and more advanced regression models (including multiple regression) The last section, Patterns in Space and Time, contains a revised version of the Time Series Analysis chapter from the second edition, and the entirely new Chapter 14, Spatial Patterns and Relationships The latter is an overview of spatial analysis, and covers point patterns (especially nearest neighbor analysis), spatial autocorrelation (variograms, join counts, Moran’s I, LISA, and G-statistics), and spatial regression (including an introduction to geographically weighted regression) Additionally, there are lesser changes too numerous to itemize We’ve placed greater emphasis on worked examples, often with accompanying graphics, and the datasets that we refer to throughout the book are available on the website that accompanies this book On the website, readers can also find answers to most of the end-of-chapter exercises See www.guilford.com/pr/burt for the online resources We have said already that this new edition adheres to the previous editions’ emphasis on explanation, rather than mere description, in its presentation of quantitative methods Several other aspects are also unchanged We have retained the coverage of time series, which of course is seldom covered in this type of book Time series data are extremely common in all branches of geography; thus, geographers need to be equipped with at least a few tools of analysis for temporal data Also, once students get to linear regression, they are well positioned to understand the basics of time series modeling In other words, ability to handle time series can be acquired at little additional cost Because time series are so common, geographers will likely have occasion to deal with temporal data regardless of their formal training in the subject We believe that even simple operations like running means should not be undertaken by individuals who not appreciate the implications of the procedure Because most students will not take a full course in time series, minimal coverage, at least, is essential in an introductory text Also, we’ve received strong positive feedback on this material from instructors PREFACE vii We have continued our practice from the second edition, of not tying the book to any particular software package We believe that most instructors use software for teaching this material, but no package has emerged as an overwhelming favorite We might gain a friend by gearing the book to a particular package, but we would alienate half a dozen more Also, since statistical software is becoming increasingly easy to use, students require less in the way of instruction And we want the book to stay current We have found that even minor changes in the formatting of output can confound students who have been directed to look for particular tables of values or particular terminology in software packages Finally, in keeping with the trend from edition to edition, what was a long book is even longer Unless it is used in a year-long course, instructors will have to be very selective with regard to what they assign With this in mind, we have attempted to make the chapters as self-contained as possible Except for the chapter on probability and sampling theory, a “pick-and-choose” approach will work reasonably well For example, we know from experience that some instructors leave out the Nonparametric Methods chapter altogether, with no downstream effects, whereas others skip various chapters and subsections within chapters If some students complain about having to skip around so much, most appreciate a book that covers more than what is taught in the course Later, when confronted with an unfamiliar method in readings or on a research project, they can return to a book whose notational quirks have already been mastered, and can understand the new technique in context with what was presented in the course As we reflect on our own bookshelves, it is precisely that kind of book that has proved most useful to us over the years We wouldn’t presume to claim that our work will have similar lasting utility, but we offer it in the belief that it is better to cover too much than too little Many people deserve our thanks for their help in preparing this book We are particularly grateful to students and teaching assistants at UCLA, Queen’s University, and the University of Wisconsin–Madison for telling us what worked and what didn’t Thanks also to the panel of anonymous reviewers for their comments on previous versions of the manuscript You improved it greatly We also very much appreciate the hard work by everyone at The Guilford Press involved with the project, especially our editor, the ever-patient and encouraging Kristal Hawkins Our production editor William Meyer also deserves particular mention for his careful attention to both the print and digital components of the project Most of all, we thank our families for so willingly accepting the cost of our preoccupation To them we dedicate the book ...ebook THE GUILFORD PRESS Elementary Statistics for Geographers Elementary Statistics for Geographers Third Edition JAMES E BURT GERALD M BARBER DAVID L RIGBY THE GUILFORD PRESS New York London... summary of data The purpose of descriptive statistics is to replace what may be an extremely large set of numbers in some dataset with a smaller number of summary measures Whenever this replacement... systems leading to the collection of large amounts of data Perhaps the largest data-gathering exercises are undertaken by governments around the world when they periodically complete a national