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Statistics and Computing Series Editors: J. Chambers D. Hand W. Ha¨rdle

Leland Wilkinson The Grammar of Graphics Second Edition With 410 Illustrations, 319 in Full Color With contributions by Graham Wills, Dan Rope, Andrew Norton, and Roger Dubbs

Leland Wilkinson SPSS Inc. 233 S. Wacker Drive Chicago, IL 60606-6307 USA leland@spss.com Series Editors: J. Chambers Bell Labs, Lucent Technologies 600 Mountain Ave. Murray Hill, NJ 07974 USA D. Hand Department of Mathematics South Kensington Campus Imperial College, London London SW7 2AZ United Kingdom W. Ha¨rdle Institut fu¨r Statistik und O¨ konometrie Humboldt-Universita¨t zu Berlin Spandauer Str. 1 D-10178 Berlin, Germany Library of Congress Control Number: ISBN-10: 0-387-24544-8 ISBN-13: 978-0387-24544-7 Printed on acid-free paper. © 2005 Springer Science+Business Media, Inc. All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, Inc., 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed in Canada. 9 8 7 6 5 4 3 2 1 springeronline.com

To John Hartigan and Amie Wilkinson

Who can hide in secret places so that I cannot see them? Do I not fill heaven and earth? Jeremiah 23.24 Cleave a piece of wood, I am there; lift up the stone and you will find me there. Gospel of Thomas 77 God hides in the smallest pieces. Caspar Barlaeus God hides in the details. Aby Warburg God is in the details. Ludwig Mies van der Rohe The devil is in the details. George Shultz Bad programmers ignore details. Bad designers get lost in details. Nate Kirby

Preface Preface to First Edition Before writing the graphics for SYSTAT in the 1980’s, I began by teaching a seminar in statistical graphics and collecting as many different quantitative graphics as I could find. I was determined to produce a package that could draw every statistical graphic I had ever seen. The structure of the program was a collection of procedures named after the basic graph types they pro- duced. The graphics code was roughly one and a half megabytes in size. In the early 1990’s, I redesigned the SYSTAT graphics package using ob- ject-based technology. I intended to produce a more comprehensive and dy- namic package. I accomplished this by embedding graphical elements in a tree structure. Rendering graphics was done by walking the tree and editing worked by adding and deleting nodes. The code size fell to under a megabyte. In the late 1990’s, I collaborated with Dan Rope at the Bureau of Labor Statistics and Dan Carr at George Mason University to produce a graphics pro- duction library called GPL, this time in Java. Our goal was to develop graphics components. This book was nourished by that project. So far, the GPL code size is under half a megabyte. I have not yet achieved that elusive zero-byte graphics program, but I do believe that bulk, in programming or in writing, can sometimes be an inverse measure of clarity of thought. Users dislike “bloatware” not only because it is a pig that wastes their computers’ resources but also because they know it usu- ally reflects design-by-committee and sloppy thinking. Notwithstanding my aversion to bulk, this book is longer than I had antic- ipated. My original intent was to outline a new paradigm for quantitative graphics using examples from publications and from SYSTAT. As the GPL project proceeded and we were able to test concepts in a working program, I began to realize that the details of the system were as important as the outlines. I also found that it was easier to write about the generalities of graphics than about the particulars. As every programmer knows, it is easier to wave one’s hands than to put them to the keyboard. And as every programmer knows in the middle of the night, the computer “wonderfully focuses the mind.” The consequence is a book that is not, as some like to say, “an easy read.” I do not apologize for this. Statistical graphics is not an easy field. With rare exceptions, theorists have not taken graphics seriously or examined the field deeply. And I am convinced that those who have, like Jacques Bertin, are not often read carefully. It has taken me ten years of programming graphics to un- derstand and appreciate the details in Bertin. I am not referring to the abstruseness of the mathematics in scientific and technical charts when I say this is not an easy field. It is easier to graph New-

x Preface ton’s law of gravitation than to draw a pie chart. And I do not mean that no one has explored aspects of graphics in depth or covered the whole field with illu- mination. I mean simply that few have viewed quantitative graphics as an area that has peculiar rules and deep grammatical structure. As a result, we have come to expect we can understand graphics by looking at pictures and speak- ing in generalities. Against that expectation, I designed this book to be read more than once. On second reading, you will discover the significance of the details and that will help you understand the necessity of the framework. Who should read this book? The simple answer is, of course, anyone who is interested in business or scientific graphics. At the most elementary level are readers who are looking for a graphical catalog or thesaurus. There are not many types of graphics that do not appear somewhere in this book. At the next level are those who want to follow the arguments without the mathematics. One can skip all the mathematics and still learn what the fundamental compo- nents of quantitative graphics are and how they interact. At the next level are those who have completed enough college mathematics to follow the notation. I have tried to build the argument, except for the statistical methods in Chapter 7, from elementary definitions. I chose a level comparable to an introductory computer science or discrete math text, and a notation that documents the al- gorithms in set terminology computer science students will recognize. I intend to reach several groups. First are college and graduate students in computer science and statistics. This is the only book in print that lays out in detail how to write computer programs for business or scientific graphics. For all the attention computer graphics courses devote to theory, modeling, anima- tion, and realism, the vast majority of commercial applications involve quan- titative graphics. As a software developer, I believe the largest business market for graphics will continue to be analysis and reporting, despite the enthusiastic predictions (driven by conventional wisdom) for data mining, visualization, animation, and virtual reality. The reason, I think, is simple. People in business and science have more trouble communicating than discovering. The second target group for this book comprises mathematicians, statisti- cians, and computer scientists who are not experts in quantitative graphics. I hope to be able to convey to them the richness of this field and to encourage them to explore it beyond what I have been able to do. Among his many ac- complishments in the fields of graphics and statistics, William Cleveland is largely responsible for stimulating psychologists (including me) to take a clos- er look at graphical perception and cognition. I hope this book will stimulate experts in other fields to examine the language of graphics. The third target group consists of statistics and computer science special- ists in graphics. These are the colleagues most likely to recognize that this book is more the assembly of a large puzzle than the weaving of a whole cloth. I cannot assume every expert will understand this book, however, for reasons similar to why expertise in procedural programming can hinder one from learning object-oriented design. Those who skim through or jump into the middle of this book are most likely to misunderstand. There are many terms in

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