Wilkinson The Grammar of Graphics

2. Auflage 2005
ISBN: 978-0-387-28695-2
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 693 Seiten

Reihe: Statistics and Computing

Presents a unique foundation for producing almost every quantitative graphic found in scientific journals, newspapers, statistical packages, and data visualization systems The new edition features six new chapters and has undergone substantial revision. The first edition has sold more than 2200 copies. Four color throughout.

Autoren/Hrsg.

Wilkinson, Leland

Inhaltsverzeichnis

1;Preface;7
2;Contents;13
3;1 Introduction;17
3.1;1.1 Graphics Versus Charts;18
3.2;1.2 Object-Oriented Design;19
3.2.1;1.2.1 What is OOD?;19
3.2.2;1.2.2 What is not OOD?;20
3.2.3;1.2.3 Why OOD?;21
3.3;1.3 An Object-Oriented Graphics System;22
3.3.1;1.3.1 Specification;22
3.3.2;1.3.2 Assembly;23
3.3.3;1.3.3 Display;23
3.4;1.4 An Example;24
3.4.1;1.4.1 Specification;25
3.4.2;1.4.2 Assembly;25
3.4.3;1.4.3 Display;26
3.4.4;1.4.4 Revision;27
3.5;1.5 What This Book Is Not;29
3.5.1;1.5.1 Not a Command Language;29
3.5.2;1.5.2 Not a Taxonomy;30
3.5.3;1.5.3 Not a Drafting Package;30
3.5.4;1.5.4 Not a Book of Virtues;31
3.5.5;1.5.5 Not a Heuristic System;32
3.5.6;1.5.6 Not a Geographic Information System;33
3.5.7;1.5.7 Not a Visualization System;33
3.6;1.6 Background;34
3.7;1.7 Sequel;34
4;Part I;37
4.1;2 How To Make a Pie;39
4.1.1;2.1 Definitions;41
4.1.1.1;2.1.1 Sets;41
4.1.1.2;2.1.2 Relations;43
4.1.1.3;2.1.3 Functions;43
4.1.1.4;2.1.4 Graphs;44
4.1.1.5;2.1.5 Compositions;44
4.1.1.6;2.1.6 Transformations;45
4.1.1.7;2.1.7 Algebras;45
4.1.1.8;2.1.8 Variables;45
4.1.1.9;2.1.9 Varsets;46
4.1.1.10;2.1.10 Frames;46
4.1.2;2.2 Recipe;47
4.1.2.1;2.2.1 Create Variables;47
4.1.2.2;2.2.2 Apply Algebra;48
4.1.2.3;2.2.3 Apply Scales;49
4.1.2.4;2.2.4 Compute Statistics;50
4.1.2.5;2.2.5 Construct Geometry;50
4.1.2.6;2.2.6 Apply Coordinates;51
4.1.2.7;2.2.7 Compute Aesthetics;52
4.1.3;2.3 Notation;54
4.1.3.1;2.3.1 Specifications;54
4.1.3.2;2.3.2 Functions;56
4.1.4;2.4 Sequel;56
4.2;3 Data;57
4.2.1;3.1 Data Functions;58
4.2.2;3.2 Empirical Data;60
4.2.2.1;3.2.1 Reshaping Data;61
4.2.2.2;3.2.2 Bootstrapping;63
4.2.3;3.3 Abstract Data;64
4.2.3.1;3.3.1 Time Series;64
4.2.3.2;3.3.2 Counts;65
4.2.4;3.4 Metadata;67
4.2.5;3.5 Data Mining;67
4.2.5.1;3.5.1 MOLAP;68
4.2.5.2;3.5.2 ROLAP;69
4.2.5.3;3.5.3 Visual Query of Databases;70
4.2.6;3.6 Sequel;70
4.3;4 Variables;71
4.3.1;4.1 Transforms;72
4.3.2;4.2 Examples;73
4.3.2.1;4.2.1 Sorting;73
4.3.2.2;4.2.2 Probability Plots;74
4.3.2.3;4.2.3 Aggregating Variables;75
4.3.2.4;4.2.4 Regression Residuals;76
4.3.3;4.3 Sequel;77
4.4;5 Algebra;79
4.4.1;5.1 Syntax;79
4.4.1.1;5.1.1 Symbols;79
4.4.1.2;5.1.2 Operators;79
4.4.1.3;5.1.3 Rules;84
4.4.2;5.2 Examples;89
4.4.2.1;5.2.1 Cross;89
4.4.2.2;5.2.2 Nest;91
4.4.2.3;5.2.3 Blend;92
4.4.3;5.3 Other Algebras;96
4.4.3.1;5.3.1 Design Algebra;96
4.4.3.2;5.3.2 Relational Algebra;96
4.4.3.3;5.3.3 Functional Algebra;98
4.4.3.4;5.3.4 Table Algebra;99
4.4.3.5;5.3.5 Query Algebra;99
4.4.3.6;5.3.6 Display Algebra;99
4.4.4;5.4 Sequel;99
4.5;6 Scales;101
4.5.1;6.1 Scaling Theory;101
4.5.1.1;6.1.1 Axiomatic Measurement;101
4.5.1.2;6.1.2 Unit Measurement;102
4.5.1.3;6.1.3 Applied Scaling;105
4.5.1.4;6.1.4 Graphics and Scales;108
4.5.2;6.2 Scale Transformations;109
4.5.2.1;6.2.1 Categorical Scales;110
4.5.2.2;6.2.2 Linear Scales;111
4.5.2.3;6.2.3 Time Scales;114
4.5.2.4;6.2.4 One-bend Scales;116
4.5.2.5;6.2.5 Two-bend Scales;121
4.5.2.6;6.2.6 Probability Scales;124
4.5.3;6.3 Sequel;125
4.6;7 Statistics;127
4.6.1;7.1 Methods;129
4.6.1.1;7.1.1 Bin;130
4.6.1.2;7.1.2 Summary;131
4.6.1.3;7.1.3 Region;131
4.6.1.4;7.1.4 Smooth;131
4.6.1.5;7.1.5 Link;134
4.6.1.6;7.1.6 Conditional and Joint Methods;135
4.6.1.7;7.1.7 Form and Function;136
4.6.2;7.2 Examples;139
4.6.2.1;7.2.1 Point;139
4.6.2.2;7.2.2 Line/Surface;141
4.6.2.3;7.2.3 Interval;147
4.6.2.4;7.2.4 Bins;149
4.6.2.5;7.2.5 Polygon;156
4.6.2.6;7.2.6 Path;160
4.6.2.7;7.2.7 Edge;161
4.6.3;7.3 Summary;168
4.6.4;7.4 Sequel;170
4.7;8 Geometry ;171
4.7.1;8.1 Examples;174
4.7.1.1;8.1.1 Functions;174
4.7.1.2;8.1.2 Partitions;184
4.7.1.3;8.1.3 Networks;187
4.7.1.4;8.1.4 Collision Modifier Examples;188
4.7.1.5;8.1.5 Splitting vs. Shading;192
4.7.2;8.2 Summary;193
4.7.3;8.3 Sequel;194
4.8;9 Coordinates;195
4.8.1;9.1 Transformations of the Plane;196
4.8.1.1;9.1.1 Isometric Transformations;199
4.8.1.2;9.1.2 Similarity Transformations;207
4.8.1.3;9.1.3 Affine Transformations;208
4.8.1.4;9.1.4 Planar Projections;212
4.8.1.5;9.1.5 Conformal Mappings;217
4.8.1.6;9.1.6 Polar Coordinates;221
4.8.1.7;9.1.7 Inversion;232
4.8.1.8;9.1.8 Bendings;233
4.8.1.9;9.1.9 Warpings;239
4.8.2;9.2 Projections onto the Plane;243
4.8.2.1;9.2.1 Perspective Projections;244
4.8.2.2;9.2.2 Stereo Pairs;248
4.8.2.3;9.2.3 Triangular (Barycentric) Coordinates;251
4.8.2.4;9.2.4 Map Projections;254
4.8.3;9.3 3D Coordinate Systems;260
4.8.3.1;9.3.1 Spherical Coordinates;260
4.8.3.2;9.3.2 Triangular-Rectangular Coordinates;261
4.8.3.3;9.3.3 Cylindrical Coordinates;262
4.8.4;9.4 High-Dimensional Spaces;264
4.8.4.1;9.4.1 Projection;264
4.8.4.2;9.4.2 Sets of Functions.;266
4.8.5;9.5 Tools and Coordinates;269
4.8.6;9.6 Sequel;270
4.9;10 Aesthetics;271
4.9.1;10.1 Continuous Scales;272
4.9.1.1;10.1.1 Psychophysics;272
4.9.1.2;10.1.2 Consequences for Attributes;274
4.9.2;10.2 Categorical Scales;277
4.9.2.1;10.2.1 Innate Categories;277
4.9.2.2;10.2.2 Learned Categories;279
4.9.2.3;10.2.3 Scaling Categories;279
4.9.2.4;10.2.4 Consequences for Attributes;280
4.9.3;10.3 Dimensions;281
4.9.3.1;10.3.1 Integral Versus Separable Dimensions;281
4.9.4;10.4 Realism;286
4.9.5;10.5 Aesthetic Attributes;290
4.9.5.1;10.5.1 Position;293
4.9.5.2;10.5.2 Size;293
4.9.5.3;10.5.3 Shape;297
4.9.5.4;10.5.4 Rotation;298
4.9.5.5;10.5.5 Resolution;299
4.9.5.6;10.5.6 Color;300
4.9.5.7;10.5.7 Texture;304
4.9.6;10.6 Examples;309
4.9.6.1;10.6.1Position;309
4.9.6.2;10.6.2 Size;310
4.9.6.3;10.6.3 Shape;312
4.9.6.4;10.6.4 Rotation;322
4.9.6.5;10.6.5 Resolution;323
4.9.6.6;10.6.6 Color;324
4.9.7;10.7 Summary;332
4.9.8;10.8 Sequel;334
4.10;11 Facets;335
4.10.1;11.1 Facet Specification;335
4.10.2;11.2 Algebra of Facets;336
4.10.3;11.3 Examples;343
4.10.3.1;11.3.1 One-Way Tables of Graphics;343
4.10.3.2;11.3.2 Multi-way Tables;345
4.10.3.3;11.3.3 Continuous Multiplots;352
4.10.3.4;11.3.4 Scatterplot Matrices (SPLOMs);353
4.10.3.5;11.3.5 Facet Graphs;354
4.10.3.6;11.3.6 Multiple Frame Models;360
4.10.4;11.4 Sequel;361
4.11;12 Guides;363
4.11.1;12.1 Scale Guides;364
4.11.1.1;12.1.1 Legends;364
4.11.1.2;12.1.2 Axes;366
4.11.1.3;12.1.3 Scale Breaks;367
4.11.1.4;12.1.4 Double Axes;368
4.11.2;12.2 Annotation Guides;368
4.11.2.1;12.2.1 Text;369
4.11.2.2;12.2.2 Form;370
4.11.2.3;12.2.3 Image;371
4.11.3;12.3 Sequel;372
5;Part 2;374
5.1;13 Space;375
5.1.1;13.1 Mathematical Space;379
5.1.1.1;13.1.1 Topological Space;379
5.1.1.2;13.1.2 Connected and Disconnected Space;380
5.1.1.3;13.1.3 Metric Space;380
5.1.1.4;13.1.4 Maps;382
5.1.1.5;13.1.5 Embeddings;382
5.1.1.6;13.1.6 Multidimensional Scaling;383
5.1.1.7;13.1.7 Geodesics;384
5.1.1.8;13.1.8 Dimensions;385
5.1.1.9;13.1.9 Connected Spaces;386
5.1.1.10;13.1.10 Fractals;389
5.1.1.11;13.1.11 Discrete Metric Spaces;392
5.1.1.12;13.1.12 Graph-Theoretic Space;393
5.1.2;13.2 Psychological Space;394
5.1.2.1;13.2.1 Spatial Models of Pre-attentive Processes;394
5.1.2.2;13.2.2 Spatial Models of Cognitive Processes;396
5.1.2.3;13.2.3 Spatial Cognition;397
5.1.3;13.3 Graphing Space;397
5.1.3.1;13.3.1 Mapping Connected Space to Euclidean Space;398
5.1.3.2;13.3.2 Mapping Discrete Space to Euclidean;405
5.1.3.3;13.3.3 Mapping Graph-Theoretic Space to Euclidean;408
5.1.3.4;13.3.4 Mapping Nested Space to Euclidean;415
5.1.4;13.4 Sequel;421
5.2;14 Time;423
5.2.1;14.1 Mathematics of Time;424
5.2.1.1;14.1.1 Deterministic Models of Time;424
5.2.1.2;14.1.2 Stochastic Models of Time;430
5.2.1.3;14.1.3 Chaotic Models of Time;434
5.2.2;14.2 Psychology of Time;440
5.2.2.1;14.2.1 Sensation;440
5.2.2.2;14.2.2 Duration;441
5.2.2.3;14.2.3 Motion;442
5.2.3;14.3 Graphing Time;443
5.2.3.1;14.3.1 Static Graphics;443
5.2.3.2;14.3.2 Dynamic Graphics;451
5.2.3.3;14.3.3 Real-Time Graphics;453
5.2.4;14.4 Sequel;465
5.3;15 Uncertainty;467
5.3.1;15.1 Mathematics of Uncertainty;467
5.3.1.1;15.1.1 Defining Uncertainty;468
5.3.1.2;15.1.2 Defining Probability;469
5.3.1.3;15.1.3 Bayes’ Theorem;470
5.3.1.4;15.1.4 The Central Limit Theorem;473
5.3.1.5;15.1.5 Interpreting Probability;474
5.3.1.6;15.1.6 Uncertainty Intervals;476
5.3.1.7;15.1.7 Model Error;479
5.3.1.8;15.1.8 Resampling;480
5.3.1.9;15.1.9 Missing Data;480
5.3.2;15.2;482
5.3.3;15.3 Graphing Uncertainty;484
5.3.3.1;15.3.1 Aesthetics;484
5.3.3.2;15.3.2 Uncertainty Intervals;493
5.3.3.3;15.3.3 Multiple Comparisons;495
5.3.3.4;15.3.4 Resampling;498
5.3.3.5;15.3.5 Indeterminacy;499
5.3.3.6;15.3.6 Missing Values;501
5.3.4;15.4 Sequel;504
5.4;16 Analysis;505
5.4.1;16.1 Variance Analysis;506
5.4.1.1;16.1.1 Cross.;506
5.4.1.2;16.1.2;507
5.4.1.3;16.1.3 Blend.;507
5.4.1.4;16.1.4 Smoothing by Design;507
5.4.1.5;16.1.5 An Example;509
5.4.2;16.2 Shape Analysis;512
5.4.3;16.3 Graph Drawing.;516
5.4.3.1;16.3.1 Networks;516
5.4.3.2;16.3.2 Trees;517
5.4.3.3;16.3.3 Directed Graphs;519
5.4.4;16.4 Sequence Analysis;521
5.4.4.1;16.4.1 Identifying Numeric Sequences;523
5.4.4.2;16.4.2 Finding Sequences in Strings;527
5.4.4.3;16.4.3 Comparing Sequences;530
5.4.4.4;16.4.4 Critical Paths;531
5.4.5;16.5 Pattern Analysis;533
5.4.5.1;16.5.1 Matrix Permutation;533
5.4.5.2;16.5.2 Canonical Data Patterns;534
5.4.5.3;16.5.3 Permuting Randomly;540
5.4.5.4;16.5.4 Permuting Systematically;541
5.4.5.5;16.5.5 Summary;548
5.4.6;16.6 Sequel;549
5.5;17 Control;551
5.5.1;17.1 Building;551
5.5.1.1;17.1.1 Procedural Languages;552
5.5.1.2;17.1.2 Object-Based Languages;553
5.5.1.3;17.1.3 Dialog Boxes;554
5.5.1.4;17.1.4 Wizards;555
5.5.1.5;17.1.5 Graphboard;555
5.5.2;17.2 Exploring;568
5.5.2.1;17.2.1 Filtering;568
5.5.2.2;17.2.2 Navigating;571
5.5.2.3;17.2.3 Manipulating;577
5.5.2.4;17.2.4 Brushing and Linking;579
5.5.2.5;17.2.5 Animating;584
5.5.2.6;17.2.6 Rotating;585
5.5.2.7;17.2.7 Transforming;586
5.5.3;17.3 Sequel;593
5.6;18 Automation;595
5.6.1;18.1 Graphics Production Language;596
5.6.1.1;18.1.1 Examples;599
5.6.1.2;18.1.2 GPL Development Environment;605
5.6.2;18.2 Visualization Markup Language;605
5.6.2.1;18.2.1 Data Definition;608
5.6.2.2;18.2.2 Structure;609
5.6.2.3;18.2.3 Style;611
5.6.2.4;18.2.4 Levels of Specification;613
5.6.2.5;18.2.5 Default Settings;614
5.6.2.6;18.2.6 Locales;615
5.6.2.7;18.2.7 Extensibility;616
5.6.2.8;18.2.8 Comparison with Other XMLs;622
5.6.2.9;18.2.9 GraphML;624
5.6.3;18.3 Summary;624
5.6.4;18.4 Sequel;625
5.7;19 Reader;627
5.7.1;19.1 The Problem;628
5.7.2;19.2 A Psychological Reader Model;630
5.7.3;19.3 A Graphics Grammar Reader Model;633
5.7.4;19.4 Research;638
5.7.5;19.5 Sequel;638
5.8;20 Coda;639
5.8.1;20.1 Napoleon’s March;639
5.8.1.1;20.1.1 The Data;639
5.8.1.2;20.1.2 The Graphic;642
5.8.1.3;20.1.3 The Meaning;645
5.8.2;20.2 Monarch Butterfly Migration;645
5.8.2.1;20.2.1 The Data;646
5.8.2.2;20.2.2 The Graphic;646
5.8.2.3;20.2.3 The Meaning;648
5.8.3;20.3 Conclusion;648
5.8.3.1;20.3.1 The Grammar of Graphics;649
5.8.3.2;20.3.2 The Language of Graphics;650
5.8.4;20.4 Sequel;650
6;References;651
7;Author Index;689
8;Subject Index;697

Leseproben

7 Statistics (p.111-112)

Statistics state the status of the state. All these s words derive from the Greek statis and Latin status, or standing. Standing (for humans) is a state of being, a condition that represents literally or figuratively the active status of an individual, group, or state. Modern statistics as a discipline arose in the early 18th century, when collection of data about the state was recognized as essential to serving the needs of its constituents. This Enlightenment perspective gave rise not only to the modern social sciences, but also to mathematical methods for analyzing data measured with error (Stigler, 1983).

In a graphical system, statistics are methods that alter the position of geometric graphs. We are accustomed to think of a chart as a display of a statistic or a statistical function (e.g., a bar chart of budget expenditures). As such, it would seem that we should begin by aggregating data, computing statistics, and drawing a chart. This would be wrong, however. By putting statistics under control of graphing functions, rather than whole charts under the control of statistics, we accomplish several things. First, we can represent more than one statistic in a frame. One graphic can represent a mean and another a median, in the same frame. Second, making statistics into graphing methods forces them to be views or summaries of the raw data rather than data themselves. In other words, the casewise data and a graphic are inextricably bound because we never break the connection between the variables and the graphics that represent them.

This allows us to drill-down, brush, and investigate values with other dynamic tools. This functions would be lost if we pre-aggregated the data. Finally, by putting statistics under the control of graphing functions, we can modularize and localize computations in a distributed system. Adding graphics to a frame is easy when we do not have to worry about the structure of the data and how aggregations were computed. We will return to this issue in Section 7.3 at the end of this chapter.

The simplest graphing method is the one students first learn for plotting algebraic functions: for every x, compute f(x) so that one may draw a graph based on the tuples of the form (x, f(x)) that comprise the graph. Students learn to construct a list of these tuples (a finite subset of the graph of the function) in order to plot selected points in Cartesian coordinates. In the functional no tation of this book, students usually draw graphs of algebraic functions using the graphing function line(position(f()).

While students learn graphing methods for polynomial and other simple algebraic functions, most charts are based on statistical functions of observed values of one or more variables. In our notation, examples of statistical graphs are produced by the functions

point(position(summary.mean())) and
line(position(smooth.linear())),

which implement the statistical graphing functions summary.mean() and smooth.linear(), respectively. Statistical functions can be complicated, but their output looks the same to their geometric clients as the output of algebraic functions. A line does not care who produced the points it needs to plot itself.