Visual Statistics

The late FORREST W. YOUNG, PhD, was Professor Emeritus of Quantitative Psychology at The University of North Carolina at Chapel Hill. As a result of a ten-year research project, Dr. Young and his students created ViSta: The Visual Statistics System. He acted as a professional consultant for the SAS Institute, Inc., Statistical Sciences, Inc., and Bell Telephone Laboratories. He authored three books and numerous journal articles. He received his PhD in psychometrics from the University of Southern California, Los Angeles. PEDRO M. VALERO-MORA, PhD, is Professor of Data Processing at the University of Valencia in Spain. He is the author of several research papers. He received his PhD in methodology in the behavioral sciences from the University of Valencia in Spain.MICHAEL FRIENDLY, PhD, is Professor in the Department of Psychology at York University in Toronto, Ontario, Canada. He received his PhD in psychometrics and cognitive psychology from Princeton University. He is the author of two books and numerous research papers.

• Part I Introduction1 Introduction1.1 Visual Statistics 61.2 Dynamic Interactive Graphies 71.2.1 An Analogy 71.2.2 Why Use Dynamic Graphies? 81.2.3 The Four Respects 81.3 Three Examples 91.3.1 Nonrandom Numbers 91.3.2 Automobile Efficiency 111.3.3 Fidelity and Marriage 141.4 History of Statistical Graphics 181.4.1 1600-1699: Measurement and Theory 181.4.2 1700-1799: New Graphic Forms and Data 191.4.3 1800-1899: Modern Graphics and the Golden Age 201.4.4 1900-1950: The Dark Ages of Statistical Graphics—The Golden Age of Mathematical Statistics 211.4.5 1950-1975: Rebirth of Statistical Graphics 221.4.6 1975-2000: Statistical Graphics Comes of Age 231.5 About Software 241.5.1 XLisp-Stat 251.5.2 Commercial Systems 261.5.3 Noncommercial Systems 261.5.4 ViSta 271.6 About Data 291.6.1 Essential Characteristics 301.6.2 Datatypes 321.6.3 Datatype Examples 341.7 About This Book 341.7.1 What This Book Is—and Isn't 341.7.2 Organization 341.7.3 Who Our Audience Is—and Isn't 371.7.4 Comics 381.7.5 Thumb-Powered Dynamic Graphics 391.8 Visual Statistics and the Graphical User Interface 401.9 Visual Statistics and the Scientific Method 401.9.1 A Paradigm for Seeing Data 411.9.2 About Statistical Data Analysis: Visual or Otherwise 422 Examples 452.1 Random Numbers 472.2 Medical Diagnosis 522.3 Fidelity and Marriage 59Part II See Data—The Process3 Interfaces and Environments 733.1 Objects 773.2 User Interfaces for Seeing Data 783.3 Character-Based Statistical Interface Objects 793.3.1 Command Line 793.3.2 Calculator 803.3.3 Program Editor 803.3.4 Report Generator 813.4 Graphics-Based Statistical Interfaces 813.4.1 Datasheets 813.4.2 Variable Window 823.4.3 Desktop 823.4.4 Workmap 833.4.5 Selector 873.5 Plots 883.5.1 Look of Plots 893.5.2 Feel of Plots 913.5.3 Impact of Plot Look and Feel 933.6 Spreadplots 943.6.1 Layout 963.6.2 Coordination 983.6.3 SpreadPlots 1003.6.4 Look of Spreadplots 1023.6.5 Feel of Spreadplots 1043.6.6 Look and Feel of Statistical Data Analysis 1043.7 Environments for Seeing Data 1113.8 Sessions and Projects 1143.9 The Next Reality 1143.9.1 The Fantasy 1143.9.2 The Reality 1163.9.3 Reality Check 1184 Tools and Techniques 1194.1 Types of Controls 1234.1.1 Buttons 1234.1.2 Palettes 1254.1.3 Menus and Menu Items 1254.1.4 Dialog Boxes 1254.1.5 Sliders 1264.1.6 Control Panels 1274.1.7 The Plot Itself 1274.1.8 Hyperlinking 1274.2 Datasheets 1284.3 Plots 1294.3.1 Activating Plot Objects 1314.3.2 Manipulating Plot Objects 1324.3.3 Manipulating Plot Dimensions 1384.3.4 Adding Graphical Elements 141Part III Seeing Data—Objects5 Seeing Frequency Data 1455.1 Data 1485.1.1 Automobile Efficiency: 1485.1.2 Berkeley Admissions Data 1485.1.3 Tables of Frequency data 1505.1.4 Working at the Categories Level 1515.1.5 Working at the Variables Level 1535.2 Frequency Plots 1575.2.1 Mosaic Displays 1575.2.2 Dynamic Mosaic Displays 1595.3 Visual Fitting of Log-Linear Models 1645.3.1 Log-Linear Spreadplot 1655.3.2 Specifying Log-Linear Models and the Model Builder Window 1665.3.3 Evaluating the Global Fit of Models and Their History 1705.3.4 Visualizing Fitted and Residual Values with Mosaic Displays 1745.3.5 Interpreting the Parameters of the Model 1765.4 Conclusions 1796 Seeing Univariate Data 1816.1 Introduction 1836.2 Data: Automobile Efficiency 1856.2.1 Looking at the Numbers 1866.2.2 What Can Unidimensional Methods Reveal? 1866.3 Univariate Plots 1906.3.1 Dotplots 1906.3.2 Boxplots 1936.3.3 Cumulative Distribution Plots 1966.3.4 Histograms and Frequency Polygons 1996.3.5 Ordered Series Plots 2086.3.6 Namelists 2096.4 Visualization for Exploring Univariate Data 2096.5 What Do We See in MPG1 2127 Seeing Bivariate Data 2157.1 Introduction 2177.1.1 Plots About Relationships 2177.1.2 Chapter Preview 2207.2 Data: Automobile Efficiency 2217.2.1 What the Data Seem to Say 2227.3 Bivariate Plots 2247.3.1 Scatterplots 2247.3.2 Distribution Comparison Plots 2337.3.3 Parallel-Coordinates Plots and Parallel Boxplots 2367.4 Multiple Bivariate Plots 2367.4.1 Scatterplot Plot Matrix 2377.4.2 Quantile Plot Matrix 2387.4.3 Numerical Plot-matrix 2387.4.4 BoxPlot Plot Matrix 2397.5 Bivariate Visualization Methods 2417.6 Visual Exploration 2427.6.1 Two Bivariate Data Visualizations 2437.6.2 Using These Visualizations 2457.7 Visual Transformation: Box-Cox 2477.7.1 The Transformation Visualization 2497.7.2 Using Transformation Visualization 2517.7.3 The Box-Cox Power Transformation 2557.8 Visual Fitting: Simple Regression 2567.9 Conclusions 2608 Seeing Multivariate Data 2638.1 Data: Medical Diagnosis 2668.2 Three Families of Multivariate Plots 2708.3 Parallel-Axes Plots 2728.3.1 Parallel-Coordinates Plot 2728.3.2 Parallel-Comparisons Plot 2768.3.3 Parallel Univariate Plots 2778.4 Orthogonal-Axes Plots 2798.4.1 Spinplot 2808.4.2 Orbitplot 2838.4.3 BiPlot 2868.4.4 Wiggle-Worm (Multivariable Comparison) Plot 2918.5 Paired-Axes Plots 2928.5.1 Spinplot Plot Matrix 2938.5.2 Parallel-Coordinates Plot Matrix 2948.6 Multivariate Visualization 2958.6.1 Variable Visualization 2958.6.2 Principal Components Analysis 2968.6.3 Fit Visualization 2988.6.4 Principal Components Visualization 3008.6.5 One More Step - Discriminant Analysis 3028.7 Summary 3048.7.1 What Did We See? Clusters! 3048.7.2 How Did We See It? 3048.7.3 How Do We Interpret It? With Diagnostic Groups! 3058.8 Conclusion 3069 Seeing Missing Values 3099.1 Introduction 3129.2 Data: Sleep in Mammals 3149.3 Missing Data Visualization Tools 3159.3.1 Missing Values Bar Charts 3169.3.2 Histograms and Bar Charts 3169.3.3 Boxplots 3169.3.4 Scatterplots 3169.4 Visualizing Imputed Values 3179.4.1 Marking the Imputed Values 3189.4.2 Single Imputation 3209.4.3 Multiple Imputation 3259.4.4 Summary of Imputation 3279.5 Missing Data Patterns 3279.5.1 Patterns and Number of Cases 3289.5.2 The Mechanisms Leading to Missing Data 3299.5.3 Visualizing Dynamically the Patterns of Missing Data 3319.6 Conclusions 337References 339Author Index 351Subject Index 355

"With contributions by highly regarded professionals in the field, Visual Statistics not only improves a student's understanding of statistics, but also builds condence to overcome problems that may have previously been intimidating." (Zentralblatt MATH 2016)"A good book about a great software system." (Psychometrika, March 2008)"The people who would benefit most from this book are those who teach courses in statistics." (AstA Advances in Statistical Analysis, 2008)"... the book admirably guides readers through the process of exploring and analyzing a variety of types of data." (The American Statistician, August 2007)"A technically well-produced book, significant in that it documents efforts these psychometrics faculty made in using visual approaches to analyze data." (CHOICE, March 2007)"... covers its subject matter skillfully, and provides great insight into the world of the dynamic visualization of statistical data." (Journal of Applied Statistics, 2007)"Forrest Young has been a leading light in developing dynamic interactive graphics for decades... so [I] am delighted to see this book appear." (Short Book Reviews, December 2006)"... the book not only improves a student's understanding of statistics, but also builds confidence to overcome problems that may have previously been intimidating... an excellent textbook" (Computing Reviews.com, November 16, 2006)