Exploring Data Tables, Trends, and Shapes

1A. Intuitive Statistics—Some Inferential Problems 4

IB. Multiplicity—A Pervasive Problem 9

1C. Some Remedies 12

ID. Theories for Data Analysis 22

IE. Uses for Mathematics 29

IF. In Defense of Controlled Magical Thinking 31

2. Fitting by Organized Comparisons: The Square Combining Table 37
Katherine Godfrey

2A. Combining Comparisons 37

2B. Two-Way Tables 39

2C. Paired Comparisons 47

2D. Analyzing Tables Containing Holes 49

2E. Summary 61

3. Resistant Nonadditive Fits for Two-Way Tables 67
John D. Emerson and Gregory Y. Wong

3A. The Simple Additive Model and Median Polish 68

3B. One Step Beyond an Additive Fit 71

3C. Assessing and Comparing Fits 79

3D. Multiplicative Fits 83

3E. Techniques for Obtaining Simple Multiplicative Fits 92

3F. Additive-Plus-Multiplicative Fits 100

3G. Some Background for Nonadditive Fits 113

3H. Summary 117

4. Three-Way Analysis 125
Nancy Cook

4A. Structure of the Three-Way Table 126

4B. Decompositions and Models for Three-Way Analysis 128

4C. Median-Polish Analysis for the Main-Effects-Only Case 130

4D. Nonadditivity and a Diagnostic Plot in Main-Effects-Only Analysis 145

4E. Analysis Using Means 158

4F. Median-Polish Analysis for the Full-Effects Case 164

4G. Diagnostic Plots for the Full-Effects Case 176

4H. Fitting the Full-Effects Model by Means 180

4I. Computation, Other Polishes, and Missing Values 182

4J. Summary 183

5. Identifying Extreme Cells in a Sizable Contingency Table: Probabilistic and Exploratory Approaches 189
Frederick Mosteller and Anita Parunak

5A. The Hypergeometric Distribution 192

5B. Assessing Outliers 195

5C. The Simulation Approach 199

5D. Applying the Simulation Approach to the Table of Archaeological Data 206

5E. An Exploratory Approach, Based on Deviations from Independence 212

5F. A Logarithmic Exploratory Approach 214

5G. Illustrations of the New Standardization 217

5H. Summary 221

51. Conclusion 223

6. Fitting Straight Lines By Eye 225
Frederick Mosteller, Andrew F. Siegel, Edward Trapido, and Cleo Youtz

6A. Method 226

6B. Results 229

6C. Summary 238

7. Resistant Multiple Regression, One Variable at a Time 241
John D. Emerson and David C. Hoaglin

7A. Resistant Lines 242

7B. Sweeping Out 246

7C. Example 250

7D. When Carriers Come in Blocks 263

7E. Summary 273

8. Robust Regression 281
Guoying Li

8A. Why Robust Regression? 282

8B. M-Estimators and W-Estimators for Regression 291

8C. Computation 304

8D. Example: The Stack Loss Data 310

8E. Bounded-Influence Regression 322

8F. Some Alternative Methods 328

8G. Summary 335

9. Checking the Shape of Discrete Distributions 345
David C. Hoaglin and John W. Tukey

9A. A Poissonness Plot 348

9B. Confidence Intervals for the Count Metameter 358

9C. When Is a Point Discrepant? 370

9D. Overall Plots for Other Families of Distributions 376

9E. Frequency-Ratio Alternatives 389

9F. Cooperative Diversity 396

9G. Double-Root Residuals 406

9H. Summary 409

10. Using Quantiles to Study Shape 417
David C. Hoaglin

10A. Diagnosing Skewness 419

10B. Diagnosing Elongation 425

IOC. Quantile-Quantile Plots 432

10D. Plots for Skewness and Elongation 442

10E. Pushback Analysis 450

10F. Summary 454

10G. Appendix 456

11. Summarizing Shape Numerically: The g-and-h Distributions 416
David C. Hoaglin

11 A. Skewness 462

11B. Elongation 479

11C. Combining Skewness and Elongation 485

11D. More General Patterns of Skewness and Elongation 490

HE. Working from Frequency Distributions 496

11F. Moments 501

11G. Other Approaches to Shape 504

11H. Summary 508

Index.