Exploring Data Tables, Trends, and Shapes

1. Theories of Data Analysis: From Magical Thinking Through Classical Statistics 1 Peris Diaconis 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.