Statistics for Lawyers

Contents......Page 16
Preface to the Second Edition......Page 8
Preface to the First Edition......Page 10
Acknowledgments......Page 14
List of Figures......Page 24
List of Tables......Page 28
1.1 Introduction to descriptive statistics......Page 32
1.2 Measures of central location......Page 34
1.2.1 Parking meter heist......Page 38
1.2.2 Taxing railroad property......Page 41
1.2.3 Capital infusions for ailing thrifts......Page 44
1.2.4 Hydroelectric fish kill......Page 45
1.2.5 Pricey lettuce......Page 46
1.2.6 Super-drowsy drug......Page 47
1.3 Measures of dispersion......Page 49
1.3.1 Texas reapportionment......Page 53
1.3.2 Damages for pain and suffering......Page 56
1.3.3 Ancient trial of the Pyx......Page 57
1.4 A measure of correlation......Page 59
1.4.1 Dangerous eggs......Page 62
1.4.2 Public school finance in Texas......Page 64
1.5 Measuring the disparity between two proportions......Page 67
1.5.1 Proficiency test with a disparate impact......Page 70
1.5.2 Bail and bench warrants......Page 71
1.5.3 Non-intoxicating beer......Page 73
2.1 Permutations and combinations......Page 74
2.1.1 DNA profiling......Page 77
2.1.2 Weighted voting......Page 80
2.1.4 A cluster of leukemia......Page 82
2.1.5 Measuring market concentration......Page 83
2.2 Fluctuation theory......Page 84
2.2.1 Tracing funds for constructive trusts......Page 86
3.1 Some fundamentals of probability calculation......Page 88
3.1.1 Interracial couple in yellow car......Page 94
3.1.2 Independence assumption in DNA profiles......Page 97
3.1.4 Telltale hairs......Page 100
3.2.1 L’affaire Dreyfus......Page 104
3.2.2 Searching DNA databases......Page 105
3.3 Bayes’s theorem......Page 106
3.3.1 Rogue bus......Page 108
3.3.2 Bayesian proof of paternity......Page 110
3.4 Screening devices and diagnostic tests......Page 112
3.4.1 Airport screening device......Page 115
3.4.2 Polygraph evidence......Page 117
3.5 Monte Carlo methods......Page 119
3.5.1 Sentencing a heroin swallower......Page 120
3.5.2 Cheating on multiple-choice tests......Page 123
3.6 Foundations of probability......Page 126
3.6.1 Relevant evidence defined......Page 128
4.1 Introduction to probability distributions......Page 130
4.2 Binomial distribution......Page 134
4.2.1 Discrimination in jury selection......Page 136
4.2.2 Educational nominating panel......Page 137
4.2.3 Small and nonunanimous juries in criminal cases......Page 138
4.2.4 Cross-section requirement for federal jury lists......Page 142
4.3 Normal distribution and a central limit theorem......Page 144
4.3.1 Alexander: Culling the jury list......Page 148
4.3.2 Castaneda: Measuring disparities......Page 149
4.4 Testing statistical hypotheses......Page 151
4.4.1 Hiring teachers......Page 153
4.5 Hypergeometric distribution......Page 154
4.5.1 Were the accountants negligent?......Page 157
4.5.2 Challenged election......Page 158
4.5.3 Election 2000: Who won Florida?......Page 159
4.6 Tests of normality......Page 165
4.6.1 Heights of French conscripts......Page 168
4.6.2 Silver “butterfly” straddles......Page 169
4.7 Poisson distribution......Page 172
4.7.2 Vaccinations......Page 175
4.7.4 Incentive for good drivers......Page 176
4.7.5 Epidemic of cardiac arrests......Page 177
4.8 Geometric and exponential distributions......Page 179
4.8.2 Network affiliation contracts......Page 181
4.8.3 Dr. Branion’s case......Page 182
5.1 Fisher’s exact test of equality for two proportions......Page 185
5.2 The chi-squared and z-score tests for the equality of two proportions......Page 188
5.2.1 Suspected specialists......Page 194
5.2.3 Police examination......Page 195
5.2.4 Promotions at a bank......Page 196
5.3 Confidence intervals for proportions......Page 197
5.3.1 Confounders and confidence intervals......Page 205
5.3.2 Paucity of Crossets......Page 206
5.3.3 Purloined notices......Page 207
5.3.4 Commodity exchange reports......Page 208
5.3.5 Discharge for dishonest acts......Page 209
5.3.8 Torture, disappearance, and summary execution in the Philippines......Page 210
5.4 Statistical power in hypothesis testing......Page 213
5.4.1 Death penalty for rape......Page 215
5.4.2 Is Bendectin a teratogen?......Page 217
5.4.3 Automobile emissions and the Clean Air Act......Page 218
5.5 Legal and statistical significance......Page 219
5.5.1 Port Authority promotions......Page 222
5.6 Maximum likelihood estimation......Page 224
5.6.1 Purloined notices revisited......Page 227
5.6.3 Peremptory challenges of prospective jurors......Page 228
6.1 Using chi-squared to test goodness of fit......Page 231
6.1.1 Death-qualified jurors......Page 233
6.1.2 Spock jurors......Page 235
6.1.3 Grand jury selection revisited......Page 236
6.1.4 Howland Will contest......Page 237
6.1.5 Imanishi-Kari’s case......Page 240
6.2 Bonferroni’s inequality and multiple comparisons......Page 242
6.2.1 Wage additives and the four-fifths rule......Page 244
6.2.2 Discretionary parole......Page 245
6.2.3 Cheating on standardized multiple-choice tests revisited......Page 246
6.3 More measures of association: Phi-squared (φ[sup(2)]) and tau B (τ[sub(B)])......Page 247
6.3.1 Preventive detention......Page 249
7.1 Student’s t -test: Hypothesis testing and confidence intervals......Page 253
7.1.1 Automobile emissions and the Clean Air Act revisited......Page 257
7.1.2 Voir dire of prospective trial jurors......Page 258
7.1.4 Student’s t -test and the Castaneda rule......Page 260
7.2 Analysis of variance for comparing several means......Page 262
7.2.1 Fiddling debt collector......Page 266
8.1 Mantel-Haenszel and Fisher methods for combining the evidence......Page 268
8.1.1 Hiring lawyers......Page 276
8.1.2 Age discrimination in employment terminations......Page 277
8.2 Meta-analysis......Page 280
8.2.1 Bendectin revisited......Page 285
9.1 The theory of random sampling......Page 287
9.1.1 Selective Service draft lotteries......Page 293
9.1.3 Mail order survey......Page 297
9.1.4 Domino effect......Page 299
9.1.5 NatraTaste versus NutraSweet......Page 301
9.1.6 Cocaine by the bag......Page 303
9.1.7 ASCAP sampling plan......Page 304
9.1.8 Current Population Survey......Page 305
9.2 Capture/recapture......Page 307
9.2.1 Adjusting the census......Page 308
10.1 Introduction......Page 313
10.2 Attributable risk......Page 315
10.2.1 Atomic weapons tests......Page 318
10.3 Epidemiologic principles of causation......Page 322
10.3.1 Dalkon Shield......Page 327
10.3.2 Radioactive “cocktails” for pregnant women......Page 330
10.3.3 Preconception paternal irradiation and leukemia......Page 333
10.3.4 Swine flu vaccine and Guillain-Barré Syndrome......Page 339
10.3.5 Silicone breast implants......Page 342
11.1 Death-density, survival, and hazard functions......Page 348
11.1.1 Valuing charitable remainders......Page 351
11.1.2 Defective house sidings......Page 352
11.1.3 “Lifing” deposit accounts......Page 353
11.2 The proportional hazards model......Page 354
11.2.2 Contaminated wells in Woburn......Page 358
11.3 Quantitative risk assessment......Page 362
11.3.1 Ureaformaldehyde foam insulation......Page 365
11.3.2 Ethylene oxide......Page 367
12.1 The sign test......Page 370
12.1.1 Supervisory examinations......Page 372
12.2 Wilcoxon signed-rank test......Page 373
12.3 Wilcoxon rank-sum test......Page 374
12.3.1 Sex discrimination in time to promotion......Page 375
12.3.2 Selection for employment from a list......Page 376
12.3.3 Sentencing by federal judges......Page 377
12.4 Spearman’s rank correlation coefficient......Page 379
12.4.1 Draft lottery revisited......Page 380
13.1 Introduction to multiple regression models......Page 381
13.1.1 Head Start programs......Page 386
13.2 Estimating and interpreting coefficients of the regression equation......Page 389
13.2.1 Western Union’s cost of equity......Page 392
13.2.2 Tariffs for North Slope oil......Page 393
13.2.3 Ecological regression in vote-dilution cases......Page 394
13.3 Measures of indeterminacy for the regression equation......Page 398
13.3.1 Sex discrimination in academia......Page 403
13.4 Statistical significance of the regression coefficients......Page 404
13.4.1 Race discrimination at Muscle Shoals......Page 408
13.5 Explanatory factors for a regression equation......Page 409
13.6 Reading multiple-regression computer printout......Page 415
13.6.1 Pay discrimination in an agricultural extension service......Page 417
13.6.2 Public school financing in the State of Washington......Page 423
13.6.3 Public school financing in Pennsylvania......Page 426
13.7 Confidence and prediction intervals......Page 427
13.7.2 Severance pay dispute......Page 430
13.7.3 Challenged absentee ballots......Page 432
13.8 Assumptions of the regression model......Page 433
13.9 Transformations of variables......Page 440
13.9.2 Sex- and race-coefficient models for Republic National Bank......Page 445
14.1 Time series......Page 448
14.1.1 Corrugated container price-fixing......Page 450
14.1.2 Puppy Chow versus Chewy Morsels......Page 451
14.1.3 Losses from infringing sales......Page 453
14.1.4 OTC market manipulation......Page 454
14.1.5 Fraud-on-the-market damages......Page 457
14.1.6 Effects of capital gains tax reductions......Page 459
14.2 Interactive models......Page 464
14.2.1 House values in the shadow of a uranium plant......Page 468
14.3 Alternative models in employment discrimination cases......Page 471
14.4 Locally weighted regression......Page 475
14.4.1 Urn models for Harris Bank......Page 477
14.5 Underadjustment bias in employment regressions......Page 478
14.5.1 Underadjustment in medical school......Page 482
14.6 Systems of equations......Page 484
14.6.1 Death penalty: Does it deter murder?......Page 486
14.7 Logit and probit regression......Page 489
14.7.1 Mortgage lending discrimination......Page 493
14.7.2 Death penalty in Georgia......Page 494
14.7.3 Deterring teenage smoking......Page 502
14.8 Poisson regression......Page 503
14.8.1 Challenger disaster......Page 504
14.9 Jackknife, cross-validation, and bootstrap......Page 506
14.9.1 Georgia death penalty revisited......Page 508
Appendix I: Calculations and Comments on the Cases......Page 512
Appendix II: Tables......Page 586
Glossary of Symbols......Page 614
List of Cases......Page 616
Bibliography......Page 620
A......Page 630
B......Page 631
C......Page 632
D......Page 634
E......Page 635
H......Page 637
K......Page 638
M......Page 639
O......Page 640
P......Page 641
R......Page 642
S......Page 644
T......Page 646
W......Page 647
Z......Page 648