1. Finkeistein, Michael O., Quantitative Methods in Law: Studies in the Application of Mathematical Probability and Statistics to Legal Problems x (New York: Free Press, 1978).Google Scholar

2. A citation count from Shepard's Law Review Citations through June 1979 is a rough measure of the influence Finkelstein's articles have had.Google Scholar

3. For lawyers with little mathematical background seeking to learn about statistics, I recommend (here listed alphabetically) David C. Baldus & James W. Cole, Statistical Proof of Discrimination (New York: McGraw-Hill Book Co., 1979) (legal applications with emphasis on interpretation); Herbert M. Blalock, Social Statistics (2d ed. New York: McGraw-Hill Book Co., 1972); John A. Ingram, Introductory Statistics (Menlo Park, Cal.: Benjamin-Cummings Publishing Co., 1974); M. J. Moroney, Facts from Figures (Baltimore: Penguin Books, 1951); Edward R. Tufte, Data Analysis for Politics and Policy (Englewood Cliffs, N.J.: Prentice-Hall, 1974) (political science applications with emphasis on regression); and especially Hans Zeisel, Say It with Figures (5th ed. New York: Harper & Row, 1968).Google Scholar

4. The book illustrates the most common applications of statistical methods to legal problems; omitted, however, is a discussion of the use of sample survey data, for example, in cases involving trade name infringement. See, e.g., President of Colby College v. Colby College-New Hampshire, 508 F.2d 804 (1st Cir. 1975); Hans Zeisel, The Uniqueness of Survey Evidence, 45 Cornell L.Q. 322 (1960). A wide variety of applications not covered in the body of Finkelstein's book are discussed or referred to in its chap. 1, Introduction to Quantitative Methods.Google Scholar

5. William B. Fairley & Frederick Mosteller, Statistics and Public Policy v (Reading, Mass.: Addison-Wesley Publishing Co., 1977).Google Scholar

6. Id. Google Scholar

7. A social science reviewer concludes that the book accomplishes its goals quite well. See Armor, David J., Book Review, 7 Contemp. Soc. 635 (1978).Google Scholar

8. Amos Tversky & Daniel Kahneman, Judgment Under Uncertainty: Heuristics and Biases, in Fairley & Mosteller, supra note 5, at 309.Google Scholar

9. Id. at 310, 311.Google Scholar

10. Id. at 324.Google Scholar

11. Finkelstein, supra note 1, at 18.Google Scholar

12. Id. at 55–57, Castaneda v. Partida, 430 U.S. 482 (1977).Google Scholar

13. Hazelwood School Dist. v. United States, 433 U.S. 299 (1977).Google Scholar

14. Finkelstein, supra note 1, at 120 (quoting N.Y. Election Law § 330(2) (McKinney 1964)).Google Scholar

15. Bickel, Peter J., Eugene A. Hammel, & J. William O’Connell, Sex Bias in Graduate Admissions: Data from Berkeley, in Fairley & Mosteller, supra note 5, at 113.Google Scholar

16. Michael O. Finkelstein & William B. Fairley, A Bayesian Approach to Identification Evidence, 83 Harv. L. Rev. 489 (1970). Major portions of the article are incorporated in Finkelstein's chapter, Two Cases in Evidence, in Finkelstein, supra note 1, at 59.CrossRefGoogle Scholar

17. The arguments have related to such diverse matters as fingerprints, blood, palm prints, ballistics, dirt particles, shoe prints, and tire marks. See, e.g., State v. Sneed, 76 N.M. 349, 414 P.2d 858 (1966); Miller v. State, 240 Ark. 340, 399 S.W. 2d 268 (1966); State v. Coolidge, 260 A.2d 547 (N.H. 1969); U.S. v. Massey, 594 F. 2d 676 (8th Cir. 1979); C. R. Kingston & P. L. Kirk, The Use of Statistics in Criminalistics, 55 J. Crim. L.C. & P.S. 514 (1964).Google Scholar

18. People v. Collins, 68 Cal. 2d 319, 438 P.2d 33, 66 Cal. Rptr. 497 (1968). See Brown, Kenneth S. & Kelly, Douglas G., Playing the Percentages and the Law of Evidence, 1970 U. Ill. L.F. 23; Vincent C. Immel, Actuarial Tables and Damage Award, 19 Ohio St. L.J. 240 (1958); Robert P. Charrow & Robert L. Smith, A Conversation About “A Conversation About Collins,” 64 Geo. L.J. 669 (1976); Sir Richard Eggleston, Evidence Proof and Probability (London: Weidenfeld & Nicholson, 1978); William B. Fairley & Frederick Mosteller, A Conversation About Collins, 41 U. Chi. L. Rev. 242 (1974); Leonard R. Jaffe, Comment on the Judicial Use of HLA Paternity Test Results and Other Statistical Evidence: A Response to Terasaki, 17 J. Fam. L, 457 (1978–79); Laurence H. Tribe, Trial by Mathematics: Precision and Ritual in the Legal Process, 84 Harv. L. Rev. 1329 (1971); Glanville Williams, The Mathematics of Proof, 1979 Crim. L. Rev. 297; Comment, Judicial Use, Misuse, and Abuse of Statistical Evidence, 47 J. Urb. L. 165 (1969–70).Google Scholar

19. Finkelstein, supra note 1, at 81–82; Fairley & Mosteller, supra note 18, and reprinted in Fairley & Mosteller, supra note 5, at 369.Google Scholar

20. The Bayesian method gives us a subjective assessment of the probability that the defendant was the source of the incriminating evidence in the case [P(S|E)], whereas classical statistical procedures when properly applied indicate in terms of relative frequency the probability that the evidence would be observed if the defendant were the source of the evidence [P(E|S)] or if he were not the source [P(E|S)]. See Finkelstein, supra note 1, at 87–91. Original publication of the proposal is cited in note 16, supra. Google Scholar

21. Tribe, supra note 18.Google Scholar

22. Finkelstein's reply to Tribe, Michael O. Finkelstein & William B. Fairley, A Comment on “Trial by Mathematics,” 84 Harv. L. Rev. 1801 (1971), reprinted in Finkelstein, supra note 1, at 288, and in Fairley & Mosteller, supra note 5, at 381. Tribe's rejoinder, Laurence H. Tribe, A Further Critique of Mathematical Proof, 84 Harv. L. Rev. 1810 (1971), is reprinted in Finkelstein, supra note 1, at 299 and in Fairley & Mosteller, supra note 5, at 389. Many of Tribe's arguments are restated in Lea Brilmayer & Lewis Hornhauser, Review: Quantitative Methods and Legal Decisions, 46 U. Chi. L. Rev. 116 (1978), a generally critical review of Finkelstein's book which also challenges the basic validity of Bayesian methods even when they are properly applied. Other recent reviews include David Kaye, Naked Statistical Evidence, 89 Yale L.J. 601 (1980); Book Note, 93 Harv. L. Rev. 1398 (1980).Google Scholar

23. See, e.g., Finkelstein's multiple regression article, in Finkelstein, supra note 1, at 211–12.Google Scholar

24. See, e.g., Paul Everett Meehl, Clinical versus Statistical Prediction: A Theoretical Analysis and a Review of the Evidence (Minneapolis: University of Minnesota Press, 1954); J. Sawyer, Measurement and Prediction, Clinical and Statistical, 66 Pysch. Bull. 178 (1966); Robert R. Holt, Yet Another Look at Clinical and Statistical Prediction: Or, Is Clinical Psychology Worthwhile? 25 Am. Psych. 337 (1970). Finkelstein refers to the Meehl book in his Introduction. Finkelstein, supra note 1, at 8 n. 19.Google Scholar

25. Kruskal, William H., Issues and Opportunities, in Fairley & Mosteller, supra note 5, at 3, 17.Google Scholar

26. In judicial settings, as Finkelstein's book so nicely demonstrates, the limitations of relevancy are established by the requirements of the substantive law, not by statistical principles.Google Scholar

27. Lester B. Lave & Eugene P. Seskin, Does Air Pollution Shorten Lives? in Fairley & Mosteller, supra note 5, at 143, 144, 149.Google Scholar

28. The minefield concept was developed in Jones v. N.Y.C. Human Res. Admin., 391 F. Supp. 1064, 1072 (S.D.N.Y. 1975), an employment discrimination case.Google Scholar

29. Finkelstein, supra note 1, at 131.Google Scholar

30. Finkelstein's unverifiable assumptions are that “(1) the level of a [small] firm's competitive activity is a function solely of its size … and (2) small firms should count in the sense that the measure should show an increase without limit (although at a decreasing rate) as the number of such firms increase[s].” Id. at 160–61.Google Scholar

31. Id. at 181.Google Scholar

32. Id. at 184.Google Scholar

33. Id. at 208–9. Finkelstein also considers measurement issues in malapportionment cases involving voting districts of unequal populations. Id. at 105–20.Google Scholar

34. Mosteller, Frederick, Assessing Unknown Numbers: Order of Magnitude Estimation, in Fairley & Mosteller, supra note 5, at 163, 175.Google Scholar

35. This point is made by Fairley in his assessment of the article in Fairley & Mosteller, supra note 5, at 158.Google Scholar

36. Dawes, Robyn M., A Case Study of Graduate Admissions: Application of Three Principles of Human Decision Making, in Fairley & Mosteller, supra note 5, at 295.Google Scholar

37. Finkelstein, supra note 1, at 238.Google Scholar

38. There is no known way to produce a precise estimate of the likely effects of measurement error or of a weak research design.Google Scholar

39. A major exception is the regression article, which contains a lucid discussion of confidence intervals. Finkelstein, supra note 1, at 222–23. This article also contains a perceptive discussion of methods available for testing the assumptions about the data, such as homoscedasticity, that are involved in regression analyses.Google Scholar

40. Bickel, Hammel, & O’Connell, supra note 15.Google Scholar

41. Theodore Colton & Robert C. Buxbaum, Motor Vehicle Inspection and Motor Vehicle Accident Mortality, in Fairley & Mosteller, supra note 5, at 131. The inspection states are clustered in the Northeast and Southwest.Google Scholar

42. Id. at 139. After controlling for the three additional variables, the differences in mortality rates between states with and states without inspection were 11.0 per 100,000 population for nonwhite males (P<.01) and 6.8 per 100,000 population for white males (P<.001).Google Scholar

43. The authors report that another study that controlled for both population density and gasoline consumption showed no statistically significant difference in mortality rates between inspection and noninspection states, “although the data showed a trend in that direction.” Also, the authors’ own comparisons of mortality rates before and after several states adopted inspection laws suggest an impact only among non white males. Id. at 140–41.Google Scholar

44. Finkelstein's book includes two legal impact studies that involve no judicial applications. Chap. 8 (pp. 249–63) considers actions for the wrongful death of a child and tests the hypotheses that state laws that allow compensation for the anguish of a deceased child's parents (a) increase the size of jury verdicts, and (b) increase the amount of variation in the size of the jury verdicts. Although the data show the jury awards to be larger in the jurisdictions that allow compensation for anguish, a statistical analysis of variance suggests that the different compensation laws probably cause very little of the observed differences in the amounts of the awards. Moreover, contrary to initial expectations, the data revealed less variation in the size of jury award in the states that allowed compensation for mental anguish. Finkelstein suggests that this result may reflect that the ban on compensation for mental anguish is selectively and arbitrarily enforced in the no-compensation states. Finkelstein's final chapter (pp. 263–98) examines the hypothesis that a substantial proportion of criminal defendants who enter guilty pleas would not have been convicted had they stood trial. On the basis of a quite compelling statistical analysis, which shows a strong negative correlation between the proportion of all defendants in federal courts who are not convicted of a crime and the percentage of guilty pleas entered, Finkelstein concludes that many of the defendants who do enter guilty pleas would have been acquitted had they gone to trial. Although the inference involves speculation, in that it does not control for the effects of other factors that may influence conviction rates, the conclusion is not implausible, and it affirms the doubts that legal scholars have had about the effect of plea bargaining practices. Both this chapter and the wrongful death study indicate what can be done with an imaginative analysis of a relatively modest data set gathered from public records.Google Scholar

45. Gilbert, John P., Richard J. Light, & Frederick Mosteller, Assessing Social Innovations: An Empirical Base for Policy, in Fairley & Mosteller, supra note 5, at 185. Alice M. Rivlin, Allocating Resources for Policy Research: How Can Experiments Be More Useful? in Fairley & Mosteller, supra note 5, at 243, also discusses the advantages of social experiments.Google Scholar

46. Gilbert, Light, & Mosteller, supra note 45, at 231–35.Google Scholar

47. Colton & Buxbaum, supra note 41.Google Scholar

48. Fairley, William B., Evaluating the “Small” Probability of a Catastrophic Accident from the Marine Transportation of Liquefied Natural Gas, in Fairley & Mosteller, supra note 5, at 331, 334.Google Scholar