Nonrandom Risk: The 1970 Draft Lottery

References

• Eckholm, E. (1986), “Status in Draft Linked to Suicide,” New York Times, March 7, p. A16. This summarizes the Hearst, Newman, and Hulley article cited below.
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• Fienberg, S. E. (1971a), “Randomization and Social Affairs: The 1970 Draft Lottery,” Science, 171, 255–261. The best and most comprehensive single resource on this issue. Includes an interesting historical sketch of randomness in social affairs.
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• Fienberg, S. E. (1971b), Comment on “Draft Lottery: Validity of Randomness,” by C. J. Scheirer, Science, 172, 630–631.
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• Fienberg, S. E. (1973), “Randomization for the Selective Service Draft Lotteries,” in Statistics by Example: Finding Models, eds. F. Mosteller, W. H. Kruskal, R. F. Link, R. S. Pieters, and G. R. Rising, Reading, MA: Addison-Wesley, pp. 1–13. (Note: There is a typographical error in Table 4, p. 13. The 1971 draft rank for May 11 is given as 243, the same rank as for November 1. It should be 293, as a study of the Rosenblatt and Filliben article cited below or a glance at the corresponding U. S. Selective Service report indicates.) A very accessible article, with a variety of analyses and a good set of questions for class use.
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• Hearst, N., Newman, T. B. and Hulley, S. B. (1986), “Delayed Effects of the Military Draft on Mortality,” New England Journal of Medicine, 314 (10), March 6, 620–624. Demonstrates a higher suicide rate among those with low lottery numbers than among those with high ranks. The question of the possible effect of the hidden variable, actual military service, is addressed as well.
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• Kitchens, L. J. (1998), Exploring Statistics (2nd ed.), Pacific Grove, CA: Brooks/Cole pp. 20, 216 (Exercise 3.97), and 682 (Exercise 10.62). Includes a data disk with both the 1970 and 1971 data.
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• Larsen, R. J., and Stroup, D. F. (1976), Statistics in the Real World, New York: Macmillan, pp. 241–245. Nonparametric approaches: Kruskal-Wallis test on the monthly ranks and Wilcoxon/Mann-Whitney rank sum test on the ranks in the first and last halves of the year.
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• Moore, D. S. (1979, 1985, 1991, and 1997), Statistics: Concepts and Controversies (1st, 2nd, 3rd, and 4th eds.), New York: Freeman. Includes a description of the 1971 procedure, of which Moore says, “It's awful, but it's random.”
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• Moore, D. S., and McCabe, G. P. (1993), Introduction to the Practice of Statistics (2nd ed.), New York: Freeman, pp. 105–107, 447–448. Uses a median trace to raise the possibility of unfairness and helps confirm this with a test of the correlation coefficient.
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• Mosteller, F., Fienberg, S. E., and Rourke, R. E. K. (1983), Beginning Statistics with Data Analysis, Reading, MA: Addison-Wesley, pp. 183–184. Interesting remarks on 1940, 1970, and 1971 lotteries.
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• Rosenbaum, D. E. (1970a), “Statisticians Charge Draft Lottery Was Not Random,” New York Times, January 4, p. 66. “If the results occur less frequently” than 5% of the time, “then the statisticians conclude that some causative factor was involved.” This makes an interesting contrast to the subsequent delicacy with which the New York Times characterizes the statistics involved in polls (“How the Poll Was Conducted”).
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• Rosenbaum, D. E. (1970b), “Draft Officials Redesign Lottery Procedures to Make the System More Random,” New York Times, June 25, p. 17. Describes the 1971 lottery procedure. “‘We would like to have a drawing this year that appears impartial, both to those professionally curious and to those whose lives are involved.’” (The spokesperson's use of “appears” shows a keen sensitivity to the issues involved.)
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• Rosenbaum, D. E. (1970c), “Draft Lottery for Youths Born in 1951 to Be Conducted Today; New System Is Hailed,” New York Times, July 1, p. 19. Some remarks comparing the 1970 and 1971 lotteries.
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• Rosenbaum, D. E. (1970d), “Second Draft Lottery Selects Call-Up Order for 1971,” New York Times, July 2, pp. 1, 12. Describes the procedure in detail, gives the rank for each day of the year, and declares that the alphabetic priority will be the one determined in the previous lottery.
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• Rosenblatt, J. R., and Filliben, J. J. (1971), “Randomization and the Draft Lottery,” Science, 171, pp. 306–308. A description and analysis of the 1971 lottery, concluding that the process was effectively random.
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• United States Selective Service System (1970), “Semi-Annual Report of the Director of Selective Service for the Period July 1 to December 31, 1969 to the Congress of the United States,” Washington: U. S. Government Printing Office, pp. 5–10. Describes the procedures and gives results by date for each month as well as by rank from first selected to last. Also gives the alphabetic lottery results. The birthdate lotteries for future years are given in successive reports, while the alphabet permutation used after 1970 is that determined in the 1970 lottery.
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• Witmer, J. A. (1992), Data Analysis: An Introduction, Englewood Cliffs, NJ: Prentice-Hall, pp. 21–24. Displays a beautifully informative set of monthly boxplots, along with the revealing median trace. These reflect the sequential mixing of the numbered capsules, which was a major source of bias.
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