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Statisticians charge draft lottery was not random.

The New York Times, 4 Jan. 1970, A66

David E. Rosenbaum

The new draft lottery is being challenged by statisticians and politicians who claim that the drawings for the lottery are not random. A federal district judge in Wisconsin has agree to hear a test case on the lottery. It comes at a time when hundreds of thousands of men have been assigned a place in the draft sequence and the first men are about to be inducted using the new lottery.

President Richard Nixon signed Nov.26 an executive order to "establish a random selection sequence" for induction. The order stipulated that the lottery would be based on birthdays but did not say how the dates should be chosen.

After a staff meeting it was decided that the 366 dates of a year should be placed in capsules and then be drawn one by one from a large bowl. A man's draft number would then correspond to the order in which his birthday was drawn. For example Sept.14 was the first date drawn and June 8 was the last number drawn. Thus a man with birthday Sept.4 would have draft number 1 and someone born June 8 would have draft number 366. Pentagon manpower specialists believe that those in the last third of the numbers (200 to 366) would escape the draft entirely.

A knowledgeable White House official said this week that "discussions that the lottery was not random are purely speculative." He added that there was no possibility of another drawing.

Senator Edward Kennedy asked the National Sciences last month to analyze the "apparent lack of randomness" in the selection. The Academy has not yet decided whether to do this or not.

The challenge to the randomness is being brought by Mr.Stodosky, a 24 year-old doctorate student in computer planning. The challenge is based on the average numbers for the men in the lottery for each month. If the system were random, each month could be expected to average around 183 or 184. Each of the first six months average above this and each of the last six months average below it. Statisticians, who have studied the lottery, say that this could occur if the capsules with later months were not mixed as thoroughly as those with early months.

Two graduate students at the University of Wisconsin have estimated that the odds against obtaining the results of the drawings by a truly random process are 50,000 to 1. Other statisticians arrived at similar results.

The articles states:

Statisticians usually work on the principle that a random test should produce results that occur at least once in 20 times under the laws of probability. If the results occur less frequently, then the statist- cians conclude that some causative factor was involved.

The lottery was set up over the weekend before the Dec. 1 drawing by Capt. Pascoe and Col. Charles R. Fox, under the observation of John H. Adams, an editor of U.S. News & World Report.

The article provides a detailed description of how they put the capsules in the box and mixed them up and finally put them in a two foot-deep bowl for the public drawing. The persons who drew the capsules generally picked ones from the top, although once in a while they would reach their hand to the middle or the bottom of the bowl.

In his article Starr comments:

It is not widely known that there was a second drawing on December 1, 1969, held to rank the twenty-six letters of the alphabet. "The order of selection from among men born on the same date would be determined by the order in which the first letters of their last, first and middle names were drawn.

DISCUSSION QUESTIONS (These are from Norton Starr's article.)

(1) Assuming males are born with equal likelihood throughout the year, was the lottery really necessary? Or was it carried out largely to convey a sense of fairness in an essentially stochastic context where the stakes happened to be very serious?

(2) Should attention have been given to twins, triplets, and other siblings to avoid multiple impacts on a given family?

(3) Were those born on February 29 treated unfairly in the 1970 lottery?

(4) The alphabetic data for 1970 seem, to the naked eye, to have their own significant bias: only three letters from the first half of the alphabet were among the first thirteen chosen. Is this apparent lack of randomness statistically significant? If so, is it of practical significance? If the answer to the latter is "no," then why was a permutation of the alphabet used in the first place?

(5) How should men lacking a middle or even a first name be handled? (This is a real-life missing data issue! Students might be encouraged to find out what was actually done.)

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