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Intro Stats Islamic Approach -- Part 2 Prob & Stats
Lecture 1 Random Samples, Concept 4: Simple Random Samples
S6: Failure of Randomness: The Vietnam Draft Lottery
Young men were chosen to fight the war in Vietnam using a DRAFT system. Names were selected by a lottery, and those selected were forced to go to fight the war in Vietnam. It was a life and death lottery. Effort was made to randomize so that all people would have an equal chance. However, these efforts were not successful, and the randomization procedure had some noticeable biases.
The days of the year (including February 29) were represented by the numbers 1 through 366 written on slips of paper. The slips were placed in separate plastic capsules that were mixed in a shoebox and then dumped into a deep glass jar. Capsules were drawn from the jar one at a time.
The first number drawn was 258 (September 14), so all registrants with that birthday were assigned lottery number 1. The second number drawn corresponded to April 24, and so forth. All men of draft age (born 1944 to 1950) who shared a birthdate would be called to serve at once.
People soon noticed that the lottery numbers were not distributed uniformly over the year. In particular, November and December births, or dates 306 to 366, were assigned mainly to lower draft numbers representing earlier calls to serve (see figure). This led to complaints that the lottery was not random as the legislation required. Analysis of the procedure suggested that mixing 366 capsules in the shoe box did not mix them sufficiently before dumping them into the jar. ("The capsules were put in a box month by month, January through December, and subsequent mixing efforts were insufficient to overcome this sequencing.")[2] Only five days in December—Dec. 2, 12, 15, 17 and 19—were higher than the last call number of 195; had the days been evenly distributed, 14 days in December would have been expected to remain uncalled.
From January to December, the rank of the average draft pick numbers were 5 4 1 3 2 6 8 9 10 7 11 12. A Monte Carlo simulation found that the probability of a random order of months being this close to the 1-12 sequence expected for unsorted slips was 0.09%
The point of this example is the real world efforts to randomize may fail to match the models of random numbers. Sometimes this becomes obvious; many other times, the failure of randomness may occur in ways which are not noticeable by us. So the best way to think about randomness is via the MODEL and METAPHOR idea mentioned at the beginning of this lecture. That is, randomness is an IDEALIZATION which exists in a theoretical perfect world. All applications of this idea in the REAL world are automatically imperfect -- as BOX put it, all models are WRONG, but some are useful. In some cases, PRETENDING that the real world satisfies ideal randomness assumption is useful for making guesses, approximate calculations, and other purposes.
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