Analytics Stories

CHAPTER 2Was the 1969 Draft Lottery Fair?

In 1969, the unpopular Vietnam War was raging, and the United States needed soldiers to fight the war. To equalize the chance of young men (born in years 1944–1950) being drafted, a draft lottery based on a man's birthday was held. A total of 366 pieces of paper (one for each possible date, including February 29) were mixed in a shoebox and placed in capsules that were placed in a large glass jar. Then the capsules were selected, and the order of selection determined a man's priority for being drafted. September 14 was chosen first, so that date was assigned #1, April 24 was drawn next, assigned #2, and so on. Men with draft numbers up to 195 were drafted. The lottery numbers for each date are listed in column G of the Data worksheet of the file DraftData.xlsx.

Statisticians quickly noticed (see www.nytimes.com/1970/01/04/archives/statisticians-charge-draft-lottery-was-not-random.html) that lottery numbers for the last few months of the year seemed to be suspiciously low, meaning that men with late-year birthdays were more likely to be drafted. Were the statisticians correct?

The Data

All we need are the lottery numbers for each calendar date. As you will see, there were likely problems with the 1969 lottery method. A different selection method was used in the July 1, 1970 lottery (for men with 1951 birthdays), and that data is included in Column H of the Data worksheet of the file DraftData.xlsx.

The Analysis

To examine whether ...