In 1970, Congress instituted a lottery for the military draft to support the unpopular war in Vietnam. All 366 possible birth dates were placed in plastic capsules in a rotating drum and were selected one by one. Eligible males born on the first day drawn were first in line to be drafted followed by those born on the second day drawn, etc. The results were criticized by some who claimed that government incompetence at running a fair lottery resulted in a tendency of men born later in the year being more likely to be drafted. Indeed, later investigation revealed that the birthdates were placed in the drum by month and were not thoroughly mixed. The columns of the file 1970lottery are month, month number, day of the year, and draft number.
a. Plot draft number versus day number. Do you see any trend?
b. Calculate the Pearson and rank correlation coefficients. What do they suggest?
c. Is the correlation statistically significant? One way to assess this is via a permutation test. Randomly permute the draft numbers and find the correlation of this random permutation with the day numbers. Do this 100 times and see how many of the resulting correlation coefficients exceed the one observed in the data. If you are not satisfied with 100 times, do it 1,000 times.
d. Make parallel boxplots of the draft numbers by month. Do you see any pattern?
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