In 1970, Congress instituted a random selection process for the military draft. All 366 possible birth dates were placed in plastic capsules in a rotating drum and were selected one by one. The first date drawn from the drum received draft number one and eligible men born on that date were drafted first. In a truly random lottery there should be no relationship between the date and the draft number. However, this dataset suggests that men born later in the year were more likely to be drafted.
While it is impossible to view this trend in a scatterplot of draft number vs. birth date, a series of side-by-side boxplots by month illustrate it clearly. The correlation between draft number and birth date is -0.226, which is significantly different from zero. A further investigation of the lottery revealed that the birthdates were placed in the drum by month and were not thoroughly mixed.
Alternatively, drawing a smoothed curve through the points also shows the pattern of decreasing priority values in the end months of the year which was not apparent in the original scatterplot. The smoothed curve here uses the lowess method.