Question

Figure 1 Correlation between Birthday and Draft Number is-0.223 On December 1, 1969, Congress instituted a random selection process for the military draft. All 366 possible birth dates were assigned a number (i.e. Jan 1st was 1, Feb 1st was 32, March 15th was 75, etc.) 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. On January 4, 1970, the New York Times ran a long article, "Statisticians Charge Draft Lottery Was Not Random." It made the point that those with birthdates later in the year seemed to have had more than their share of low lottery numbers and hence were more likely to be drafted. Discussion Item Comment on the following graphs. What would you conclude from the scatterplot and correlation? What additional conclusions can be made from the side-by-side boxplots? Can you find any explanation on the internet? What do you think about the box plots? Scatterplot of 1970 DRAFT NUMBER vs DAY Figure 2 Side by side box plots of draft number vs. month Boxplot of 1970 DRAFT NUMBER 200 TA

Comment on the graphs in the picture. What would you conclude from the scatterplot and correlation? What additional conclusions can be made from the side-by-side boxplots? Can you find any explanation on the internet? What do you think about the box plots?

Answer 1

From the scatter plot, we can see that the plot does not have any pattern. Therefore, increase or decrease the value of the draft number does not effect on the variable day and vice versa. Hence, we can conclude that there is not a relationship between the variable draft number and day means that the correlation value is near zero.

In the side-by-side boxplots of draft number against the months, most of the month has the symmetric distribution of draft number and the significant difference of draft number may be occurred only between the months of March and December.