Exploring the 1970 Draft Data During Vietnam War



Exploring the 1970 Draft Data During Vietnam War

In order to randomize a man's risk of being drafted, a lottery was held in which a draft number from 1 to 366 (the day of February 29 is included) was assigned to each day of the year. In the accompanying data file, you can see which day corresponds to which draft number. Months and such are also listed. The first day to be chosen was September 14, so men born on that day had draft # 1 and were called first. Locate that info in the data to be sure you understand how to read the file.

You are going to explore whether or not the draft numbers appear to be random as claimed. There are many ways to do this, but you are going to make a scatter plot and then a bar graph of some medians. In class I will provide Excel instructions.

Make a Scatterplot

On the x-axis, the data in column A will appear, and on the y-axis the data in column E.

Make a Bar Graph of Medians

You will have Excel compute the median draft number for each month. So you will end up with 12 medians, one for each month. Then on the x-axis, you will put the month names or month numbers, and the height of each bar will be the median for that month.

Questions to Answer

1. Which birthday was the safest one for a man to have; that is, which birthday was the last one to be picked in the lottery?

2. What birthday was picked 10th in the lottery?

3. Does the scatterplot reveal any obvious trend, or are the dots seemingly randomly scattered about? Note that your scatterplot would form a straight line if Jan 1 was picked first and Jan 2 was picked second and Jan 3 was picked third, and so on, in perfect order.

4. Which month has the highest bar (the highest median draft number) on your bar graph? In general, does this mean that people born this month are lucky or unlucky concerning their draft number?

5. Reading from Jan to Dec, from left to right, do the bars of the bar graph overall trend up, trend down, or do they follow no trend?

6. Overall, which birthdays were more likely to be called sooner, those early in the year or those late in the year? (see your bar graph) (Understand that draft numbers #5 is undesirable and #360 is desirable.) I am asking you if it was better to be born early in the year or later in the year with regards to the draft.

7. They went to lengths to create a “random” draft order. Was this necessary? Do you think that which day of the year you are born on is already random, so that it would be fair to call people in order based on Jan 1 gets called first and Jan 2 gets called second, etc?

8. If you were born on February 29, would you consider a procedure wherein each birthday is equally likely to be chosen to be a fair shake for you? Explain fully.

What you must hand in

You must staple and hand in three things: your scatterplot, your bar graph, and your typed answers to the questions. Answer in full, reasonable English sentences where it applies. You are to do the work to make the graphs yourself. The main object of this lesson is to handle an absolutely real data set yourself and to work with so many numbers that a computer is extremely helpful. So use a computer and do it yourself! A secondary object is for you to confront an instance of statistics with life or death consequences.

Historical Note: It was reported in the New York Times on January 4, 1970 that the lottery was not random. The process of selection was modified for 1971.

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