Question

2. Bigger sample is not always better – one of the worst statistical mistakes ever made in the history of statistics happened in the 1936 U.S. Presidential Election. The incumbent president Franklin Roosevelt of the Democratic Party and Alf Landon of the Republican Party are the two main presidential candidates. Look the event up at this webpage http://www.math.upenn.edu/~deturck/m170/wk4/lecture/case1.html and answer the following questions.

1. Find the Literary Digest’s pre-election prediction for Roosevelt and Landon, in percentage of popularity vote. (One percentage for Roosevelt and one for Landon.)
2. Find the 1936 Presidential election result for Roosevelt and Landon, in percentage of popularity vote.

(One percentage for each.)

3. Find the sample size used by Literary Digest.
4. The Literary Digest’s sample has a problem with the selection bias. Identify the target population, sampling frame and briefly explain why there was a selection bias.
5. The Literary Digest’s sample also has a problem with the non-response bias. Report the number of surveys sent, number of surveys received, and calculate the non-response rate (in %).
6. The Literary Digest’s sample has a problem with the response bias. Mind you that the US is in their eighth year of the Great Depression. Briefly explain how the Great Depression has anything to do with the response bias.
7. Find the sample size used by George Gallop.
8. What was his (George Gallup’s) pre-election prediction for Roosevelt, in percentage of popularity vote? (Please look this question (h) up on the internet. The numbers may vary from different sources or web sites. Just pick one and it will not be marked based on the accuracy of the numbers.)

Answer 1

a.) The Literary Digest's pre-election prediction was as follows:

Presidential Candidate	Pre-election prediction by Literary Digest
Alfred Landon	57%
Franklin Roosevelt	43%

b.) The 1936 Presidential election results were as follows:

Presidential Candidate	Election Results
Alfred Landon	38%
Franklin Roosevelt	62%

c.) Literary Digest's sample size was around 2.4 million, making it one of the largest polls ever created.

d.) Literary Digest's target population was the citizens of the United States.

The sampling frame (the source of materials from where the sample is drawn) was composed of:

• every telephone directory in the United States,
• magazine subscriptions,
• rosters of clubs and associations
• other sources.

The selection bias in this case stemmed from the fact that the mailing list was mostly comprised of middle to upper-class voters, those who had enough money to have things such as magazine subscriptions, memberships to clubs or a telephone which was a luxury at the time.  This in turn excluded the lower-class from the mailing list and therefore from the survey making the sample not representative of the country as a whole.

e.)

Surveys sent:	10 million
Surveys received:	2.4 million
Surveys NOT received:	10 - 2.4 = 7.6 million

Therefore, the non-response rate was:

f.) The people expected to respond to the survey were American citizens voting for the President. Being that American citizens were living through the Great Depression, it is not unconceivable that many were disillusioned with their country and leader. Many could have thought that their country had forsaken them, and therefore, were unwilling to participate in the survey. Another possibility is that they were completely focused on surviving, that they thought of a survey as something insignificant or trivial compared to the rest of life's challenges and therefore did not participate in the survey.

g.) George Gallup used a much smaller sample size of 50,000.

h.) George Gallup's pre-election prediction for Franklin Roosevelt was 56%.