Questions: In 1936, the magazine Literary Digest incorrectly predicted that Alf Landon would defeat Franklin Roosevelt in the presidential election. It based its prediction on 2.4 million responses out of 10 million sample ballots it sent to its own subscribers, individuals in telephone directories, and lists of automobile owners. What type of bias might have caused this error? I. Nonresponse bias II. Voluntary response bias III. Undercoverage A. I only B. II only C. I and II only D. I, II, and III E. II and III

In 1936, the magazine Literary Digest incorrectly predicted that Alf Landon would defeat Franklin Roosevelt in the presidential election. It based its prediction on 2.4 million responses out of 10 million sample ballots it sent to its own subscribers, individuals in telephone directories, and lists of automobile owners. What type of bias might have caused this error?
I. Nonresponse bias
II. Voluntary response bias
III. Undercoverage
A. I only
B. II only
C. I and II only
D. I, II, and III
E. II and III

Transcript text: In 1936, the magazine Literary Digest incorrectly predicted that Alf Landon would defeat Franklin Roosevelt in the presidential election. It based its prediction on 2.4 million responses out of 10 million sample ballots it sent to its own subscribers, individuals in telephone directories, and lists of automobile owners. What type of bias might have caused this error? I. Nonresponse bias II. Voluntary response bias III. Undercoverage A. I only B. II only C. I and II only D. I, II, and III E. II and III

Solution

What type of bias might have caused the error in the Literary Digest's prediction?

Understanding the context

The Literary Digest sent out 10 million sample ballots to its subscribers, individuals in telephone directories, and automobile owners. It received 2.4 million responses, which it used to predict that Alf Landon would defeat Franklin Roosevelt. However, this prediction was incorrect.

Analyzing potential biases

Nonresponse bias

Nonresponse bias occurs when the individuals who do not respond to a survey differ significantly from those who do. In this case, the 7.6 million individuals who did not respond might have had different voting preferences compared to the 2.4 million who did respond. This could lead to a biased prediction.

Analyzing potential biases

Voluntary response bias

Voluntary response bias occurs when individuals self-select to participate in a survey, leading to a sample that is not representative of the population. The Literary Digest's survey was voluntary, as only those who chose to respond did so. This could result in a biased sample, as individuals with strong opinions (e.g., Landon supporters) might be more likely to respond.

Analyzing potential biases

Undercoverage

Undercoverage occurs when some groups in the population are not adequately represented in the sample. The Literary Digest's sample was drawn from its own subscribers, telephone directories, and automobile owners, which likely excluded lower-income individuals who did not have telephones or cars. This undercoverage could lead to a biased prediction, as the excluded groups might have had different voting preferences.

The biases that might have caused the error in the Literary Digest's prediction are: