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In advance of the 1936 Presidential Election, a magazine titled Literary Digest released the results of an opinion poll predicting that the republican candidate Alf Landon would win by a large margin. The magazine sent post cards to approximately 10,000,000 prospective voters. These prospective voters were selected from the subscription list of the magazine, from automobile registration lists, from phone lists, and from club membership lists. Approximately 2,300,000 people returned the postcards. a. Think about the state of the United States in 1936. Explain why a sample chosen from magazine subscription lists, automobile registration lists, phone books, and club membership lists was not representative of the population of the United States at that time. b. What effect does the low response rate have on the reliability of the sample? c. Are these problems examples of sampling error or non sampling error? d. During the same year, George Gallup conducted his own poll of 30,000 prospective voters. His researchers used a method they called "quota sampling" to obtain survey answers from specific subsets of the population. Quota sampling is an example of which sampling method described in this module?

Step by step solution

01

Understanding Historical Context (1936)

In 1936, not all demographic groups in the United States had equal access to telephones, cars, or the ability to join clubs. The Great Depression had affected much of the population, meaning many lower-income individuals did not have the financial means for these luxuries, nor could they afford magazine subscriptions. Therefore, selecting a sample from these sources would disproportionately favor wealthier individuals, who were more likely to be Republicans during that era.

02

Analyzing Sample Representativeness

A representative sample should reflect the demographics of the entire population. Because the sample was derived from lists that skewed towards wealthier individuals, it didn't accurately reflect the broader population, which included many people without the means for cars, phones, club memberships, or subscriptions. Thus, it was not representative of the U.S. population.

03

Impact of Low Response Rate

The fact that only 2,300,000 out of 10,000,000 sent postcards back represents a response rate of 23%. A low response rate like this reduces the reliability of the sample, as those who did not respond may have different views from those who did. This non-response bias can significantly skew results.

04

Identifying Error Types

The problems identified, such as sample selection bias and low response rate, are examples of non-sampling error. Non-sampling errors arise from issues in the sample collection process, rather than from the sample size itself. In contrast, sampling error is due to the natural variability in samples of a particular size.

05

Understanding Quota Sampling

Quota sampling involves dividing the population into specific subgroups, or quotas, and collecting data from a specific number of people within each subgroup. It is a form of non-probability sampling where researchers ensure each subgroup is represented adequately. In the context of the Gallup poll, this method ensured a more balanced representation of various demographic groups compared to random sampling from biased lists.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Representative Sample

A representative sample is essential to accurately reflect the demographics and characteristics of an intended population. Let's break this down. Imagine you want to understand the opinions of the entire United States, just like in the 1936 Presidential Election scenario. This means including all the different groups within that country like different income levels, ethnicities, and ages.

In the Literary Digest poll, using sources like magazine subscriptions and automobile lists mainly included wealthier individuals. During the 1930s, amidst the Great Depression, most Americans could not afford these luxuries. Therefore, this sample was not representative of the broader population, which included many lower-income individuals lacking access to such resources.

Ensuring a representative sample helps avoid bias and allows findings to be generalizable to the entire population. Without it, any predictions or conclusions drawn, such as those regarding election outcomes, can be misleading.

Non-Sampling Error

Non-sampling errors occur due to factors other than the sample's size and can significantly affect the validity of survey results. These errors arise from problems in the way samples are collected or the survey process itself.

Here are common types of non-sampling errors:

• **Selection Bias**: When the method of selecting participants over-represents certain groups, as seen with the Literary Digest poll focusing on wealthier citizens.
• **Non-response Bias**: Occurs when individuals who do not respond differ significantly from those who do. The 23% response rate in 1936 likely meant many views were missed due to those who didn't return the postcard.
• **Measurement Error**: Errors due to poorly designed survey questions which may lead to inaccurate responses.

These errors impact the reliability of the poll results. Understanding and minimizing non-sampling errors is crucial to conducting accurate surveys and assessments.

Quota Sampling

Quota sampling is a specific method aimed at ensuring the representation of different subgroups within a population. This technique involves setting quotas to ensure sufficient representation from each subgroup.

For instance, in the Gallup poll from 1936, quota sampling was used to address the very issues faced by the Literary Digest poll. By dividing prospective voters into groups based on traits such as age, income, and location, researchers ensured that each segment was adequately represented. This way, the sample was more reflective of the whole population, ensuring more accurate and balanced survey results.

Unlike random sampling, quota sampling is non-probability based, meaning it's structured deliberately to reflect the diversity of the population. This can be particularly useful in ensuring that minority or harder-to-reach groups are not left out of the study's results, providing a more holistic view of the data being collected.