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Anytime we conduct a survey, we must take care to avoid undercoverage. Suppose we plan to select 500 names from the city phone book, call their homes between noon and 4 p.m., and interview whoever answers, anticipating contacts with at least 200 people. a) Why is it difficult to use a simple random sample here? b) Describe a more convenient, but still random, sampling strategy. c) What kinds of households are likely to be included in the eventual sample of opinion? Excluded? d) Suppose, instead, that we continue calling each number, perhaps in the morning or evening, until an adult is contacted and interviewed. How does this improve the sampling design? e) Random-digit dialing machines can generate the phone calls for us. How would this improve our design? Is anyone still excluded?

Step by step solution

01

Understanding Simple Random Sample Challenges

Using a simple random sample is difficult in this scenario because the city phone book might not include all households (such as those with unlisted numbers or using only cell phones), leading to undercoverage.

02

Proposing a Convenient Random Strategy

A more convenient random sampling strategy could involve using random-digit dialing, which allows the selection of both listed and unlisted numbers, potentially including households that are not present in the phone book.

03

Identifying Included and Excluded Households

Households that are likely to be included are those with landlines and available during call hours. Excluded households include those with only cell phones, unlisted numbers, or those unavailable during calling hours such as working households.

04

Extending Call Times to Improve Sampling

By continuing to call each number at different times of the day, the likelihood of reaching someone increases, thus reducing bias by including more households, particularly those unavailable during initial calling hours.

05

Enhancing Design with Random-Digit Dialing

Random-digit dialing improves the design by potentially reaching a broader range of households, both listed and unlisted. However, it may still exclude households with no phone service at all.

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Key Concepts

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

Understanding Undercoverage

Undercoverage occurs when certain groups are not adequately represented in a survey sample. In the context of sampling from a phone book, undercoverage can happen if some households don't use landlines or have unlisted numbers. This means that a portion of the population is systematically missed.

To consider undercoverage further:

• Households relying solely on cellphones may not appear in the phone book.
• Unlisted numbers also go unrepresented.
• Time-constrained calling can miss adults who are at work or otherwise unavailable during specific hours.

Addressing undercoverage is crucial to ensure that survey results are as representative as possible of the larger population.

Exploring Random Sampling

Random sampling is a method where every individual or household has an equal chance of being selected. The idea is to avoid bias and make the sample representative of the entire population. Most importantly:

• This method reduces selection bias significantly.
• Random sampling must be done thoughtfully to ensure fair representation.

Even though random sampling is ideal, challenges arise when certain groups are harder to reach, such as those with cell phones only or non-listed numbers, which can lead to undercoverage.

Steps to Achieving a Simple Random Sample

A simple random sample is a subset of a population where each member has an equal probability of being chosen, without bias. This is often difficult with phone surveys due to incomplete lists, as is the case with phonebooks:

• Phonebooks often exclude cell-only households, leading to incomplete sampling frames.
• Time-limited calling hours can prevent equal access to participation.

For a population where not all members can be listed, alternative strategies like randomized digit dialing are needed to better approximate a simple random sample.

Advantages of Random-Digit Dialing

Random-digit dialing (RDD) is a method where calls are made to randomly generated phone numbers. This technique aims to overcome some limitations associated with using phone directories. Here's why it's effective:

• Reaches both listed and unlisted numbers, including cell phones.
• Increases the likelihood of contacting a broader demographic.

However, households with no phone service are still excluded, and surveys must adjust for such biases to maintain accuracy.