Question

According to Pew Research, the contact rate (probability of contacting a selected household) was \(69 \%\) in 1997 and \(76 \%\) in 2003 . However, the cooperation rate (probability of someone at the contacted household agreeing to be interviewed) was \(58 \%\) in 1997 and dropped to \(38 \%\) in 2003 . a) What is the probability (in 2003) of obtaining an interview with the next household on the sample list? (To obtain an interview, an interviewer must both contact the household and then get agreement for the interview.) b) Was it more likely to obtain an interview from a randomly selected household in 1997 or in \(2003 ?\)

Short answer

a) 28.9% in 2003. b) It was more likely in 1997.

Step-by-step solution

Understand the Given Information

To solve the problem, we begin by identifying the relevant data. In 2003, the contact rate is 76% and the cooperation rate is 38%. In 1997, the contact rate is 69% and the cooperation rate is 58%.

Calculate Probability in 2003

The probability of obtaining an interview in 2003 requires both contacting the household and getting their cooperation. This means we multiply the contact rate by the cooperation rate for 2003:\[ P(\text{interview in 2003}) = 0.76 \times 0.38 \]

Perform the Calculation for 2003

Calculate the probability using the values obtained:\[ P(\text{interview in 2003}) = 0.76 \times 0.38 = 0.2888 \] which equals 28.88%, or approximately 28.9%.

Calculate Probability in 1997

Similarly, calculate the probability of obtaining an interview in 1997 by multiplying the corresponding contact rate by the cooperation rate:\[ P(\text{interview in 1997}) = 0.69 \times 0.58 \]

Perform the Calculation for 1997

Complete the calculation for 1997:\[ P(\text{interview in 1997}) = 0.69 \times 0.58 = 0.4002 \] which equals 40.02%, or approximately 40.0%.

Compare the Probabilities

Looking at the probabilities calculated: 28.9% in 2003 and 40.0% in 1997, it is evident that the probability of obtaining an interview was higher in 1997 than in 2003.

Key concepts

Contact Rate

Contact rate is a crucial aspect of many studies and surveys. It represents the probability or likelihood of successfully reaching out to a household that is on your participant list. In simpler terms, it's how often you can make contact with the people you want to talk to. This matters a lot in research because if you can't reach people, you can't gather the necessary data.
For example, in 2003, Pew Research had a contact rate of 76%, meaning that for every 100 households they attempted to reach, they were able to contact 76 of them. This rate increased from 1997, where the likelihood was slightly lower at 69%.
Ultimately, the contact rate helps researchers understand part of the challenge in gathering data and how efficiently they can reach participants.

Cooperation Rate

The cooperation rate is another significant metric in survey research. This rate indicates the probability that someone from a contacted household will agree to participate in the survey or interview. It's key to getting valuable insights, as contacting a household isn't enough — they need to be willing to cooperate.
In 1997, Pew reported a cooperation rate of 58%. This means that over half of the contacted people agreed to participate. However, this dropped drastically to 38% by 2003. This decrease highlights challenges researchers face, like increasing resistance or survey fatigue among potential respondents.
Understanding cooperation rates can help researchers modify their approach to increase the likelihood of participation.

Interview Probability

Interview probability combines both the contact rate and the cooperation rate to determine the overall likelihood of successfully completing an interview. Calculating this probability helps researchers estimate how many households will participate, allowing them to plan resources and time effectively.
For instance, the probability of conducting an interview in 2003 was found by multiplying the contact rate of 76% by the cooperation rate of 38%. This results in an interview probability of approximately 28.9%.
In 1997, these probabilities were 69% for contact and 58% for cooperation, leading to an interview probability of about 40%.

• Contact must occur.
• Cooperation must be given for the interview.

These two factors are multiplied because both events must happen for an interview to take place.

Yearly Comparison

Yearly comparison is vital in analyzing trends and changes over time. By comparing the data from different years, researchers can identify improvements or declines and make strategic adjustments.
In this case, comparing the probability of obtaining an interview between 1997 and 2003 shows a clear decrease from 40% to 28.9%. This suggests that while households were more contactable in 2003, they were less willing to participate in interviews compared to 1997.
This insight is valuable for understanding shifts in public willingness to engage in surveys and can guide future strategies to enhance response rates.