A statistician needs to survey a sample of 50 people that is representative of voters in his community. He prepared a list of phone numbers of 50 randomly selected, expected voters. Next morning, he came to work at 8:00 and began to make calls. By 11:00 a.m., his survey was done. Don't discuss what is not said. Discuss what is wrong with what is said.
How does he find a population to make random choices from? Who has phones that are listed in the phone book? Even more problematic, who doesn't, so the sample will be biased? People without phones? Unlisted numbers? Cell phones?
What is wrong with the scenario described is the assumption that making phone calls between 8:00 a.m. and 11:00 a.m. will provide a representative sample of voters in the community.
There are several issues with this approach:
1. Time bias: The time at which phone calls are made can introduce a bias in the sample. People who are more likely to be available and answer calls during that specific time frame may have different characteristics compared to those who are not available. For example, individuals who work during the day may not be reachable during those hours, leading to an underrepresentation of certain demographics.
2. Non-response bias: It is important to consider that not everyone will answer the phone or be willing to participate in the survey. This can introduce a non-response bias if the people who choose not to participate have different opinions or characteristics compared to those who do.
3. Exclusion of certain groups: By relying solely on phone numbers, the survey excludes individuals who do not have access to phones or have chosen not to provide their phone numbers. This exclusion may lead to an underrepresentation of specific demographics, potentially skewing the results.
To ensure a more representative sample, the statistician should employ random sampling techniques that encompass different times of the day, employ diverse contact methods (e.g., phone, email, in-person), and include strategies to mitigate non-response bias. Additionally, efforts should be made to ensure the sample includes a diverse range of individuals with various demographic characteristics to accurately represent the community's voters.