Question

In a large city school system with 20 elementary schools, the school board is considering the adoption of a new policy that would require elementary students to pass a test in order to be promoted to the next grade. The PTA wants to find out whether parents agree with this plan. Listed below are some of the ideas proposed for gathering data. For each, indicate what kind of sampling strategy is involved and what (if any) biases might result. a) Put a big ad in the newspaper asking people to log their opinions on the PTA Web site. b) Randomly select one of the elementary schools and contact every parent by phone. c) Send a survey home with every student, and ask parents to fill it out and return it the next day. d) Randomly select 20 parents from each elementary school. Send them a survey, and follow up with a phone call if they do not retum the survey within a week.

Short answer

Option a: voluntary response - response bias. Option b: cluster sampling - cluster bias. Option c: convenience sampling - non-response bias. Option d: stratified random sampling - minimal bias.

Step-by-step solution

Analyze Option a

This strategy involves placing an ad in the newspaper and inviting people to log their opinions on a website. This is an example of voluntary response sampling, where participants self-select to provide their input. Potential bias includes a response bias, as those with strong opinions (either for or against) are more likely to participate, whereas indifferent parents might not bother logging in their opinions. This could result in an overrepresentation of extreme views.

Analyze Option b

This method involves randomly selecting one elementary school and contacting every parent by phone. This is a cluster sampling strategy, as the sample is taken from a single cluster (school) of the population. The potential bias here could stem from cluster bias, as the opinions in the chosen school may not be representative of all schools due to regional or cultural variations.

Analyze Option c

In this approach, a survey is sent home with every student, asking parents to return it the next day. This is an example of convenience sampling, since the survey is distributed to all students, expecting a prompt return. Bias can occur if a significant number of surveys are not returned, particularly from busier or less engaged parents, leading to non-response bias.

Analyze Option d

This strategy involves randomly selecting 20 parents from each school, sending them a survey, and following up with a phone call. This is a stratified random sampling method, where subgroups (schools) are represented. By ensuring every school is included, it reduces the bias risk present in cluster sampling. The follow-up call also helps to mitigate non-response bias, making this a more balanced strategy.

Key concepts

Voluntary Response Sampling

Voluntary response sampling is a method where participants choose to partake in the survey on their own. This sampling strategy can often result in biased outcomes, as it tends to attract individuals with strong opinions on either side of the issue.
This means those with moderate or indifferent views might not respond, leading to skewed results.
For instance, in our exercise, placing an advertisement and asking people to share their opinions on the PTA website is a classic example of voluntary response sampling.
To combat its inherent bias, it's crucial to consider strategies that will encourage a more diverse pool of participants to provide their feedback.

Cluster Sampling

Cluster sampling is a method where the population is divided into separate groups, known as clusters, and a sample of these clusters is chosen for data collection.
In the example from our exercise, randomly selecting one elementary school out of twenty and surveying every parent from that school is a form of cluster sampling.
However, a significant drawback is that if a single cluster does not represent the larger population well, the results could suffer from cluster bias.
This means that the specific characteristics of the chosen school, like regional or socio-economic factors, could influence responses and make them non-representative of the entire city.

Convenience Sampling

Convenience sampling is a strategy where a sample is taken from a group that is easy to reach and access. It's a quick and straightforward method but often leads to biases.
In the exercise, sending a survey home with every student and asking for its return the next day is an example of convenience sampling.
The potential for bias arises when those surveys aren't returned, especially by parents who are too busy or less inclined to engage, resulting in non-response bias.
To enhance the reliability of this method, follow-up actions should be considered to capture responses from initially non-responsive participants.

Stratified Random Sampling

Stratified random sampling involves dividing the population into distinct subgroups (strata) that share similar characteristics and then taking a random sample from each group.
In our scenario, selecting 20 parents at random from each school exemplifies this methodology, ensuring representation across all schools.
This approach can significantly reduce biases, especially those present in cluster sampling, as it considers all strata of the population.
Moreover, adding a follow-up, like a phone call, further decreases the risk of non-response bias, making it a robust method for collecting representative data.