Question

In Exercises 9–12, identify the type of sample and explain why the sample is biased. A sportswriter wants to determine whether baseball coaches think wooden bats should be mandatory in collegiate baseball. The sportswriter mails surveys to all collegiate coaches and uses the surveys that are returned.

Short answer

The type of sampling used is a convenience sample, and the sample is biased. It's likely that coaches who choose to respond feel more strongly about the issue, are more enthusiastic about participating in surveys, or have more time to fill in and return the survey, compared to those who didn't respond. Thus, the resulting sample is biased in their favor, which is inappropriate as it provides a non-representative sample of all collegiate baseball coaches.

Step-by-step solution

Identify the Type of Sample

The first step is to identify the type of sample in this exercise. The sportswriter mailed surveys to all collegiate coaches, thus trying to survey a whole population (which would have been a census), but in the end, he surveyed only a certain group that responded. Therefore, they used a 'convenience sample' as they only used surveys that were easy to get back.

Recognize the Bias

The bias arose because not all of the collegiate baseball coaches returned the surveys. The assumption the sportswriter is making here is that those who returned the surveys are representative of all collegiate baseball coaches, which may not be the case. Some coaches might have strong opinions about the issue and thus make the effort to return the survey, whereas others (who may have different opinions) may not feel strongly enough about the issue to make the effort to return the survey. This could skew the results.

Explain the Nature of Bias

This sampling method is biased because it probably over-represents the views of those who have stronger feelings or opinions on the matter, while under-representing those who may not feel as strongly about the matter or may have different views. Thus, the final survey result would not be an accurate representation of 'whether baseball coaches think wooden bats should be mandatory in collegiate baseball'.

Key concepts

Convenience Sample

A 'convenience sample' is a type of non-probability sampling where subjects are selected due to their convenient accessibility and proximity to the researcher. In the context of the sportswriter's survey on collegiate baseball coaches, the decision to use the surveys that were returned falls under this category. Convenience sampling can often lead to significant bias because it does not draw from a true cross-section of the population.

For example, coaches with a strong preference regarding the use of wooden bats may be more motivated to respond, while those indifferent or with less strong opinions may disregard the survey, resulting in a skewed distribution of responses. Such a sample lacks the diversity required to generalize the results to the whole population. To improve upon this method, researchers should aim to include a strategy for encouraging or even incentivizing a larger and more diverse array of respondents to take part in the survey.

Survey Methodology

Survey methodology encompasses the techniques used in collecting data from or about a set of respondents to infer the broader population characteristics. A well-implemented survey considers factors such as the sampling frame, the size and selection of the sample, the questionnaire design, and the data collection method.

In the exercise, the sportswriter appears to have an initial good approach by evidently reaching out to all collegiate coaches (as the sampling frame) but fails to implement a proper collection method since only voluntarily returned surveys are counted. To improve this methodology, the sportswriter should adopt a more strategic approach, perhaps by following up with non-respondents or using stratified random sampling to ensure different subgroups within the population are adequately represented.

Representative Sample

A 'representative sample' is a subset of a population that seeks to accurately reflect the characteristics of the larger group. To be representative, a sample must be randomly selected, and all members of the population must have an equal chance of being included.

The sample in the sportswriter's survey potentially excludes a significant portion of the population with different views or levels of apathy towards the survey topic — not reflective of the diversity within the entire population of collegiate baseball coaches. To correct this, the sportswriter should have used a random sampling technique where each coach had an equal opportunity to be selected, providing a more accurate picture of the collective opinion. Such a method would increase the reliability of the survey results and allow valid generalizations to be made about the opinions of all collegiate baseball coaches on the mandatory use of wooden bats.