A researcher is interested in studying the possible relationship between a person's yearly income and whether or not they need to wear corrective lenses. To investigate, the researcher conducts an observational study by surveying a sample of 750 adults who are currently employed full-time and records whether or not the participant needs to wear corrective lenses, age, and the participant's yearly income. From the results, the researcher creates two groups: corrective lenses and no corrective lenses. Then he compares the average yearly income between the two groups. (a) Why might the researcher have chosen to perform an observational study (by conducting a survey) and not a randomized experiment (by assigning participants to either the corrective lenses or no corrective lenses group 5 ? at random)? Choose the best answer from the choices below. For a randomized experiment to be performed, the researcher must ask people in the population to volunteer to take part. This would mean that there would not be any chance to include people who wear corrective lenses in the sample. For a randomized experiment to be performed, the researcher would have to randomly assign participants to either the corrective lenses group or the no corrective lenses group. But whether or not a person needs to wear corrective lenses is out of the researcher's control. O A randomized experiment should never be performed when it is possible to perform an observational study. When groups are randomly assigned, the researcher cannot control the types of participants in each group, making the results of a randomized experiment unreliable. (b) The variable employment status is not a possible confounder in this study. Choose the best reason why. A variable is a confounder if its effect on the outcome cannot be distinguished from the effect on the outcome from different treatments. (In our context, the outcome is yearly income, and the treatments are needing corrective lenses and not needing corrective lenses.) In this study, both treatment groups (corrective lenses and no corrective lenses) were similarly comprised of only participants who were employed full-time. Thus, the researcher designed the study so that a participant's employment status would not be a confounder. A variable is a confounder if, based on its value, it prohibits some members of the sample from participating in the study. For this study, all of the participants in the sample had full-time employment status. So, each person in the sample could participate since they could be placed into one of the two groups. (c) The variable age is a possible confounder in this study. Choose the best reason why. O A variable is a confounder if, based on its value, it prohibits some members of the sample from participating in the study. For this study, there may be some people in the sample who have a birthday during the study. Thus, their age would change during the study, making it not possible for them to participate. A variable is a confounder if its effect on the outcome cannot be distinguished from the effect on the outcome from different treatments. (In our context, the outcome is yearly income, and the treatments are needing corrective lenses and not needing corrective lenses.) There is already a noticeable difference between the two groups of participants in terms of wearing corrective lenses. It's possible the participants in the corrective lenses group differ from the participants in the no corrective lenses group in other characteristics, such as age, making it difficult to determine which variable is affecting yearly income. (d) Suppose the researcher is interested in reducing the effect that differences in age might have on yearly income between the corrective lenses and no corrective lenses. What is a reasonable approach for the researcher to take? Choose the best answer from the choices below. The researcher could increase the sample size. Increasing the sample size helps to reduce the effect that confounding variables have on the outcome of the study. Because there are so many possible levels of education, it would be necessary to have a sample size much larger than 500 adults in order to have enough variety for a reasonable study. The researcher could divide the participants in the corrective lenses group into two groups: those with a college degree and those without a college degree. She could divide the participants in the no corrective lenses group in the same manner. Then she could compare the average yearly income between the corrective lenses and no corrective lenses groups, by education level. The researcher could aim to select a participant who wears corrective lenses and then find a participant who does not wear corrective lenses and is older than the corrective lenses participant. She could continue to create pairs of participants in this way, such that each pair contains one participant with and one without corrective lenses and such that the participant without the corrective lenses is always older. Then she could compare the average yearly income between the corrective lenses group (being younger) and the no corrective lenses group (being older). A researcher is interested in studying the possible relationship between a person's yearly income and whether or not they need to wear corrective lenses. To investigate, the researcher conducts an observational study by surveying a sample of 750 adults who are currently employed full-time and records whether or not the participant needs to wear corrective lenses, age, and the participant's yearly income. From the results, the researcher creates two groups: corrective lenses and no corrective lenses. Then he compares the average yearly income between the two groups. (a) Why might the researcher have chosen to perform an observational study (by conducting a survey) and not a randomized experiment (by assigning participants to either the corrective lenses or no corrective lenses group 5 ? at random)? Choose the best answer from the choices below. For a randomized experiment to be performed, the researcher must ask people in the population to volunteer to take part. This would mean that there would not be any chance to include people who wear corrective lenses in the sample. For a randomized experiment to be performed, the researcher would have to randomly assign participants to either the corrective lenses group or the no corrective lenses group. But whether or not a person needs to wear corrective lenses is out of the researcher's control. O A randomized experiment should never be performed when it is possible to perform an observational study. When groups are randomly assigned, the researcher cannot control the types of participants in each group, making the results of a randomized experiment unreliable. (b) The variable employment status is not a possible confounder in this study. Choose the best reason why. A variable is a confounder if its effect on the outcome cannot be distinguished from the effect on the outcome from different treatments. (In our context, the outcome is yearly income, and the treatments are needing corrective lenses and not needing corrective lenses.) In this study, both treatment groups (corrective lenses and no corrective lenses) were similarly comprised of only participants who were employed full-time. Thus, the researcher designed the study so that a participant's employment status would not be a confounder. A variable is a confounder if, based on its value, it prohibits some members of the sample from participating in the study. For this study, all of the participants in the sample had full-time employment status. So, each person in the sample could participate since they could be placed into one of the two groups. (c) The variable age is a possible confounder in this study. Choose the best reason why. O A variable is a confounder if, based on its value, it prohibits some members of the sample from participating in the study. For this study, there may be some people in the sample who have a birthday during the study. Thus, their age would change during the study, making it not possible for them to participate. A variable is a confounder if its effect on the outcome cannot be distinguished from the effect on the outcome from different treatments. (In our context, the outcome is yearly income, and the treatments are needing corrective lenses and not needing corrective lenses.) There is already a noticeable difference between the two groups of participants in terms of wearing corrective lenses. It's possible the participants in the corrective lenses group differ from the participants in the no corrective lenses group in other characteristics, such as age, making it difficult to determine which variable is affecting yearly income. (d) Suppose the researcher is interested in reducing the effect that differences in age might have on yearly income between the corrective lenses and no corrective lenses. What is a reasonable approach for the researcher to take? Choose the best answer from the choices below. The researcher could increase the sample size. Increasing the sample size helps to reduce the effect that confounding variables have on the outcome of the study. Because there are so many possible levels of education, it would be necessary to have a sample size much larger than 500 adults in order to have enough variety for a reasonable study. The researcher could divide the participants in the corrective lenses group into two groups: those with a college degree and those without a college degree. She could divide the participants in the no corrective lenses group in the same manner. Then she could compare the average yearly income between the corrective lenses and no corrective lenses groups, by education level. The researcher could aim to select a participant who wears corrective lenses and then find a participant who does not wear corrective lenses and is older than the corrective lenses participant. She could continue to create pairs of participants in this way, such that each pair contains one participant with and one without corrective lenses and such that the participant without the corrective lenses is always older. Then she could compare the average yearly income between the corrective lenses group (being younger) and the no corrective lenses group (being older)