_ DESCRIPTIVE STATISTICS Identifying confounders and ways to eliminate them in an... V 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 samplj of 450 adults who are currently employed fulltime and records whether or not the participant needs to wear corrective lenses, the partiCipant's education level, and the participant's year1y income. From the results, the researcher creates two groups: corrective lenses and no corrective lenses. Then she 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 at random)? Choose the best answer from the choices below. C) An observational study should always be performed Instead of a randomized experiment, so that the researcher can control the number of groups, the sizes of the groups, and which types of participants are in each group. EEI O For a randomized experiment to be performed, the researcher must ask people in the mpulation 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. IEEI O 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. (b) The variable employment status is not a possible confounder in this study. Choose the best reason why. 0 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 fulltime employment status. So, each person in the sample could ESCRIPTIVE STATISTlCS Identifying confounders and ways to eliminate them in an... 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, all of the participants in the sample had fulltime employment status. 30, each person in the sample could participate since they could be placed into one of the two groups. G 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 fullatime. Thus, the researcher deSlgned the study so that a participant's employment status would not be a confounder. m E El (c) The variable education level is a possible confounder In tl'IlS study. Choose the best reason why. 0 A variable is a confounder it, based on its value, it prohibits some members of the sample from participating in the study. For this study, there may be some people who did not graduate from high school making it not possible for them to participate in the study. IZJEI O 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 education level, making it difcult to determine which variable is affecting yearly income. m DESCRIPTIVE STATISTICS Identifying confounders and ways to eliminate them in an... V (d) Suppose the researcher is interested in reducing the effect that differences in education level might have on yearly income between the corrective lenses and no corrective lenses groups. What is a reasonable approach for the researcher to take? Choose the best answer from the choices below. 0 The researcher could aim to select a participant who wears corrective lenses and then find another participant who does not wear corrective lenses and has the same education level as the participant who wears corrective lenses. She could continue to create pairs of participants in this way, such that each pair of participants with and without corrective lenses has the same education level. This would result in two groups, each comprised of participants with a similar education levels. Then the researcher could compare the average yearly income between the two groups. 0 The researcher could divide the partiCIpants in the corrective lenses group into two groups: those under 50 years and those 50+ years old. She could divide the participants in the no corrective lenses group into two groups: those With a college education and those without. Then she could compare the yearly income between the 50+ years old group and the college educated group. O 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 450 adults in order to have enough variety for a reasonable study. mm m IZIEIEEI DE SCRIPTlVE STATISTICS Identifying and reducing statistical bias v E Leila is the owner of Pie In The Sky, a pizza place in a small city with a population of 60,000. She wants to gather some information about the food preferences of the city's reSidents. She decides to ask every customer who comes into her restaurant one day the following question. which do you prefer to eatr hamburgers or pizza? Of the 23 customers who came into the restaurant that day, 19 said they preferred pizza and the rest said they preferred hamburgers. m (a) Identify and describe the most prominent source of bias in Leila's study. X \\(3 Choose the best answer from the choices below. 0 E H O The bias comes from the sampling clone in the study. Only Leila's customers were asked the question, making the sample a sample of convenience. I? O The bias comes from the fact that the customers were not allowed to voluntarily choose to be in the sample. Volunteers are more likely to have characteristics that reect the population as a whole. RI 0 The bias comes from the phrasmg of the question and the context in which it is asked. The responses are unlikely to accurately reect the customers' preferences. 0 The bias comes from having too many of the customers not respond to the question. These customers might answer the question differently than those who did. 0 There is no or very little bias in Leila's study. The sample size is smaller than 30. Samples of this size are very unlikely to have outliers, meanino that the sample will have characteristics that reect the population as a whole. l Explanation l : DE schPTIVE STATISTICS t:||:||::- ya '_' Identifying and reducing statistical bias V question differently than those who did. 0 There is no or very little bias In Leila's study. The sample size is smaller than 30. Samples of this size are very unlikely to have outliers, meaning that the sample will have characteristics that reect the population as a whole. (b) Describe something Leila could have done to reduce the most prominent source of bias in the study. Choose the best answer from the choices below. 0 Put up a poll asking the question on the pizza place's website. This way Leila makes sure that the respondents ll"l the sample are volunteers. 0 Change the phrasmg of the question and make sure that the customers who came to the pizza place could answer the question anonymously. That way the customers' answers would be more likely to accurately reect their preferences. 0 Offer a free slice of pizza to any customer who answers the question. This way the number of customers not answering the question would be decreased. 0 Modify the study by asking the question to a random sample of the city's residents instead ofjust customers coming to the pizza place. This way the sample is no longer a sample of convenience. 0 As the sample size is sufciently small, the study has no or very little bias. so, there is nothing Leila needed to have done to reduce bias. Kundan V Espaol m IKIEIEEI 1:: DE SCRIPTIVE STATISTICS Understanding the differences between designed experiments... V FE. A pharmaceutical company has developed a new u vaccine. To test its effectiveness, the company recruits 1000 volunteers to participate. The participants are divided into two groups. Care is taken to make the two groups similar in composition with respect to factors such as race, gender, and medical history. One group is given the new vaccine. The other group is given a placebo {a saline solution that looks like the vaccine but contains no vaccine). The participants are not aware of whether they are receiving the vaccine or the placebo. The doctors giving the injection are also unaware of which participants are in which group. Six months later, the participants are contacted. For each group, the percentage of participants who contracted the u at any point over the six months is recorded. The company will compare these percentages between the two groups. m (a) First choose whether the procedure described above is an observational study or a designed experiment. Then further categorize the procedure by choosing the correct type of observational study or designed experiment. E O Observational study 0 Designed experiment E O prospective O doublerblind [I O retrospective 0 completely randomized E (b) which one of the following best describes the explanatory (independent) and response (dependent) variables? 0 "he explanatory variable is receiving the vaccine or not and the response variable is the percentage of participants who contracted the flu. 0 "he explanatory variable is the percentage of participants who contracted the u and the response variable is receiving the vaccine or not. DE SCRIPTIVE STATISTICS Understanding the dierences between designed experiments... _ (""5 V 0 me explanatory variable is the percentage of partiCipants who contracted the u and the response variable is receiving the vaccine or not. 0 The explanatory variable is the medical history and the response variable is the percentage of participants who contracted the u. O The explanatory variable is receiving the vaccine or not and the response variable is the medical history. (c) Suppose there is a significant difference in the percentage of participants who contracted the u between the two groups. Has the company found evidence to support a claim that the difference in u contraction is caused by the vaccine? Choose the best answer below. 0 No. There is no procedure, however wellsdesigned, that can give evidence to support a claim of a causesandreffect relationship. 0 No. Because the participants don't know if they were receiving the vaccine or the piacebo, it is not possible to nd evidence to support any claim about a relationship between the percentage of partiCipants who contracted the u and whether or not the participants received the vaccine. 0 Yes. It's possible as long as the procedure was welldesigned and all other variables that might inuence the result were controlled for