EscmanE STATISTICS Identifying confounders and ways to eliminate them in an... V A dietary researcher studying grocery expenses is interested in the possible effect that having a vegetarian diet has on a single (unmarried) person's monthly grocery bill. To investigate, the researcher conducts an observational study by contacting a sampl_e of 100 single adults who are homeowners. The researcher gathers the following information from each participant: dietary habits (vegetarian or meatieater), monthly grocery bill, yeariy income and education level. From the data, the researcher creates two groups: vegetarians and meataeaters. Then he compares the average monthly grocery bill between the two groups. (a) Why might the researcher have chosen to perfom'l an observational study (by gathering information about participants' current behaviors) and not a randomized experiment (by assigning participants to either the vegetarian or meateating group at random)? Choose the best answer from the choices below. 0 In a randomized experiment, it could be that some participants who do not eat meat would be assigned to the meat, eating group, meaning that they'd be forced to eat meat. It would not be ethical to force people to eat meat. 0 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. O For a randomized experiment to be performed, the researcher must ask people in the [Epulation to volunteer to take part. This would mean that there would not be any chance to include vegetarians in the sample. (b) The variable home ownership 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, there were no participants in the sample who did not own a home. So, each person in the sample could i: IESIZRIPTIVE STATl STl [:5 Identifying confounders and ways to eliminate them in an... V Espaul (b) The variable home ownership 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, there were no participants in the sample who did not own a home. So, each person in the sample could participate in the study. m 0 A variable is a confounder if its effect on the outcome cannot be distinguished from the eect on the outcome from different treatments. (In our context, the outcome is the monthly grocery bill, and the treatments are being a vegetarian and being a meateater.) In this study, both treatment groups (vegetarian and meateater) were similarly comprised of only participants who owned a home. Thus, the researcher designed the study so that whether or not a participant owns a home would not be a confounder. E El (c) The variable education .ievef is a possible confounder in this study. Choose the best reason why. 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 the monthly grocery billr and the treatments are being a vegetarian and being a meatreater.) There is already a noticeable difference between the two groups of participants in terms of dietary habits. It's possible the participants in the vegetarian group differ from the participants in the meateeating group in other characteristics, such as education level, making it difficult to determine which variable is affecting the monthly grocery hill. 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, there may be some people who did not graduate from high school making it not possible for them to DEscRiPIive SIATlSTICZS Identifying confounders and ways to eliminate them in an... ' U I - _V ery bill. 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 who did not graduate from high school making it not possible for them to participate in the study. (d) Suppose the researcher is interested in reducing the effect that differences in education level might have on monthly grocery bills between the vegetarian and meateating groups. What is a reasonable approach for the researcher to take? Choose the best answer from the choices below. 0 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. A sample size of at least 1000 participants is recommended to control for unwanted variation in a study. 0 The researcher could divide the participants in the vegetarian group into two groups: those with at least some college education and those without any college education. She would diVIdE the meateating participants in the same way. Then the average monthly grocery bill could be compared between the vegetarians and meateaters, by education level. 0 The researcher could aim to select a vegetarian and then nd a meateater who has a higher education level than the vegetarian. She could continue to create pairs of participants in this way, such that each pair contained one vegetarian and one meateater and such that the meateating participant in the pair always has a higher education level. Then she could compare the average monthly grocery bills between the vegetarian group (having a lower education level) and the meateating group (having a higher education level). . Tc-rrris (ii Usi: Privacy C'cntiz-r Accc-ss i bil iW DESCRIPTIVE STATISTICS Understanding the differences between designed experiments... V A market researcher for a local grocery store is interested in determining whether women are more likely than men to buy the chocolate milk brand Caocow. (If sor the researcher would recommend that advertising for Caocow be geared more toward women.) To investigate, the researcher selects a sample of 175 females and a sample of 175 males from the store's customer database. The selected customers' monthly shopping trends are digitally monitored by the researcher through the use of a customer loyalty card. After six months, the percentage of shoppers who have purchased Caocow is compared between the two groups. (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 El O Observational study 0 Designed experiment 0 prospective O doubleblind O retrospective 0 completely randomized E E (b) which one of the following best describes the explanatory (independent) and response (dependent) variables? 0 The explanatory variable is the brand of chocolate milk and the response variable is the percentage of shoppers who have purchased Caocow. O The explanatory variable is the percentage of shoppers who have purchased Caocow and the response variable is gender. 0 THF' F-ynlanr-itnrv variahls- is Flnl'iFlr and Hit: rF-zznnnciz- unriI-ihln3 it: the nF-rnantnrie nf shnnnerl: whn have niirrhaqrIri Canrnw 3 DESCRIPTIVE STATISTlCIS Understanding the differences between designed experiments... V Espa ol (b) Whlul one of the following best describes the explanatory (independent) and response (dependent) variables? 0 The explanatory variable is the brand of chocolate milk and the response variable is the percentage of shoppers who have purchased Caocow. O The explanatory variable is the percentage of shoppers who have purchased Caocow and the response variable is gender. O The explanatory variable is gender and the response variable is the percentage of shoppers who have purchased Caocow. III 0 The explanatory variable is gender and the response variable is the brand of chocolate milk. E (c) Suppose there is a Significant difference between the percentage of female shoppers who purchased Caocow and the percentage of male shoppers who purchased Caocow. Would the researcher be welljustified in claiming that the difference in percentage was caused by the Shopper's gender? Choose the best answer below. EIEI 0 Yes. Because the procedure used data gathered over an extended period of time (six months), the data set will be large. So, claiming a causesandreffect relationship is wellrjustified. O No. The researcher has only found evidence to support a claim that a shopper's gender is associated With the decision to purchase Caocow. O No. There is no procedure, however welldesigned, that can give evidence to support a claim of a causeandeffect relationship