Math 221 - Chapter 1
Questions about causality are usually phrased in the form of ___ questions.
"What if...?"
A difference between two groups in an observational study that can explain why the outcomes were very different between the groups is called what? A treatment variable An outcome variable A causality A confounding variable
A confounding variable
Which of the following is used to summarize two potentially related categorical variables? Choose the correct answer below. Stacked table Histogram A two-way table Frequency table
A two-way table
A group of educators wants to determine how effective tutoring is in raising students' grades in a math class, so they arrange free tutoring for those who want it. Then they compare final exam grades for the group that took advantage of the tutoring and the group that did not. Suppose the group participating in the tutoring tended to receive higher grades on the exam. Does that show that the tutoring worked? If not, explain why not and suggest a confounding variable. A. Because this was an observational study, it only shows an association; it does not show that the tutoring worked. It could be that more motivated students attended the tutoring and that was what caused the higher grades. B. Because this was an observational study, it only shows an association; it does not show that the tutoring worked. It could be that an insufficient number of students were studied to show that the tutoring worked. C. The study shows that the tutoring worked.
A. Because this was an observational study, it only shows an association; it does not show that the tutoring worked. It could be that more motivated students attended the tutoring and that was what caused the higher grades. note: You can never draw cause-and-effect conclusions from observational studies because of potential confounding variables. An observational study can conclude only that there is an association between the treatement variable and the outcome variable.
Which of the following is an identifying mark of an observational study? A. Subjects in the study are put into the treatment group or the control group either by their own actions or by the decision of someone not involved in the research study. B. Researchers observe but do not interact with subjects in an experiment. C. Subjects are often given a placebo or harmless pill that they believe is actually an effective treatment. D. Observational studies are controlled experiments.
A. Subjects in the study are put into the treatment group or the control group either by their own actions or by the decision of someone not involved in the research study.
Why is random assignment used to assign people to treatment groups and control groups in a controlled experiment? A. To make the groups as similar as possible, minimizing bias. B. To ensure that the researchers do not know which groups subjects are members of. C. To ensure that the groups have equal numbers. D. To make sure that the percentage of men and women in each group is exactly the same.
A. To make the groups as similar as possible, minimizing bias.
A study looked at the effects of light on female mice. Fifty mice were randomly assigned to a regimen of 12 hours of light and 12 hours of dark (LD), while another fifty mice were assigned to 24 hours of light (LL). Researchers observed the mice for two years. Four of the LD mice and 12 of the LL mice developed tumors. The accompanying table summarizes the data. Complete parts a through c. LD LL Tumor 4 12 No Tumors 46 38 . Determine the percentage of mice that developed tumors from each group (LL and LD). Compare them and comment. In the LD mice, 8% developed tumors. In the LL mice, 24% developed tumors. The LD mice developed tumors at a lower rate than the LL mice. QUESTION 1. Was this a controlled experiment or an observational study? How do you know? A. This was an observational study because there was a treatment and a control group. B. This was a controlled experiment because there were more than 50 mice. C. This was a controlled experiment because there were two groups that were assigned by the researchers. D. This was an observational study because there were two groups that were assigned by the researchers. QUESTION 2. Can we conclude that light for 24 hours a day causes an increase in tumors in mice? Why or why not? A. Because it was an observational study, it can be concluded that light for 24 hours a day causes an increase in tumors in mice. B. This was an observational study and an observational study can never be used to infer causation. C. Because it was a controlled experiment, it can be concluded that light for 24 hours a day causes an increase in tumors in mice. D. This was a controlled experiment and a controlled experiment can never be used to infer causation.
Answer 1 - C. This was a controlled experiment because there were two groups that were assigned by the researchers. Answer 2 - C. Because it was a controlled experiment, it can be concluded that light for 24 hours a day causes an increase in tumors in mice. Your answer is correct.
A study looked at people treated for heart disease and reported lower death rates for those who received a coronary bypass (CABG) compared to those who received a stent. The adverse outcomes were greater with stenting. Was this an observational study or a controlled experiment? How do you know? Can we say that the use of CABG causes a better success rate? Why or why not? The beginning of the abstract is given below. We identified patients with multivessel disease who received drug-eluting stents or underwent CABG between October 1 and December 31 of the following year, and we compared adverse outcomes (death, death or myocardial infarction, or repeat revascularization) through December 31 two years after the initial study, after adjustment for differences in baseline risk factors among the patients. Was this an observational study or a controlled experiment? How do you know? A. This was a controlled experiment because there was a control group and a treatment group. B. This was a controlled experiment because there was no random assignment and the study looked at records. C. This was an observational study because there was no random assignment and the study looked at records. D. This was an observational study because there was a control group and a treatment group. QUESTION 2 Can we say that the use of CABG causes a better success rate? Why or why not? A. Because this was an observational study, it only shows an association; it does not show that the use of CABG causes a better success rate. B. It cannot be said that the use of CABG causes a better success rate because an insufficient number of patients were studied. C. Because this was a controlled experiment, it can be said that the use of CABG causes a better success rate.
Answer 1 - C. This was an observational study because there was no random assignment and the study looked at records. note 1: An observational study is when the subjects are put into the treatment or control groups by their own actions. A controlled experiment is when the subjects are put into the treatment or control groups by the researchers. Answer 2 - A. Because this was an observational study, it only shows an association; it does not show that the use of CABG causes a better success rate. note 2: You can never draw cause-and-effect conclusions from observational studies because of potential confounding variables. An observational study can conclude only that there is an association between the treatment variable and the outcome variable.
A pair of college students have decided to test vitamin C to see whether it prevents colds. They recruit 500 students with a sign-up sheet, containing a numbered list. The first half of those on the sheet (Numbers 1-250) are asked to take 500 mg of vitamin C per day, and the second half are told not to use vitamin C. At the end of the school year, participants are asked how many colds they had. How would you improve this study, and why? Select all the ways this study could be improved. A. The researchers should not know who is taking vitamin C or the placebo. B. The students should not know if they are taking vitamin C or a placebo. C. Half of the students should have been given a placebo. D. The students should be randomly assigned to the treatment.
Answers: A, B, C, D The gold standard for experiments involves a large sample size, being controlled and randomized, being double-blind, and utilizing a placebo if appropriate.
Of the following, which is the only method of data collection suitable for making conclusions about causal relationships? A. Observational studies B. Controlled experiments C. Anecdotes D. All three are suitable.
B. Controlled experiments
Which of the following is NOT one of the criteria for the "gold standard" for experiments? A. Large sample size B. Equal sample sizes for control and treatment group C. Double-blinding, in which neither the subjects nor researchers know who is in which group D. Random assignment of subjects to treatment or control groups
B. Equal sample sizes for control and treatment group
A study was done to see whether a smaller dose of flu vaccine could be used successfully. In this study, the usual amount of vaccine was injected into half the patients, and the other half of the patients had only a small amount of vaccine injected. The response was measured by looking at the production of antibodies. In the end, the lower dose of vaccine was just as effective as a higher dose for those under 65 years old. What more do we need to know to be able to conclude that the lower dose of vaccine was equally effective at preventing the flu for those under 65? A. This is an observational study and causation cannot be inferred. B. The patients need to be randomly assigned the full or lower dose. Without randomization there could be bias, however, with randomization we can infer causation. C. This is a controlled experiment and causation cannot be inferred. D. The sample size must be at least 500 to ensure the sample size is large enough to infer causation.
B. The patients need to be randomly assigned the full or lower dose. Without randomization there could be bias, however, with randomization we can infer causation. The gold standard for experiments involves a large sample size, being controlled and randomized, being double-blind, and utilizing a placebo if appropriate. With randomization, the experiment can be used to infer causation.
A study reported on the effects of optimism on health. Researchers studied the emotional styles of 334 subjects and then squirted a cold virus in the noses of these subjects. Those who scored high on "energy, happiness, and relaxation" were significantly less likely to develop colds. Is this study evidence that you can reduce your chance of catching colds by training yourself to be more relaxed and happy? Explain your answer. A. The sample size is not large enough to establish causation. B. Because everyone was given the treatment it can be inferred that a change in happiness would change the likelihood of catching a cold. C. Because this was not a randomized experiment causation cannot be inferred. It is possible that healthier people tend to be happier.
C. Because this was not a randomized experiment causation cannot be inferred. It is possible that healthier people tend to be happier. note: It is reasonable to assume that 334 people is a large enough sample size for such a study. An observational study can never show causation. Because there could be lurking variables it can only show association. Only a controlled experiment can show causation.
Which of the following is a reason we can never draw cause-and-effect conclusions from observational studies? A. Researchers may be biased in the observations they choose to record. B. Observational studies often do not involve a large enough sample to draw cause-and-effect conclusions. C. Potential confounding variables may explain the differences between groups rather than the treatment variable. D. Observational studies are not scientific in nature.
C. Potential confounding variables may explain the differences between groups rather than the treatment variable.
Why is it not possible to conclude which sport is the most dangerous by looking at the number of injuries in the accompanying data table? A. The source of the data is unreliable. B. The sports in the table are not listed by order of frequency. C. The sports have different numbers of participants. D. The sports have different rules and penalties.
C. The sports have different numbers of participants.
Why are percentages or rates often better than counts for making comparisons? A. They are more statistically significant than counts. B. They are more accurate than counts. C. They take into account possible differences among the sizes of the groups. D. Percentages allow us to compare groups that are not similar.
C. They take into account possible differences among the sizes of the groups.
A study reported on the effects of vitamin C in breast milk on preventing allergies in infants. Researchers analyzed levels of vitamin C in the breast milk of some new mothers who had decided whether to take vitamin C during their pregnancy. The highest levels of vitamin C were associated with a 30 percent lower risk of allergies in the infants. Was this an observational study or a controlled experiment? On the basis of this study, can you conclude that vitamin C lowers the risk of allergies in infants? Why or why not? A. This is an observational study and causation can be inferred. B. This is a controlled experiment and causation can be inferred. C. This is a controlled experiment and causation cannot be inferred. D. This is an observational study and causation cannot be inferred.
C. This is an observational study and causation cannot be inferred. note: An observational study can not be used to show causation. This is an observational study because researchers did not determine which group the subjects were in. Only a controlled experiment can be used to show causation if the appropriate standards are satisfied.
The variable "eye color" is an example of what type of variable? Numerical Categorical Algebraic Contextual
Categorical
Which of the following questions should be asked when developing an understanding of data? A. Who collected the data? B. How were the variables measured? C. What variables were measured? D. All of these questions are important.
D. All of these questions are important.
What are two basic types of variables in statistics? Choose the correct answer below. Numerical and categorical Numerical and contextual Numerical and algebraic Contextual and categorical
Numerical and categorical
In an experiment studying the association between a treatment variable and an outcome variable, the group of people who do NOT receive the treatment are called what? The control group The non-treatment group The treatment group The placebo group
The control group
The outcome variable in a question about causality is also referred to as what? The control group The predicting variable The response variable The treatment variable
The response variable
The study of statistics rests on what two major concepts? Variation and number Variation and data Data and context Average and variation
Variation and data
Indicate whether the study is an observational study or a controlled experiment. A group of boys is randomly divided into two groups. One group watches violent cartoons for one hour, and the other group watches cartoons without violence for one hour. The boys are then observed to see how many violent actions they take in the next two hours, and the two groups are compared.
a controlled experiment
Indicate whether the study is an observational study or a controlled experiment. A researcher wonders whether the order in which people taste beverages influences their preferences. Students are told by the researcher to drink from two unmarked cups. The researcher assigns one group of students to drink Beverage A first and then Beverage B. The researcher assigns the other group to drink Beverage B first and then Beverage A. The subjects are asked whether they prefer the first or the second beverage.
a controlled experiment.
A student watched picnickers with a large cooler of soft drinks to see whether teenagers were less likely than adults to choose diet soft drinks over regular soft drinks. A. an observational study B. a controlled experiment
an observational study
Indicate whether the study is an observational study or a controlled experiment. A researcher was interested in the effects of exercise on academic performance in elementary school children. She went to the recess area of an elementary school and identified some students who were exercising vigorously and some who were not. The researcher then compared the grades of the exercisers with the grades of those who did not exercise.
an observational study.
The process of representing categorical variables with numbers (such as letting a 1 represent "smoker" and a 0 represent "non-smoker") is called _______.
coding.
Data are more than just numbers, because data have _____________ .
context
The number of times a value is observed in a data set is called a ______.
frequency
In statistics, the data we work with is just one part of a bigger picture called the ____________.
population
Categorical variables are also referred to as ______ variables.
qualitative
The circles shown to the right are similar, but not exactly the same. This is an example of ____________.
variation
