## Section1.6Exercises

### SubsectionExercises

###### 1Migraine and acupuncture

A migraine is a particularly painful type of headache, which patients sometimes wish to treat with acupuncture. To determine whether acupuncture relieves migraine pain, researchers conducted a completely randomized controlled study where 89 females diagnosed with migraine headaches were randomly assigned to one of two groups: treatment or control. 43 patients in the treatment group received acupuncture that is specifically designed to treat migraines. 46 patients in the control group received placebo acupuncture (needle insertion at nonacupoint locations). 24 hours after patients received acupuncture, they were asked if they were pain free. Results are summarized in the contingency table below.  1 G Allais et al. “Ear acupuncture in the treatment of migraine attacks: a randomized trial on the efficacy of appropriate versus inappropriate acupoints”. In: Neurological Sci. 32.1 (2011), pp. 173-175

 Pain free Yes No Total Group Treatment 10 33 43 Control 2 44 46 Total 12 77 89
1. What percent of patients in the treatment group were pain free 24 hours after receiving acupuncture? What percent in the control group? Answer

Treatment: $10/43 = 0.23 \rightarrow$23%. Control: $2/46 = 0.04 \rightarrow$4%.

2. Based on your findings in part  a, which treatment appears to be more effective for migraines? Answer

There is a 19% difference between the pain reduction rates in the two groups. At first glance, it appears patients in the treatment group are more likely to experience pain reduction from the acupuncture treatment.

3. Do the data provide convincing evidence that there is a real pain reduction for those patients in the treatment group? Or do you think that the observed difference might just be due to chance? Answer

Answers may vary but should be sensible. Two possible answers: $^1$Though the groups' difference is big, I'm skeptical the results show a real difference and think this might be due to chance. $^2$The difference in these rates looks pretty big, so I suspect acupuncture is having a positive impact on pain.

###### 2Sinusitis and antibiotics, Part I

Researchers studying the effect of antibiotic treatment for acute sinusitis compared to symptomatic treatments randomly assigned 166 adults diagnosed with acute sinusitis to one of two groups: treatment or control. Study participants received either a 10-day course of amoxicillin (an antibiotic) or a placebo similar in appearance and taste. The placebo consisted of symptomatic treatments such as acetaminophen, nasal decongestants, etc. At the end of the 10-day period patients were asked if they experienced significant improvement in symptoms. The distribution of responses are summarized below.  2 J.M. Garbutt et al. "Amoxicillin for Acute Rhinosinusitis: A Randomized Controlled Trial" JAMA: The Journal of the American Medical Association 307.7 (2012), pp. 685-692.

 Self-reported significant improvement in symptoms Yes No Total Group Treatment 66 19 85 Control 65 16 81 Total 131 35 166
1. What percent of patients in the treatment group experienced a significant improvement in symptoms? What percent in the control group?
2. Based on your findings in part a, which treatment appears to be more effective for sinusitis?
3. Do the data provide convincing evidence that there is a difference in the improvement rates of sinusitis symptoms? Or do you think that the observed difference might just be due to chance?
###### 3Identify study components, Part I

Identify (i) the cases, (ii) the variables and their types, and (iii) the main research question in the studies described below.

1. Researchers collected data to examine the relationship between pollutants and preterm births in Southern California. During the study air pollution levels were measured by air quality monitoring stations. Specifically, levels of carbon monoxide were recorded in parts per million, nitrogen dioxide and ozone in parts per hundred million, and coarse particulate matter (PM$_{10}$) in $\mu g/m^3\text{.}$ Length of gestation data were collected on 143,196 births between the years 1989 and 1993, and air pollution exposure during gestation was calculated for each birth. The analysis suggested that increased ambient PM$_{10}$ and, to a lesser degree, CO concentrations may be associated with the occurrence of preterm births.  3 B. Ritz et al. "Effect of air pollution on preterm birth among children born in Southern California between 1989 and 1993". In: Epidemiology 11.5 (2000), pp. 502-511. Answer

(i) 143,196 eligible study subjects born in Southern California between 1989 and 1993.

(ii) Measurements of carbon monoxide, nitrogen dioxide, ozone, and particulate matter less than 10$\mu g/m^3$ (PM$_{10}$) collected at air-quality-monitoring stations as well as length of gestation. These are continuous numerical variables.

(iii) The research question: “Is there an association between air pollution exposure and preterm births?”

2. The Buteyko method is a shallow breathing technique developed by Konstantin Buteyko, a Russian doctor, in 1952. Anecdotal evidence suggests that the Buteyko method can reduce asthma symptoms and improve quality of life. In a scientific study to determine the effectiveness of this method, researchers recruited 600 asthma patients aged 18-69 who relied on medication for asthma treatment. These patients were split into two research groups: one practiced the Buteyko method and the other did not. Patients were scored on quality of life, activity, asthma symptoms, and medication reduction on a scale from 0 to 10. On average, the participants in the Buteyko group experienced a significant reduction in asthma symptoms and an improvement in quality of life.  4 J. McGowan. "Health Education: Does the Buteyko Institute Method make a difference?" In: Thorax 58 (2003). McDowan:2003 Answer

(i) 600 adult patients aged 18-69 years diagnosed and currently treated for asthma.

(ii) The variables were whether or not the patient practiced the Buteyko method (categorical) and measures of quality of life, activity, asthma symptoms and medication reduction of the patients (categorical, ordinal). It may also be reasonable to treat the ratings on a scale of 1 to 10 as discrete numerical variables.

(iii) The research question: “Do asthmatic patients who practice the Buteyko method experience improvement in their condition?”

###### 4Identify study components, Part II

Identify (i) the cases, (ii) the variables and their types, and (iii) the main research question of the studies described below.

1. Researchers studying the relationship between honesty, age and self-control conducted an experiment on 160 children between the ages of 5 and 15. Participants reported their age, sex, and whether they were an only child or not. The researchers asked each child to toss a fair coin in private and to record the outcome (white or black) on a paper sheet, and said they they would only reward children who report white. Half the students were explicitly told not to cheat and the others were not given any explicit instructions. In the no instruction group probability of cheating was found to be uniform across groups based on child's characteristics. In the group that was explicitly told to not cheat, girls were less likely to cheat, and while rate of cheating didn't vary by age for boys, it decreased with age for girls.  5 Alessandro Bucciol and Marco Piovesan. “Luck or cheating? A field experiment on honesty with children”. In: Journal of Economic Psychology 32.1 (2011), pp. 73-78.

2. In a study of the relationship between socio-economic class and unethical behavior, 129 University of California undergraduates at Berkeley were asked to identify themselves as having low or high social-class by comparing themselves to others with the most (least) money, most (least) education, and most (least) respected jobs. They were also presented with a jar of individually wrapped candies and informed that they were for children in a nearby laboratory, but that they could take some if they wanted. Participants completed unrelated tasks and then reported the number of candies they had taken. It was found that those in the upper-class rank condition took more candy than did those in the lower-rank condition.  6 P.K. Piff et al. "Higher social class predicts increased unethical behavior". In: proceedings of the National Academy of Sciences (2012).

###### 5Fisher's irises

Sir Ronald Aylmer Fisher was an English statistician, evolutionary biologist, and geneticist who worked on a data set that contained sepal length and width, and petal length and width from three species of iris flowers (setosa, versicolor and virginica). There were 50 flowers from each species in the data set.  7 R.A Fisher. The Use of Multiple Measurements in Taxonomic Problems". In: Annals of Eugenics 7 (1936), pp. 179-188

1. How many cases were included in the data? Answer

$50 \times 3 = 150\text{.}$

2. How many numerical variables are included in the data? Indicate what they are, and if they are continuous or discrete. Answer

Four continuous numerical variables: sepal length, sepal width, petal length, and petal width.

3. How many categorical variables are included in the data, and what are they? List the corresponding levels (categories). Answer

One categorical variable, species, with three levels: setosa, versicolor, and virginica.

###### 6Smoking habits of UK residents

A survey was conducted to study the smoking habits of UK residents. Below is a data matrix displaying a portion of the data collected in this survey. Note that “£” stands for British Pounds Sterling, “cig” stands for cigarettes, and “N/A” refers to a missing component of the data.  8 Stats4Schools, Smoking.

 sex age marital Income smoke 1 Female 42 Single Under £2,600 Yes 12 cig/day 12 cig/day 2 Male 44 Single £10,400 to £15,600 No N/A N/A 3 Male 53 Married Above £ Yes 6 cig/day 6 cig/day $\vdots$ $\vdots$ $\vdots$ $\vdots$ $\vdots$ $\vdots$ $\vdots$ $\vdots$ 1691 Male 40 Single £2,600 to £5,200 Yes 8 cig/day 8 cig/day
1. What does each row of the data matrix represent?

2. How many participants were included in the survey?

3. Indicate whether each variable in the study is numerical or categorical. If numerical, identify as continuous or discrete. If categorical, indicate if the variable is ordinal.

###### 7Generalizability and causality, Part I

Identify the population of interest and the sample in the studies described in Exercise 1.6.3. Comment on whether or not the results of the study can be generalized to the population and if the findings of the study can be used to establish causal relationships.

Population of interest: all births in Southern California. Sample: 143,196 births between 1989 and 1993 in Southern California. If births in this time span can be considered to be representative of all births, then the results are generalizable to the population of Southern California. However, since the study is observational, the findings do not imply causal relationships.

Population: all 18-69 year olds diagnosed and currently treated for asthma. Sample: 600 adult patients aged 18-69 years diagnosed and currently treated for asthma. Since the sample consists of voluntary patients, the results cannot necessarily be generalized to the population at large. However, since the study is an experiment, the findings can be used to establish causal relationships.

###### 8Generalizability and causality, Part II

Identify the population of interest and the sample in the studies described in Exercise 1.6.4. Comment on whether or not the results of the study can be generalized to the population and if the findings of the study can be used to establish causal relationships.

###### 9Relaxing after work

The 2010 General Social Survey asked the question, “After an average work day, about how many hours do you have to relax or pursue activities that you enjoy?” to a random sample of 1,155 Americans. The average relaxing time was found to be 1.65 hours. Determine which of the following is an observation, a variable, a sample statistic, or a population parameter.

1. An American in the sample. Answer

Oversvation

2. Number of hours spent relaxing after an average work day. Answer

Variable

Sample Statistic

4. Average number of hours all Americans spend relaxing after an average work day. Answer

Population parameter

Suppose you want to estimate the percentage of videos on YouTube that are cat videos. It is impossible for you to watch all videos on YouTube so you use a random video picker to select 1000 videos for you. You find that 2% of these videos are cat videos. Determine which of the following is an observation, a variable, a sample statistic, or a population parameter.

1. Percentage of all videos on YouTube that are cat videos

2. 2

3. A video in your sample

4. Whether or not a video is a cat video

###### 11GPA and study time

A survey was conducted on 218 undergraduates from Duke University who took an introductory statistics course in Spring 2012. Among many other questions, this survey asked them about their GPA and the number of hours they spent studying per week. The scatterplot below displays the relationship between these two variables.

1. What is the explanatory variable and what is the response variable? Answer

Explanatory: number of study hours per week. Response: GPA.

2. Describe the relationship between the two variables. Make sure to discuss unusual observations, if any. Answer

There is a slight positive relationship between the two variables. One respondent reported a GPA above 4.0, which is a data error. There are also a few respondents who reported unusually high study hours (60 and 70 hours/week). The variability in GPA also appears to be larger for students who study less than those who study more. Since the data become sparse as the number of study hours increases, it is somewhat difficult to evaluate the strength of the relationship and also the variability across different numbers of study hours.

3. Is this an experiment or an observational study? Answer

Observational.

4. Can we conclude that studying longer hours leads to higher GPAs? Answer

Since this is an observational study, a causal relationship is not implied.

###### 12Income and education

The scatterplot below shows the relationship between per capita income (in thousands of dollars) and percent of population with a bachelor's degree in 3,143 counties in the US in 2010.

1. What are the explanatory and response variables?

2. Describe the relationship between the two variables. Make sure to discuss unusual observations, if any.

3. Can we conclude that having a bachelor's degree increases one's income?

###### 13Propose a sampling strategy, Part I

A large college class has 160 students. All 160 students attend the lectures together, but the students are divided into 4 groups, each of 40 students, for lab sections administered by different teaching assistants. The professor wants to conduct a survey about how satisfied the students are with the course, and he believes that the lab section a student is in might affect the student's overall satisfaction with the course.

1. What type of study is this? Answer

Observational.

2. Suggest a sampling strategy for carrying out this study. Answer

The professor suspects students in a given section may have similar feelings about the course. To ensure each section is reasonably represented, she may choose to randomly select a fixed number of students, say 10, from each section for a total sample size of 40 students. Since a random sample of fixed size was taken within each section in this scenario, this represents stratified sampling.

###### 14Propose a sampling strategy, Part II

On a large college campus first-year students and sophomores live in dorms located on the eastern part of the campus and juniors and seniors live in dorms located on the western part of the campus. Suppose you want to collect student opinions on a new housing structure the college administration is proposing and you want to make sure your survey equally represents opinions from students from all years.

1. What type of study is this?

2. Suggest a sampling strategy for carrying out this study.

###### 15Internet use and life expectancy

The scatterplot below shows the relationship between estimated life expectancy at birth as of 2012  9 CIA Factbook, Country Comparison: Life Expectancy at Birth, 2012. and percentage of internet users in 2010  10 ITU World Telecommunication/ICT Indicators database, World Telecommunication/ICT Indicators Database, 2012. in 208 countries.

1. Describe the relationship between life expectancy and percentage of internet users. Answer

The relationship between life expectancy and percentage of internet users is positive, non-linear, and somewhat strong.

2. What type of study is this? Answer

This is an observational study.

3. State a possible confounding variable that might explain this relationship and describe its potential effect. Answer

Countries in which a higher percentage of the population have access to the Internet are most probably developed countries which also tend to have a higher quality of life in general and also better health care. Whether or not the country is developed is a lurking variable here, since level of Internet access varies for underdeveloped, developing, and developed countries. (Note: Answers may vary.)

###### 16Stressed out, Part I

A study that surveyed a random sample of otherwise healthy high school students found that they are more likely to get muscle cramps when they are stressed. The study also noted that students drink more coffee and sleep less when they are stressed.

1. What type of study is this?

2. Can this study be used to conclude a causal relationship between increased stress and muscle cramps?

3. State possible confounding variables that might explain the observed relationship between increased stress and muscle cramps.

###### 17Random digit dialing
The Gallup Poll uses a procedure called random digit dialing, which creates phone numbers based on a list of all area codes in America in conjunction with the associated number of residential households in each area code. Give a possible reason the Gallup Poll chooses to use random digit dialing instead of picking phone numbers from the phone book. Answer

Sampling from the phone book would miss unlisted phone numbers, so this would result in bias. People who do not have their numbers listed may share certain characteristics, e.g. consider that cell phones are not listed in phone books, so a sample from the phone book would not necessarily be a representative of the population.

###### 18Haters are gonna hate, study confirms

A study published in the Journal of Personality and Social Psychology asked a group of 200 randomly sampled men and women to evaluate how they felt about various subjects, such as camping, health care, architecture, taxidermy, crossword puzzles, and Japan in order to measure their dispositional attitude towards mostly independent stimuli. Then, they presented the participants with information about a new product: a microwave oven. This microwave oven does not exist, but the participants didn't know this, and were given three positive and three negative fake reviews. People who reacted positively to the subjects on the dispositional attitude measurement also tended to react positively to the microwave oven, and those who reacted negatively also tended to react negatively to it. Researcher concluded that “some people tend to like things, whereas others tend to dislike things, and a more thorough understanding of this tendency will lead to a more thorough understanding of the psychology of attitudes.”  11 Justin Hepler and Dolores AlbarracÍn Attitudes without objects - Evidence for a dispositional attitude, its measurement, and its consequences". In: Journal of personality and social psychology 104.6(2013), p. 1060.

1. What are the cases?

2. What is (are) the response variable(s) in this study?

3. What is (are) the explanatory variable(s) in this study?

4. Does the study employ random sampling?

5. Is this an observational study or an experiment? Explain your reasoning.

6. Can we establish a causal link between the explanatory and response variables?

7. Can the results of the study be generalized to the population at large?

###### 19Family size
Suppose we want to estimate household size, where a “household” is defined as people living together in the same dwelling, and sharing living accommodations. If we select students at random at an elementary school and ask them what their family size is, will this be a good measure of household size? Or will our average be biased? If so, will it overestimate or underestimate the true value? Answer

The estimate will be biased, and it will tend to overestimate the true family size. For example, suppose we had just two families: the first with 2 parents and 5 children, and the second with 2 parents and 1 child. Then if we draw one of the six children at random, 5 times out of 6 we would sample the larger family.

###### 20Flawed reasoning

Identify the flaw(s) in reasoning in the following scenarios. Explain what the individuals in the study should have done differently if they wanted to make such strong conclusions.

1. Students at an elementary school are given a questionnaire that they are asked to return after their parents have completed it. One of the questions asked is, “Do you find that your work schedule makes it difficult for you to spend time with your kids after school?” Of the parents who replied, 85% said “no”. Based on these results, the school officials conclude that a great majority of the parents have no difficulty spending time with their kids after school.

2. A survey is conducted on a simple random sample of 1,000 women who recently gave birth, asking them about whether or not they smoked during pregnancy. A follow-up survey asking if the children have respiratory problems is conducted 3 years later, however, only 567 of these women are reached at the same address. The researcher reports that these 567 women are representative of all mothers.

3. An orthopedist administers a questionnaire to 30 of his patients who do not have any joint problems and finds that 20 of them regularly go running. He concludes that running decreases the risk of joint problems.

###### 21City council survey

A city council has requested a household survey be conducted in a suburban area of their city. The area is broken into many distinct and unique neighborhoods, some including large homes, some with only apartments, and others a diverse mixture of housing structures. Identify the sampling methods described below, and comment on whether or not you think they would be effective in this setting.

1. Randomly sample 50 households from the city. Answer

Simple random sampling. This is usually an effective method as it assigns equal probability to each household to be picked.

2. Divide the city into neighborhoods, and sample 20 households from each neighborhood. Answer

Stratified sampling. This is an effective method in this setting since neighborhoods are unique and this method allows us to sample from each neighborhood.

3. Divide the city into neighborhoods, randomly sample 10 neighborhoods, and sample all households from those neighborhoods. Answer

Cluster sampling. This is not an effective method in this setting since the resulting sample will not contain households from certain neighborhoods and we are told that some neighborhoods are very different from others.

4. Divide the city into neighborhoods, randomly sample 10 neighborhoods, and then randomly sample 20 households from those neighborhoods. Answer

Multi-stage sampling. This method will suffer from the same issue discussed in part (d).

5. Sample the 200 households closest to the city council offices. Answer

Convenience sampling. This is not an effective method since it will result in a biased sample for households that are similar to each other (in the same neighborhood) and the sample will not contain any houses from neighborhoods far from the city council offices.

###### 22Sampling strategies

A statistics student who is curious about the relationship between the amount of time students spend on social networking sites and their performance at school decides to conduct a survey. Various research strategies for collecting data are described below. In each, name the sampling method proposed and any bias you might expect.

1. He randomly samples 40 students from the study's population, gives them the survey, asks them to fill it out and bring it back the next day.

2. He gives out the survey only to his friends, making sure each one of them fills out the survey.

3. He posts a link to an online survey on Facebook and asks his friends to fill out the survey.

4. He randomly samples 5 classes and asks a random sample of students from those classes to fill out the survey.

5. He stands outside the student center and asks every third person that walks out the door to fill out the survey.

Below are excerpts from two articles published in the NY Times:

1. An article titled Risks: Smokers Found More Prone to Dementia states the following  12 R.C. Rabin. Risks: Smokers Found More Prone to Dementia". In: New York Times (2010).: "Researchers analyzed data from 23,123 health plan members who participated in a voluntary exam and health behavior survey from 1978 to 1985, when they were 50-60 years old. 23 years later, about 25% of the group had dementia, including 1,136 with Alzheimer's disease and 416 with vascular dementia. After adjusting for other factors, the researchers concluded that pack-a-day smokers were 37% more likely than nonsmokers to develop dementia, and the risks went up with increased smoking; 44% for one to two packs a day; and twice the risk for more than two packs." Based on this study, can we conclude that smoking causes dementia later in life? Explain your reasoning. Answer

No, this is an observational study.

2. Another article titled The School Bully Is Sleepy states the following  13 T. Parker-Pope. The School Bully Is Sleepy". In: New York Times (2011).: "The University of Michigan study, collected survey data from parents on each child's sleep habits and asked both parents and teachers to assess behavioral concerns. About a third of the students studied were identified by parents or teachers as having problems with disruptive behavior or bullying. The researchers found that children who had behavioral issues and those who were identified as bullies were twice as likely to have shown symptoms of sleep disorders." A friend of yours who read the article says, "The study shows that sleep disorders lead to bullying in school children." Is this statement justified? If not, how best can you describe the conclusion that can be drawn from this study? Answer

This statement is not justified; it implies a causal association between sleep disorders and bullying. However, this was an observational study. A better conclusion would be “School children identified as bullies are more likely to suffer from sleep disorders than non-bullies.”

Given the anonymity afforded to individuals in online interactions, researchers hypothesized that shy individuals might have more favorable attitudes toward Facebook, and that shyness might be positively correlated with time spent on Facebook. They also hypothesized that shy individuals might have fewer Facebook “friends” as they tend to have fewer friends than non-shy individuals have in the offline world. 103 undergraduate students at an Ontario university were surveyed via online questionnaires. The study states "Participants were recruited through the university's psychology participation pool. After indicating an interest in the study, participants were sent an e-mail containing the study's URL." Are the results of this study generalizable to the population of all Facebook users?  14 E.S. Orr et al. The infuence of shyness on the use of Facebook in an undergraduate sample". In: CyberPsychology & Behavior 12.3 (2009), pp. 337-340.

###### 25Stressed out, Part II

In a study evaluating the relationship between stress and muscle cramps, half the subjects are randomly assigned to be exposed to increased stress by being placed into an elevator that falls rapidly and stops abruptly and the other half are left at no or baseline stress.

1. What type of study is this? Answer

Experiment

2. Can this study be used to conclude a causal relationship between increased stress and muscle cramps? Answer

Yes

###### 26Light and exam performance

A study is designed to test the effect of light level on exam performance of students. The researcher believes that light levels might have different effects on males and females, so wants to make sure both are equally represented in each treatment. The treatments are fluorescent overhead lighting, yellow overhead lighting, no overhead lighting (only desk lamps).

1. What is the response variable?

2. What is the explanatory variable? What are its levels?

3. What is the blocking variable? What are its levels?

###### 27Vitamin supplements

In order to assess the effectiveness of taking large doses of vitamin C in reducing the duration of the common cold, researchers recruited 400 healthy volunteers from staff and students at a university. A quarter of the patients were assigned a placebo, and the rest were evenly divided between 1g Vitamin C, 3g Vitamin C, or 3g Vitamin C plus additives to be taken at onset of a cold for the following two days. All tablets had identical appearance and packaging. The nurses who handed the prescribed pills to the patients knew which patient received which treatment, but the researchers assessing the patients when they were sick did not. No significant differences were observed in any measure of cold duration or severity between the four medication groups, and the placebo group had the shortest duration of symptoms. 15 C. Audera et al. Mega-dose vitamin C in treatment of the common cold: a randomised controlled trial". In: Medical Journal of Australia 175.7 (2001), pp. 359-362.

Experiment, as the treatment was assigned to each patient.

2. What are the explanatory and response variables in this study? Answer

Response: Duration of the cold. Explanatory: Treatment, with 4 levels: placebo, 1g, 3g, 3g with additives.

3. Were the patients blinded to their treatment? Answer

Patients were blinded.

Double-blind with respect to the researchers evaluating the patients, but the nurses who briefly interacted with patients during the distribution of the medication were not blinded. We could say the study was partly double-blind.

5. Participants are ultimately able to choose whether or not to use the pills prescribed to them. We might expect that not all of them will adhere and take their pills. Does this introduce a confounding variable to the study? Explain your reasoning. Answer

No. The patients were randomly assigned to treatment groups and were blinded, so we would expect about an equal number of patients in each group to not adhere to the treatment.

###### 28Light, noise, and exam performance

A study is designed to test the effect of light level and noise level on exam performance of students. The researcher believes that light and noise levels might have different effects on males and females, so wants to make sure both are equally represented in each treatment. The light treatments considered are fluorescent overhead lighting, yellow overhead lighting, no overhead lighting (only desk lamps). The noise treatments considered are no noise, construction noise, and human chatter noise.

1. What type of study is this?

2. How many factors are considered in this study? Identify them, and describe their levels.

3. What is the role of the sex variable in this study?

###### 29Music and learning
You would like to conduct an experiment in class to see if students learn better if they study without any music, with music that has no lyrics (instrumental), or with music that has lyrics. Briefly outline a design for this study. Answer

Recruit 30 friends and randomly assign them to three groups: no music, instrumental music, and music with lyrics. Have each participant read a passage to learn about a new concept, and then give them a short quiz assessing what they have learned. Compare the number of questions participants got correct on average across the three groups.

###### 30Soda preference

You would like to conduct an experiment in class to see if your classmates prefer the taste of regular Coke or Diet Coke. Briefly outline a design for this study.

###### 31Exercise and mental health

A researcher is interested in the effects of exercise on mental health and he proposes the following study: Use stratified random sampling to ensure representative proportions of 18-30, 31-40 and 41-55 year olds from the population. Next, randomly assign half the subjects from each age group to exercise twice a week, and instruct the rest not to exercise. Conduct a mental health exam at the beginning and at the end of the study, and compare the results.

1. What type of study is this? Answer

Experiment.

2. What are the treatment and control groups in this study? Answer

Treatment is exercise twice a week. Control is no exercise.

3. Does this study make use of blocking? If so, what is the blocking variable? Answer

Yes, the blocking variable is age.

4. Does this study make use of blinding? Answer

No.

5. Comment on whether or not the results of the study can be used to establish a causal relationship between exercise and mental health, and indicate whether or not the conclusions can be generalized to the population at large. Answer

This is an experiment, so a causal conclusion is reasonable. Since the sample is random, the conclusion can be generalized to the population at large. However, we must consider that a placebo effect is possible.

6. Suppose you are given the task of determining if this proposed study should get funding. Would you have any reservations about the study proposal? Answer

Yes. Randomly sampled people should not be required to participate in a clinical trial, and there are also ethical concerns about the plan to instruct one group not to participate in a healthy behavior, which in this case is exercise.

###### 32Chia seeds and weight loss

Chia Pets — those terra-cotta figurines that sprout fuzzy green hair — made the chia plant a household name. But chia has gained an entirely new reputation as a diet supplement. In one 2009 study, a team of researchers recruited 38 men and divided them randomly into two groups: treatment or control. They also recruited 38 women, and they randomly placed half of these participants into the treatment group and the other half into the control group. One group was given 25 grams of chia seeds twice a day, and the other was given a placebo. The subjects volunteered to be a part of the study. After 12 weeks, the scientists found no significant difference between the groups in appetite or weight loss.  16 D.C. Nieman et al. Chia seed does not promote weight loss or alter disease risk factors in overweight adults". In: Nutrition Research 29.6 (2009), pp. 414-418.

1. What type of study is this?

2. What are the experimental and control treatments in this study?

3. Has blocking been used in this study? If so, what is the blocking variable?

4. Has blinding been used in this study?

5. Comment on whether or not we can make a causal statement, and indicate whether or not we can generalize the conclusion to the population at large.

Researchers studying the effect of TV watching while studying on school performance conducted the following studies. For each study determine (i) the type of study (observational or experiment), (ii) if there is random sampling, (iii) if there is random assignment, (iv) state the scope of the conclusions of the study, and (v) note if stratifying, blocking, or neither of these techniques were used in the study.

1. Researchers randomly sampled 100 high school students and asked them whether or not they watched TV while studying. They found that the mean grade point average of students who did not watch TV while studying was significantly higher than the mean grade point average of students who did watch TV while studying. Answer

(i) Observational study.

(ii) There is random sampling.

(iii) There is no random assignment.

(iv) Since only random sampling from a known population is performed, one may infer the characteristics of the sample tend to mirror corresponding characteristics of the population. Therefore, we can say that among high school students those who do not watch TV while doing homework tend to do better on average. However we cannot infer causation based on this study.

(v) Neither stratifying nor blocking was used in this study.

2. Researchers randomly sampled 50 female and 50 male high school students and asked them whether or not they watched TV while studying. They found that the mean grade point average of both males and females who did not watch TV while doing homework was significantly higher than the mean grade point average of students who did watch TV while doing homework. Answer

(i) Observational study.

(ii) There is random sampling.

(iii) There is no random assignment.

(iv) Since only random sampling from a known population is performed, one may infer the characteristics of the sample tend to mirror corresponding characteristics of the population. Therefore, we can say that among high school males and females those who do not watch TV while doing homework tend to do better on average. However we cannot infer causation based on this study.

(v) Stratifying (separating into groups during the process of sampling) is used but no blocking.

3. Researchers randomly sampled 100 high school students and randomly assigned them into two study groups. Throughout the school year, one group was told to study in a room with a TV on while the other was told to study in silence. At the end of the year the researchers compared the grade point averages of the two groups and found that the mean grade point average of students who did not watch TV while studying was significantly higher than the grade point average of students who did watch TV while studying. Answer

(i) Experiment.

(ii) There is random sampling.

(iii) There is random assignment.

(iv) Since both random sampling and random assignment to groups are performed, one may draw cause-effect inferences about the sample results, as well as generalize to the larger population from which the sample was drawn. Therefore, we can say that there appears to be a cause-and-effect relationship between watching TV while doing homework and low grade point averages.

(v) Neither stratifying nor blocking was used in this study.

Researchers investigating the effect of studying while watching TV on school performance conducted the following studies. For each study determine (i) the type of study (observational or experiment), (ii) if there is random sampling, (iii) if there is random assignment, (iv) state the scope of the conclusions of the study, and (v) note if stratifying, blocking, or neither of these techniques were used in the study.

1. Researchers randomly sampled 50 female and 50 male high school students. Half of the females and half of the males were randomly assigned to study in a room with a TV and the remainder studied without a TV. They found that the mean grade point average of both males and females who did not watch TV while studying was significantly higher than those who did watch TV while studying.

2. Researchers surveyed the first 100 students who showed up to prom. They found that the mean grade point average of students who did not watch TV while studying was higher than the mean grade point average for students who did watch TV while studying.

3. Researchers surveyed the first 50 male and 50 female students who showed up to prom. They found that the mean grade point average of both males and females who did not watch TV while doing homework was higher than the mean grade point average of students who did watch TV while studying.

Suppose a friend of yours wants to design his own study for evaluating the effect of TV watching on school performance. He proposes comparing the grade point averages of everyone in his homeroom class who do and do not watch TV while doing homework, and extending the results of this study to draw conclusions about all high schoolers. Indicate any mistakes with this design, keeping in mind that the goal of the study is to assess the causal relationship between TV watching and school performance for high schoolers. Answer

A sample of everyone in your homeroom class is not a random sample of all high schoolers, therefore findings from this study should not be generalized to all high schoolers. Also, this is an observational study with no random assignment, therefore causal inferences cannot be drawn.

Suppose two friends of yours want to design their own study for evaluating the effect of TV watching on school performance. They propose the following designs. Indicate any mistakes with these designs, keeping in mind that the goal of the study is to assess the causal relationship between TV watching and school performance for high schoolers.

1. Randomly sample 100 students from the entire school. Reserve two classrooms for a study session and the first 50 people that show up get assigned to the room where the TV will be on and the rest to the room where they can study in silence for a final exam. Then compare the average grades of the two groups at the end of the semester.

2. Age and involvement in extracurricular activities may be factors that affect the academic performance of a student, so these characteristics should be blocked for when studying the effect of watching TV while studying. To achieve this aim, sample 10 first-years, 10 sophomores, 10 juniors, and 10 seniors, 5 of which are heavily involved with extracurricular activities and 5 of which are not from each class. Then ask them whether they watch TV while they study, and compare the average GPAs of those who do and do not.

###### 37Running on electrolytes
Suppose you would like to design a study evaluating whether consuming a sports drink that replenishes electrolytes can make you run faster. You were able to recruit 50 students to participate in your study. Describe how you can use matched pairs design and blinding for this study. Answer

Match subjects on attributes that might be associated with running faster: age, height, weight, fitness level, running experience, etc. Then, randomly assign one student from each pair to consume a sports drink that replenishes electrolytes and the other to consume a placebo drink (a drink that looks and tastes the same but does not replenish electrolytes). Then, time the students running the same pre-specified distance (e.g. 1 mile) and compare the average finishing times for the two groups.

###### 38Improving life satisfaction

In a study evaluating the effectiveness of a positive psychology group intervention, forty middle schoolers who were identified as being less than delighted with their lives (reported life satisfaction scores between 1 and 6 on a 7-point scale) were randomly assigned to receive the intervention (treatment) or not receive the intervention (control). These students were first matched on attributes such as sex, socioeconomic group, race/ethnicity, and age, such that each student in the treatment group had a matched counterpart in the control group. Researchers found that life satisfaction of students in the intervention group increased significantly, while the control group declined during the same period (although this change was not statistically significant).  17 Shannon M Suldo et al. Increasing middle school students' life satisfaction: Efficacy of a positive psychology group intervention". In: Journal of happiness studies 15.1 (2014), pp. 19-42.

1. What type of study is this?

2. What type of design is used in this study?

3. Can the results of this study be used to establish a causal link between the intervention and increased life satisfaction in middle schoolers?

###### 39Alfalfa plants
Researchers were interested in the effect that acid has on the growth rate of alfalfa plants. They created three treatment groups in an experiment: low acid ($+$), high acid ($\triangle$), and control (Ο). The alfalfa plants were grown in a Styrofoam cups arranged near a window and the height of the alfalfa plants was measured after five days of growth. The experiment consisted of 6 cups for each of the 3 treatments, for a total of 18 observations. Which of the following designs is preferable? Note that the dotted line indicates the location of the window. Explain your reasoning. Answer

Design B is the most appropriate since there are an equal number of cups from each group at each of the possible distances from the window (2 cups from each group are next to the window, 2 cups from each group are middle distance from the window, 2 cups from each group are far from the window). This is important since the amount of sunlight is likely an important factor in the plants' growth.

2. We instead decide to bake each batch simultaneously on the same tray, and decide to block for proximity to the back of the oven. Two blocking schemes shown below are under consideration. For each scheme, cookies made with the recipe from the website are indicated with a $+$ and cookies made with the other recipe are indicated with a Ο . The dashed line marks the back of the oven. Which of the blocking schemes, A or B, is better for this experiment? Explain your answer.