Smoking habits of UK residents. (1.10, p. 20) 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 “\(\pounds\)” stands for British Pounds Sterling, “cig” stands for cigarettes, and “N/A” refers to a missing component of the data.

1. What does each row of the data matrix represent? Each row of the data represents an observation corresponding to one participant. The attributes corresponding to each particpant includes, gender, age, marital status, gross income, smoker or non-smoker, cigarettes smoked/day on weekend, and cigarettes smoked/day on weekday

2. How many participants were included in the survey? The first column of the last row of data matrix shows 1691 - implying that there were a total of 1691 participants 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.

1. sex - categorical and not ordinal
2. age - numberical - discrete (based on the sample diplayed - the age variable seems to take only integers. However, increasing the accuracy of the age, i.e., increasing decimal places, may allow the variable to be treated as continuous)
3. marital - categorical and not ordinal
4. grossIncome - categorical - ordinal
5. smoke - categorical and not oridinal
6. amtWeekends - numerical - discrete
7. amtWeekdays - numerical - discrete

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Cheaters, scope of inference. (1.14, p. 29) Exercise 1.5 introduces a study where researchers studying the relationship between honesty, age, and self-control conducted an experiment on 160 children between the ages of 5 and 15¹. 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 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. Differences were observed in the cheating rates in the instruction and no instruction groups, as well as some differences across children’s characteristics within each group.

1. Identify the population of interest and the sample in this study. The population of interest is the complete population of children who are between ages 5 & 15 years and the sample is the set of 160 children on which the experiment was conducted.

2. 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.

If the sample of 160 students chosen for the study can be considered representative of whole population of children between the ages 5 to 15 years then the results can be generalized for the whole population. As there is no information provided on the sampling methodology, and the representativeness of the sample we cannot fully conclude on this.Further, since the results are from an experimental study, it can be used to establish causal relationships.

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Reading the paper. (1.28, p. 31) 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:

“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.

We cannot conclude the causal relationship between smoking and dementia as the study is an observational study. However we can show an association between smoking and dementia.

2. Another article titled The School Bully Is Sleepy states the following:

“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?

Since this is an observational study, we cannot conclude that sleep disorders leads to bullying. However an association between sleep disorders and bulling can be shown.

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Exercise and mental health. (1.34, p. 35) A researcher is interested in the effects of exercise on mental health and he proposes the following study: Use stratified random sampling to ensure rep- resentative 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? This is an example of experimental study given the fact that the participants are divided into two separate treatment groups.

2. What are the treatment and control groups in this study? The group that has been instructed to exercise twice a week is the treatment group and other group that has been instructed not to exercise is the control group.

3. Does this study make use of blocking? If so, what is the blocking variable? Yes the study makes use of blocking. The blocking variable is age in this study.

4. Does this study make use of blinding? No - the participants know that they are not part of the treatment group as they are told not to exercise

5. Comment on whether or not the results of the study can be used to establish a causal rela- tionship between exercise and mental health, and indicate whether or not the conclusions can be generalized to the population at large. Yes - as this is an experimental study, the results can be used to establish causal relationhip between exercise and mental health. Also, since the stratified random sampling has been used to ensure population representativeness, the results can be generalized to larger population. Although as mentioned in the below paragrpaph - there are some reservations that I have around the research proposal - resolving the same can further reinforce the accuracy of the results of the experimental study.

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? The reservation that I would have is if exercising twice a week is enough to cause any measurbale change in the mental health. May be we could have differet groups that can be asked to exercise at different frequencies. Also the type of exercise that the participants are performing needs to be detailed - different people have different definitions of exericse. Further, the duration for which the participants are required to perform exercise has not been clearly articulated.Lastly, the current physical fitness of the participants should also be considered while doing blocking - participants who already indulge in regular physical activity may not be sensitive to twice a week of exercise and hence will not manifest any or minimal change in mental health, i.e., if there is a causality between the two.