Chapter 1 - Introduction to Data

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.

(a) What does each row of the data matrix represent?

A single individual’s response to the survey.

(b) How many participants were included in the survey?

1691 per the matrix above (although the dataset has 1693 observations)

(c) 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.

Below is a list of the variables and their properties

1. sex - categorical(nominal),
2. age - numerical(discrete),
3. marital - categorical(nominal),
4. grossIncome - categorical(ordinal),
5. smoke - categorical(ordinal),
6. amtWeekends - numerical(discrete),
7. amtWeekdays - numerical(discrete)

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.

(a) Identify the population of interest and the sample in this study.

Population would be all children between the ages of 5 and 15 and the sample is 160 children.

(b) Comment on whether or not the results of the study can be generalized to the population, andif the findings of the study can be used to establish causal relationships.

For these results to be generalize a the following conditions need to be met:

1. The sample is selected randomly
2. The sample size should be large enough to be representative and selected from various different geographical regions
3. Samples to control and testing groups are assigned randomly.

Since the above question statement does not indicate any of these conditions being met, we can conclude that generalizing the results of this study would not be appropriate.

Reading the paper. (1.28, p. 31) Below are excerpts from two articles published in the NY Times:

(a) 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.

As an observational study we cannot derive causality from this study. Additionally, there is no discussion regarding radomization and a control group. At best we can conclude that there might be a correlation between smoking and demetia but not causality.

(b) 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?

This statement is not justified because as before this study is observational in nature without any discussions of randomization or control groups. Additionally, the information acquired is not from objective primary sources but subjective secondary sources that can introduce bias into the results. additionally, twice as likely as a statement seems misleading, twice a very samll number would still be infact a small number.

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.

(a) What type of study is this?

controlled, experimental and randomized

(b) What are the treatment and control groups in this study?

Those instructed not to exercise are in the control group. Those instructed to exercise twice a week are the treatment group.

(c) Does this study make use of blocking? If so, what is the blocking variable?

Age groups are the blocking variable in the study

(d) Does this study make use of blinding?

No since the patients have clear instructions on what to do and what not to do.

(e) 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 because the sample is selected randomly and assigned randomly to control and treatment groups

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

Overall the study proposal seems sound however before funding I would ask the following questions:

1. Duration- How long is the study to last

2. Blocking- Why was everyone above 55 grouped into a single block

3. Exercise Intensity and Duration- There does not seem to be directions on the intensity or kind of exercise or how long to exercise