1.8 Smoking habits of UK residents

  1. What does each row of the data matrix represent?

Each row of the data matrix represents a case or an observation.

  1. How many participants were included in the survey?

There are 1691 particapants in the survey.

  1. 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.

gender: Categorical

age: Numerical Continuous

maritalStatus: Categorical

highestQualification: Categorical ordinal

nationality: Categorical

ethnicity: Categorical

Gross Income: Categorical ordinal

region: Categorical

Smoke: Categorical

amtWeekends: Numerical Discrete.

amtWeekedays: Numerical Discrete.

type: Categorical

1.10 Cheaters, scope of inference

  1. Identify the population of interest and the sample in this study

The population of interest are children between the age of 5 and 15. The sample is 160 children.

  1. 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.

It is said that researchers conducted an EXPERIMENT. If the experiment was PROPERLY done and met ALL the following principles: Control, Randomize, Replicate, Block it means that the results of the study can be generalized to the population and the results of the study can be used to esteblish casual relationships.

1.28 Reading the paper

  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.”

We can not conclude that smoking causes dementia later in life as sample was not randomized. The participants were only volunteers so the result can be biased.

  1. Another article titled The School Bully Is Sleepy states the following:62 “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 is an observation and not an experiment with randomly picked sample. Even if we say that there is some correlation in the observation, but it is not imply causation. Confounding Variables can be the real reasons of the dementia.

1.36 Exercise and mental health

A researcher is interested in the e↵ects 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.he results.

  1. What type of study is this?

    Prospective experiment

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

    Treatment group: group that excercising twice a week. Control group: group not excercising at all.

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

    Answer: Yes. Blocking variables are variables that are known or suspected to affect the response variable. In this case blocking variable is Age.

  4. Does this study make use of blinding?

    It is not clear form the experiment if the experimental units know whether they are in the control or treatment group. If the experimental units do not know then study use blinding.

  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.

If the experiment was PROPERLY done and met ALL the following principles: Control, Randomize, Replicate, Block it means that the results of the study can be generalized to the populationa and the results of the study can be used to esteblish casual relationships. From the details provided the study is a proper experiment and can be used to esteblish casual relationships.

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

I think duration and quality of sleep, diet, intensiveness of work are all the examples of blocks for the experiment.

1.48 Stats scores

scores <- c(57, 66, 69, 71, 72, 73, 74, 77, 78, 78, 79, 79, 81, 81, 82, 83, 83, 88, 89, 94)
summary(scores)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   57.00   72.75   78.50   77.70   82.25   94.00
boxplot(scores, main = "Final Exam Scores")

1.50 Mix-and-match. Describe the distribution in the histograms below and match them to the box plots.

    • 2 unimodal, symmetric (normally distributed)
    • 3 uniform
    • 1 unimodal right skewed

1.56 Distributions and appropriate statistics, Part II

For each of the following, state whether you expect the distribution to be symmetric, right skewed, or left skewed. Also specify whether the mean or median would best represent a typical observation in the data, and whether the variability of observations would be best represented using the standard deviation or IQR. Explain your reasoning.

  1. Housing prices in a country where 25% of the houses cost below $350,000, 50% of the houses cost below $450,000, 75% of the houses cost below $1,000,000 and there are a meaningful number of houses that cost more than $6,000,000.

Distribution is a right skewed as there are less number of houses that cost more than 1000000 forming a long tail to the right. For a skewed distribution IQR or median will be the best representation of a typical observation in the data. The houses with prices above 6000000 is an outlier and can change mean or standard deviation significantly.

  1. Housing prices in a country where 25% of the houses cost below $300,000, 50% of the houses cost below $600,000, 75% of the houses cost below $900,000 and very few houses that cost more than $1,200,000.

Data is symmetrically distributed. Median/IQR is preferred because of existence of a few outliers.

  1. Number of alcoholic drinks consumed by college students in a given week. Assume that most of these students don’t drink since they are under 21 years old, and only a few drink excessively.

Distribution is a right skewed. Median/IQR are preferred for the reasons explained in the answer a) question.

  1. Annual salaries of the employees at a Fortune 500 company where only a few high level executives earn much higher salaries than the all other employees.

Data is symmetrically distributed. Median/IQR is preferred because of existence of a few outliers.

1.70 Heart transplants

  1. Based on the mosaic plot, is survival independent of whether or not the patient got a trans- plant? Explain your reasoning.

Based on the mosaic plot survival is dependent on the treatment, but we can get the result by chance.

  1. What do the box plots below suggest about the efficacy (effectiveness) of the heart transplant treatment.

The box plot suggest that the heart transplant increases the survival rate for a longer period of time.

  1. What proportion of patients in the treatment group and what proportion of patients in the control group died?

Based on the mosaic graph: Treatment group: 3/5 Control group: 6/7

  1. One approach for investigating whether or not the treatment is effective is to use a random- ization technique.

  1. What are the claims being tested? H0 - survival does NOT depend on the treatment H1 - survival does depend on the treatment

  2. The paragraph below describes the set up for such approach, if we were to do it with- out using statistical software. Fill in the blanks with a number or phrase, whichever is appropriate.

We write alive on the cards equivalent to the number of people in control and treatment group (1/7 and 2/5 respectively) representing patients who were alive at the end of the study, and dead on cards equivalent to the number of people in control and treatment group (6/7 and 3/5 respectively) representing patients who were not. Then, we shuffle these cards and split them into two groups: one group of size equivalent to the original treatment group representing treatment, and another group of size equivalent of the original control group representing control. We calculate the difference between the proportion of dead cards in the treatment and control groups (treatment - control) and record this value. We repeat this 100 times to build a distribution centered at 0. Lastly, we calculate the fraction of simulations where the simulated differences in proportions are 3/5 - 6/7 (-0.257).If this fraction is low, we conclude that it is unlikely to have observed such an outcome by chance and that the null hypothesis should be rejected in favor of the alternative.

  1. What do the simulation results shown below suggest about the effectiveness of the trans- plant program?

The simulation results allows to reject the NULL hypothesis. We can conclude that heart transplat increase time being alive. The observed differences between the two proportions was due to effect of transplantation.