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.
Each row represents an observation or instance with values for the given variables or columns.
There were 1691 participants included in the survey as indicated by the number of rows in the table.
There are two main categories of variables - Categorical and Numerical which are further divided into Categorical Nominal and Ordinal (Ordered) and Numerical Continuous and Numerical Discrete.
Categorical ordinal variables - grossIncome (because it can be ordered) Categorical nominal variables - sex, marital, smoke (These variables are not ordered/ranked, it doesn’t make sense for these variables to be ordered) Numerical continuous - Age (It can take on continuous values) Numerical discrete - amtWeekdays, amtWeekdays (Number of cigarettes smoke can only be whole numbers)
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.
The population is “all children between the ages of 5 and 15” while the sample is the chosen 160 children in that age group selected for this study by the researchers.
Yes, the results can be generalized provided that the children are representative of the population at large. Secondly, causation can be inferred from a randomized experiment. This is an experimental study as half the students have been assigned a “treatment” and the other half were treated as the “control” group. We are making the assumption here that the children were assigned randomly to the two groups.
Reading the paper. (1.28, p. 31) Below are excerpts from two articles published in the NY Times:
“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.
Correlation does not imply causation, dementia may have been caused by a confounding factor. The participants voluntarily participated hence it’s an observational study rather than an experimental one and causation can only be inferred from a randomized experiment. Also, this sample may not be representative of the wider population as the particpants self-selected, for example perhaps they participated for monetary benefit in the study and belong to a lower socio-economic group. Hence, gaining access to a well-balanced diet and exercising maybe a problem for this subset of the population, a few of the factor perhaps affecting the onset of the disease aside from smoking.
“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?
The answer is similar to the one above. The data collection method was a survey rather than an experimental study. Such an observational study cannot be used to draw inferences regarding the causation of a child’s sleep habits on bullying. Perhaps there is a lurking factor involved. We can conclude at best that a child’s sleep habits are correlated with bullying.
source(“more/arbuthnot.R”)
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.
An experimental study as subjects were chosen using random sampling and half were assigned a “treatment” which in this case is “exercising twice a week” while the other half were the “control group” and were told not to exercise.
The 3 treatment groups are - 18-30 exercise, 31-40 exercise and 41-55 exercise groups. The 3 control groups are - 18-30 don’t exercise, 31-40 don’t exercise and 41-55 don’t exercise groups.
Age is the blocking variable, the three blocks are 18-30, 31-40 and 41-55.
The experiment is definitely not a double-blind situation as the control group (participants) are aware that they form part of the control group as they have been told not to exercise. So, in this case one of the two groups (participants, researchers) is aware, so it cannot be a double-blind study. It’s unclear if the researchers are aware which participants are part of the control or the treatment group, if they are aware, the study is not blind.
This is a randomized experimental study, hence causation can be inferred. Conclusions can be generalized.
It’s unclear how long the study is for, as it may be difficult for study particpants to adhere strictly to the rules which in turn could affect results.
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. Available at https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1307694↩