Exam 1: Collecting Data in Reasonable Ways

Which of the following statistical studies is an observational study? ​

The following paragraph describes an actual study. After reading the description, determine whether the study is an observational or experimental study. Justify your answer with specific references to the information in the study. ​ "Before the opening of the new International Airport and the termination of the old airport, children near both sites were recruited into aircraft-noise groups (aircraft noise at present or pending) and control groups with no aircraft noise and closely matched for socio-economic status. A total of 326 children (mean age = 10.4 years) took part in three data-collection waves, one before and two after the switch-over of the airports. After the switch to the new airport, long-term memory and reading were found to be impaired in the noise group at the new airport, and improved in the formerly noise-exposed group at the old airport."

Suppose you want to know how many times per month people of Portland go shopping. You interviewed fifty women from Portland selected randomly. Is the sample likely to be representative of the population of interest?

A friend of yours, who is not taking statistics, wonders why it is that anyone would choose to take a sample. "Obviously," she says, "you would get better information from a census." In a short paragraph, explain why it is that statisticians take samples rather than taking a census.

Selection bias can occur if volunteers only are used in a study.

In evaluating an experiment, how would you determine if a variable is an explanatory variable or a response variable?

The two paragraphs below discuss aspects of two studies, each of which exhibit a bias. For each study, decide whether the problem is selection bias, response bias, or nonresponse bias, and in a few sentences explain why you chose your answer. (a)One part of the Nurses' Health Study is concerned with possible causes of skin cancer. Nurses were asked about different behaviors and aspects of their health when they entered the study. Then, the nurses were given the questionnaire again if they were diagnosed with cancer. When the questionnaires were analyzed, the investigators discovered that after the nurses were diagnosed with cancer they tended to report a reduced ability to tan. It is thought that the shift in reporting might be caused by an awareness of their diagnosis. (b)One part of the Demographic and Health Surveys Program is concerned with measures of malnutrition. Investigators measure physical aspects of growing children, and attempt to document the physical characteristics of a population at different ages. Sadly, in some countries many children die early, and thus a bias is introduced in the study when the investigators can not collect the data from the deceased children.

In competitive sports, video recorders have been used more frequently in recent years. The idea behind the recorder is that coaches can replay training sessions for more effective feedback to the athlete. Some people believe video recording may make the athletes more nervous and actually decrease their performance. You have been asked to design an experiment to address this issue for competitive high school tennis players. You have decided to use the accuracy of tennis serves as your response variable, and the number of successful serves out of 100 as your performance measure. The subjects for your experiment are 60 high school male competitive tennis players of varying ability who have volunteered for the experiment. (a)Describe the treatments in your experiment (b)One possible confounding variable is the experience levels of the players. Explain how you would control this variable? (c)Can the results of this experiment be generalized to all male tennis players? Why or why not?

Increasing sample size will generally eliminate bias in a sample.

In evaluating an experiment, how would you determine if a variable is an explanatory variable or an extraneous variable?

Bias is a serious problem that sometimes arises when one takes a sample. (a)In a few sentences, explain generally what bias is. (b)What is the distinction between response bias and non-response bias?

Which of the following statements is false? ​

Bias, the tendency for samples to differ from the corresponding population in some systematic way, might be due to: (a) selection bias, (b) response bias, and/or (c) nonresponse bias. In a few sentences, discuss the differences among these different biases.

Random assignment to treatments will guarantee groups that are exactly alike for experimental purposes.

As long as the sample size is small relative to the population, there is little practical difference between sampling with replacement and sampling without replacement.

A pharmaceutical company wants to test its new drug that is designed to help balding men grow more hair. From their records of past customers, the company has data on about 5,000 men. The data contains information about the men's hair color, age, and percent of baldness. (A partial list is given below.) For their anticipated experiment, they want to take a sample that is representative of their customers. ​ (a)Briefly describe how you would select a simple random sample of size n = 20 from this list of customers. (b)Describe in a short paragraph why you might wish to use a stratified random sample.

A study is commissioned to determine whether piglets gain body mass more rapidly when a certain hormone is introduced into their feed. In January, a random sample of 40 10-week-old piglets receives a diet that includes the hormone. Sixteen weeks later, the average weight increase is determined. A similar experiment is conducted the following June with a random sample of 36 piglets, except the hormone is removed from the diet. ​ Which of the following do you think represents the most serious flaw in this study? ​

Random assignment of volunteers should result in comparable experimental groups.

Suppose that two experiments were conducted to compare the effects of two new insect repellants. In Experiment X, a simple random sample was taken from the population of River City, and the citizens were randomly assigned to repellant A and repellant B. In Experiment Y, a stratified random sample was taken from the population of River City, and the citizens were randomly assigned to repellant A and repellant B. (River City has 4 geographic areas of town, the NE, NW, SE, and SW quadrants; 100 people from each quadrant were sampled for Experiment B.)The results of the experiments were the same: fewer insects landed on the arms that had been treated with insect repellant A. (a)For each experiment, X and Y, discuss whether one can legitimately infer from each of these experiments that repellant A is better than B? Why or why not? (b)For each experiment, X and Y, discuss whether one can legitimately generalize to the population of River City from each of these experiments? Why or why not?

Three methods for random sampling are: (a) simple random sampling, (b) stratified random sampling, and (c) cluster sampling. In a few sentences, discuss the similarities and differences among these sampling methods. Specifically, what sampling circumstances would lead you to choose each of these methods?