Exam 1: Collecting Data in Reasonable Ways

Random assignment of volunteers to treatments will, on average, result in comparable experimental groups.

Response bias occurs when responses are not actually obtained from all individuals selected for inclusion in the sample.

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

Two of the basic sampling methods studied in statistics are the simple random sample and the stratified random sample. How do these methods of sampling differ?

What is the defining characteristic of a simple random sample?

One part of the Demographic and Health Surveys Program is concerned with measures of malnutrition. Investigators measure physical characteristics of children, at different ages. Sadly, in some countries, many children die early, and thus a bias is introduced in the study because the investigators cannot collect data from the deceased children.

In competitive sports coaches may record athletes' practice sessions to provide more effective feedback to the athlete. Some coaches 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. The proportion of successful first serves will be the response variable. The subjects for the experiment are 60 high school male competitive tennis players of varying ability who have volunteered for the experiment. a) Describe the treatment(s) in your experiment b) The experience levels of the players is one possible confounding variable. In a few sentences, 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?

If the sample size is small relative to the population size, there is little practical difference in the results of sampling with replacement and sampling without replacement.

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

River City is seeking to compare the effects of two mosquito sprays, A and B, to be used in the insect control plan for their park system. Consider the following two plans for a statistical study: • In Plan #1, a simple random sample of plots of park land would be taken from the population of River City parks. Either treatment A or B would be randomly assigned to each of the plots. • In Plan #2, a simple random sample of plots of park land would be taken from the population of River City park areas that are rarely visited. Either treatment A or B would be randomly assigned to each of the plots. a) Consider study plan #1: i) Would it be appropriate to infer a cause-and-effect relationship if the results of the two treatments differ? Why or why not? ii) Could the results be generalized to all areas of the park land? Why or why not? b) Consider study plan #2: i) Would it be appropriate to infer a cause-and-effect relationship if the results of the two treatments differ? Why or why not? ii) Could the results be generalized to all areas of the park land? Why or why not?

Six species of wood-pecking birds are known to damage homes. Woodpeckers are protected by the Federal Migratory Bird Treaty Act, and homeowners must control them by nonlethal methods. Over a three-month period, investigators evaluated the use of mirrors, artificial snakes, and artificial owls as woodpecker deterrents. Homeowners' yards were classified into 4 categories: (1) no trees; (2) lightly wooded yards; (3) wooded yards; and (4) heavily wooded yards. The homes were visited at least 4 times to establish baseline damage rates (number of new holes per day) before using any deterrent. Deterrents were randomly assigned to the homes in each category and changes in the damage rate were recorded at the end of the experimental time period. The design used was a randomized block design. (a) What is the explanatory variable (factor) for this experiment? (b) What is the response variable for this experiment? (c) After completing the study, someone suggested that amount of rainfall might affect woodpecker activity and that homes in areas that receive more rainfall might show greater damage. Is this something that the investigator should be worried about? If yes, explain why; if no, explain what aspect of the design of the experiment eliminates this worry.

A consumer group is performing an experiment to evaluate the tartar-fighting properties of different brands of toothpaste. Three brands of toothpaste are being compared in a randomized comparative experiment. (There is no "do-not-brush" control group.) 300 adult volunteers of varying ages (100 for each toothpaste brand) have been randomly assigned to the treatments. The toothpaste for each brand is delivered in containers that are the same except for the letters, X, Y, and Z prominently displayed. A team of dentists, blind to the identities of the toothpaste brands, will evaluate the levels of tartar on the subjects' teeth after 2 months of use. The subjects have been instructed to brush their teeth as they normally do during the course of the experiment. (a) What is the explanatory variable (factor) for this experiment? (b) What is the response variable for this experiment? (c) After the onset of the experiment, it was discovered that a significant number of volunteers using Brand Y toothpaste recently enrolled in a short class on health practices, and one of the lessons involved instruction in effective brushing techniques. If none of the volunteers using Brands X and Z enrolled in the class, how would this affect the consumer group's interpretation of the results of the experiment?

Explain how you would determine if a variable is an explanatory variable or a response variable? Again, you may use an example to support your answer but not as a substitute for an explanation.

One part of the Nurses Health Study focuses on possible causes of skin cancer. Nurses were asked about different behaviors and aspects of their health when they entered the study. Those nurses subsequently diagnosed with cancer were given the questionnaires again. Investigators discovered that after the diagnosis the nurses tended to report a reduced ability to tan. The investigators concluded that the shift in reporting might be caused by an awareness of their diagnosis.

Random subpopulations of a population are called strata.

A study is an observational study if the investigator observes the behavior of a response variable after one or more factors have been manipulated.

We have distinguished two types of studies: observational and experimental. Briefly explain the difference between these two types of study. You may use an example to support your answer but not as a substitute for an explanation.

A common classroom practice is to have students exchange their quizzes for grading. This practice is hypothesized to reduce time between quiz and feedback to students, thus resulting in higher achievement. Your history teacher, aware of your statistical prowess, has asked you to design an experiment to test this theory. You have decided to use the final exam (not graded by students) as your response measure. Your history teacher has three classes, one early in the morning, one at noon, and one late in the afternoon. Each class contains 30 students. (a) Describe the treatments you will use in your experiment (b) One possible confounding variable is the time of day; students may be more alert at certain times of the day than at other times. Describe a method that could be used to control this variable. Students have already been assigned their schedules, and these cannot be changed. (c) Do you feel the results of your experiment could be generalized to math classes? Explain why or why not.

An anthropologist is studying the strength of fragments of pottery ("sherds") found in three archeological sites in the Phoenix Basin area of Arizona. Her study involves applying force to the sherds until they break, so she plans to use only a small sample of available artifacts. Her data contains the location of the sherd (site), and the weight and thickness of the sherd. A partial list of the data is shown below. Sherd \# Site Weight () Thick () 1 Sacaton 14.7 5.41 2 Sacaton 14.6 5.75 3 Gila Plain 17.9 7.09 4 Sacaton 14.7 6.14 5 Gila Plain 13.1 5.11 6 Casa Grande 18.5 6.51 7 Casa Grande 13.4 5.92 \ldots \ldots \ldots \ldots 1000 Gila Plain 14.6 4.01 a) Briefly describe a process to select a simple random sample of size n = 20 from this list of sherds. You may assume that you have a random number table to work with, but do NOT carry out the process you describe. b) Briefly describe how a stratified random sample could be selected with strata corresponding to archeological sites.

A simple random sample of size n is by definition a sample that is selected in a manner to guarantee each individual in the population an equal chance of selection.