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Exam 2: Collecting Data Sensibly

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Question 1

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The method of control wherein an extraneous variable is held constant is called blocking.

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Question 2

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Two factors are extraneous if their effects on the response variable cannot be distinguished from one another.

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

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 treatment is any particular combination of values for the explanatory variables.

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

A control group provides a baseline for comparison to a treatment group.

The following paragraph describes an actual study. After reading the description, determine whether the study is an observational study or an experiment. Justify your answer with specific references to the information in the study. "We compared paired daytime and night counts of wild brook trout, brown trout, and rainbow trout made by the same snorkelers in five streams during August 1994. Overall, we counted 109 trout in the daytime and 333 trout at night. We speculate that trout counted at night were present during the daytime but were hidden from view. Biologists should consider that trout behavior and susceptibility to being seen might vary a great deal between daytime and night, even during summer. In some streams, the majority of trout may not be seen during the daytime."

Blocking is a technique that can be used to filter out the effects of extraneous factors.

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.

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.

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?

If the subjects as well as the person measuring the response are aware of the treatment assigned to the subject, only single-blinding is being used.

Random subpopulations of a population are called strata.

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

Suppose that two experiments were conducted to assess the effect of a new insect repellant. In Experiment A, a simple random sample was taken from the population of River City. In Experiment B, a simple random sample from a group of volunteers from the population of River City was used. The results of the experiments were the same: fewer insects landed on the arms that had been treated with the insect repellant. The volunteers were randomly assigned to the two treatments in both experiments. (a) For each experiment, A and B, discuss whether one can legitimately infer a cause-and-effect relation between the use of the repellant and fewer insects landing from each of these experiments? Why or why not? (b) For each experiment, A and B, discuss whether one can legitimately generalize to the population of River City from each of these experiments? Why or why not?

Random assignment of volunteers should result in comparable experimental groups.

Increasing sample size will generally eliminate bias in a sample.

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?

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.