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Chapter 9. Producing Data: Experiments
Experiments
Definition. The individuals studied in an experiment are often called subjects, particularly when they are peo- ple. The explanatory variables in an experiment are often called factors. A treatment is any specific experimental condition applied to the subjects. If an experiment has sev- eral factors, a treatment is a combination of specific values of each factor.
Example. Example 9.2 page 214. Notice the individuals (subjects), factors, treatments, and response variables.
Example S.9.1. Women Hate the Stooges! It is commonly held that males are much fonder of the Three Stooges than females. Explain an experiment that could be performed to test this idea. What are the individuals, factors, treatments, and response variables of your experiment?
How to Experiment Badly
Note. A common way to perform an experiment (see Exam- ple 9.3) is outlined as:
Subjects −→ Treatment −→ Measure response
In a controlled laboratory setting, this may be suitable, but “in the field” it is quite possible that such a simple experiment can be misleading and confounded by lurking variables. The next subsection describes a better approach.
Randomized Comparative Experiments
Definition. An experiment that uses both comparison of two or more treatments and chance assignment of subjects to treatments is a randomized comparative experiment.
Definition. In a completely randomized experimental design, all the subjects are allocated at random among all the treatments.
Note. It is common in many experiments, especially those testing drug treatments, to have a group which is not subject to any treatment. This group is called a control group.
and use the Simple Random Sample Applet provided by the publishers of our book to generate the numbers—notice that it simulates a lottery with numbered balls (the Applet will gener- ate no more than 40 numbers in a sample)... Next, let’s assign the 40 subjects from the sample (we call them “Group 1”) to this class and the remaining 40 subjects (“Group 2”) to the other section of Probability and Statistics which is taught at the same time. The treatment for Group 1 is exposure to ex- amples and data gathering experience based on the films of the Three Stooges. The treatment for Group 2 is a standard non- Stooge presentation of the same material (the control group). To measure responses, we can use student score on the com- mon departmental final. We then have the following outline of this completely randomized comparative experiment:
The subjects are the students, the treatments are the two dif- ferent types of classes (Stooges/Standard), and the response variable is the score on the departmental final. Notice that by performing the experiment on classes that are taught at the same time, we are avoiding the lurking variable of “time of day of the class.” However, there is still one very obvious lurking variable: the instructor(s). Since different instructors can have dramatically different teaching approaches, this cer- tainly could have an effect much greater than the treatment! An alternative experiment might adjust for this by moving students from one section of our Probability and Statistics class to another section we are teaching at a different time. In practice, this would be a logistical nightmare, since it would potentially change students schedules and it would also bring back concerns over the lurking variable of “time of day.” By the way, any such actual manipulation of students of this sort would require approval by ETSU’s Institutional Review Board (IRB).
Cautions about Experimentation
Note. A placebo is a dummy treatment. Many medical patients respond favorably to any treatment, even a placebo, perhaps because they trust doctors. The response to a dummy treatment is called the placebo effect.
Definition. In a double-blind experiment, neither the subjects nor the people who interact with them know which treatment each subject is receiving.
Note. The text comments: “The most serious potential weakness of experiments is lack of realism: the subjects or treatments or setting of an experiment may not realistically duplicate the conditions we really want to study.”
Matched Pairs and Other Block Designs
Note. The text states (pages 224 and 225): “A match pairs design compares just two treatments. Choose pairs of subjects that are as closely matched as possible. Use chance to decide which subject in a pair gets the first treatment.... That is, the random assignment of subjects to treatments is done within each matched pair, not for all subjects at once.... Matched
pairs are one kind of block design, with each pair forming a block.”
Definition. A block is a group of individuals that are known before the experiment to be similar in some way that is expected to affect the response to the treatments. In a block design, the random assignment of individuals to treatments is carried out separately within each block.
Example S.9.3. Women Hate the Stooges 2. Let’s reconsider the question raised in Example S.9.1: Do men like the Three Stooges more than women? If we find this cred- ible, then we might think that using the Three Stooges films in Probability and Statistics would affect male and female stu- dents differently. Create a block design where the blocks are based on gender, but the subjects are then assigned to the two possible treatments (Stooge/Standard) at random.
Example. Exercise 9.25 page 229.
Example. Exercise 9.42 page 233. Repeat, but in the con- text of a Three Stooges related question.
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