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How would you use a completely randomized experiment in each of the following settings? Is a placebo being used or not? Be specific and give details. (a) A veterinarian wants to test a strain of antibiotic on calves to determine their resistance to common infection. In a pasture are 22 newborn calves. There is cnough vaccine for 10 calves. However, blood tests to determine resistance to infection can be done on all calves. (b) The Denver Police Department wants to improve its image with teenagers. \(\mathrm{A}\) uniformed officer is sent to a school one day a week for 10 weeks. Each day the officer visits with students, eats lunch with students, attends pep rallies, and so on. There are 18 schools, but the police department can visit only half of these schools this semester. A survey regarding how teenagers view police is sent to all 18 schools at the end of the semester. (c) A skin patch contains a new drug to help people quit smoking. A group of 75 cigarette smokers have volunteered as subjects to test the new skin patch. For one month, 40 of the volunteers receive skin patches with the new drug. The other volunteers receive skin patches with no drugs. At the end of two months, each subject is surveyed regarding his or her current smoking habits.

Step by step solution

01

Setting Up the Experiment for Calves

Randomly assign 10 of the 22 calves to receive the antibiotic, ensuring all calves have an equal chance of selection. The remaining 12 calves serve as the control group, receiving no treatment. After a period, conduct blood tests on all calves to compare the resistance to infection between the treated and untreated groups. This experiment doesn't use a placebo.

02

Designing the Police Department Experiment

Randomly select 9 out of the 18 schools for the police officer to visit, ensuring each school has an equal probability of being chosen. The remaining schools serve as the control group without visits. At the semester's end, conduct surveys in all schools to evaluate the students' perceptions of the police. This experiment doesn't use a placebo.

03

Structuring the Smoking Cessation Experiment

Divide the 75 volunteers randomly into two groups. Assign 40 volunteers to receive skin patches with the actual drug and the remaining 35 to receive placebo patches without the drug. After two months, survey all participants to assess changes in smoking habits. This experiment uses a placebo for the control group.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Randomized Experiment

A randomized experiment is a powerful method used in statistics to test hypotheses. It involves randomly allocating participants or subjects into different groups to receive varying treatments. This randomness ensures that each subject has an equal probability of being assigned to any group, thus minimizing potential biases.
In the context of the first exercise, calves are randomly selected to either receive an antibiotic or not. The selection is done in such a way that each of the 22 calves has an equal chance to be part of the treatment group. Similarly, in the second and third scenarios, schools and volunteers are randomly chosen to receive interventions or act as control groups.

• Randomization is crucial as it ensures comparability between groups, which strengthens the reliability of the experimental results.
• It helps in making valid inferences about causal relationships between the variables under study.

Placebo Effect

The placebo effect refers to the phenomenon where participants in an experiment experience perceived or actual improvements in their condition despite receiving a non-active treatment. This effect highlights the importance of psychological and physiological factors related to participants' expectations. In the smoking cessation experiment, placebo patches are used for the control group. These patches contain no active drug but are administered in the same way as the treatment patches. By including a placebo, researchers can gauge how much of the result is due to the actual drug and how much is simply due to participants' belief that they are receiving treatment.
Using a placebo is particularly relevant when the psychological aspect, such as motivation and belief in the treatment, might influence outcomes. It is essential in ensuring the integrity of the experiment's findings by isolating the drug's true effects from those induced by expectation.

Control Group

A control group is a fundamental component in experimental design. It consists of participants who do not receive the experimental treatment or intervention. Instead, they serve as a baseline group against which the effects of the treatment group are measured. In the first exercise involving calves, the control group comprises the 12 calves that do not receive the antibiotics. Similarly, in the second scenario, the schools not visited by police officers function as the control group, and in the smoking cessation experiment, those receiving the placebo patches are the control.

• A well-defined control group enables researchers to determine the effect of the independent variable (e.g., the drug, police visits).
• It increases the study's validity by accounting for external factors that could otherwise skew the results.

Sampling Techniques

Sampling techniques are methods used to select a subset of individuals from a larger population to participate in a study. These techniques are crucial for ensuring that the sample accurately represents the population, thus allowing researchers to generalize findings. In all three experimental setups described, different sampling techniques are utilized to ensure unbiased study conditions:

• **Random Sampling:** This ensures every subject or location has an equal chance of being chosen, as seen in the random selection of calves, schools, and volunteers.
• **Stratified Sampling (if implied):** This could involve dividing populations into subgroups and ensuring proportional representation, though not explicitly mentioned, it emphasizes an organized approach for potential future applications.

Each technique boasts its own benefits, but the main goal remains creating a sample that closely reflects the entire group of interest. Proper sampling reduces error and bias, lending greater credibility to the research findings.