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A social worker wants to examine methods that can be used to deter truancy. Three hundred chronically truant students volunteer for the study. Because the social worker believes that socioeconomic class plays a role in truancy, she divides the 300 volunteers according to household income. Of the 300 students, 120 fall in the low-income category, 132 fall in the middle-income category, and the remaining 48 fall in the upper-income category. The students within each income category are randomly divided into three groups. Students in group 1 receive no intervention. Students in group 2 are treated with positive reinforcement in which, for each day the student is not truant, he or she receives a star that can be traded in for rewards. Students in group 3 are treated with negative reinforcement such that each truancy results in a 1-hour detention. However, the hours of detention are cumulative, meaning that the first truancy results in 1 hour of detention, the second truancy results in 2 hours, and so on. After a full school year, the total number of truancies are compared. (a) What type of experimental design is this? (b) What is the response variable in this experiment? (c) What are the treatments? (d) What variable serves as the block? (e) Draw a diagram similar to Figure \(7,8,\) or 10 to illustrate the design.

Step by step solution

01

- Identify the experimental design

The experiment is divided into blocks based on household income, and within each block, the subjects are randomly assigned to different treatment groups. This is an example of a blocked design.

02

- Determine the response variable

The response variable is the total number of truancies at the end of the school year.

03

- List the treatments

The treatments are: 1) No intervention, 2) Positive reinforcement (receiving a star for each day of non-truancy that can be traded for rewards), and 3) Negative reinforcement (each truancy results in cumulative detention time).

04

- Identify the block variable

The block variable is the socioeconomic class of the students (low-income, middle-income, upper-income).

05

- Draw a diagram

Create a diagram similar to Figure 7, 8, or 10 illustrating the experimental design.1. Divide the 300 students into three blocks based on income: 120 low-income, 132 middle-income, 48 upper-income.2. Within each block, randomized assignment to three groups (Group 1, Group 2, Group 3) as follows: - Low-income: 40 students to each group - Middle-income: 44 students to each group - Upper-income: 16 students to each group3. Apply the corresponding treatments to each group.

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Key Concepts

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

Experimental Design

An experimental design is a structured method used to conduct research in a controlled way. It helps to establish cause-and-effect relationships by manipulating an independent variable and observing the effect on a dependent variable. In this experiment, the social worker uses a blocked design. This means she takes a large group of students and divides them into smaller groups, or 'blocks', based on a specific characteristic—in this case, household income. This helps control for any variations that might exist within different socioeconomic classes, ensuring a clearer comparison of the treatments being applied. Each block is then randomly divided into treatment groups, ensuring that the effects of the treatments can be attributed more directly to the treatments themselves, rather than other factors.

Response Variable

The response variable in an experiment is what the researcher measures to determine the effect of the treatments. It is the outcome of interest. In this case, the response variable is the total number of truancies each student has at the end of the school year. By focusing on this variable, the social worker can see how effective each treatment is in reducing truancy. It's essential to clearly define the response variable upfront to maintain the precision and integrity of the experiment. This way, any changes can be directly linked to the specific interventions applied to the students.

Treatments in Experiments

Treatments are the different conditions or interventions applied to the experimental units—in this case, the students. Each group of students receives a different treatment. There are three distinct treatments in this study:

• No intervention (Group 1): Students continue as they normally would without any added measures.
• Positive reinforcement (Group 2): Students earn stars for each day they are not truant. These stars can be traded for rewards, encouraging regular attendance.
• Negative reinforcement (Group 3): Truancy results in cumulative detention time. The more truancies, the more detention hours a student accumulates.

These treatments are given to see which method, if any, best reduces truancy among the students. By comparing the number of truancies across the different groups, the social worker can identify the most effective strategy.

Blocking Variable

A blocking variable is a characteristic used to create blocks that help control for variability in an experiment. In this study, the blocking variable is the students' socioeconomic class. Students are divided into three blocks: low-income, middle-income, and upper-income categories. This division is crucial because it addresses the potential influence socioeconomic status might have on truancy rates. By blocking on this variable, the researcher ensures that comparisons between treatments are fair and not biased by different socioeconomic backgrounds. This way, the study's outcome reflects the true effectiveness of the treatments, unaffected by the different backgrounds of the students involved.