Final answer:
The multi-group pretest/posttest design has two main purposes: to evaluate the effectiveness of an intervention, and to control for external variables with a control group and one or more experimental groups. The groups in the described study are matched, as the same students are pretested and posttested.
Step-by-step explanation:
Purposes of Multi-Group Pretest/Posttest Design
The multi-group pretest/posttest design serves two main purposes: First, it evaluates the effectiveness of a specific intervention or treatment. Secondly, it helps to control for external variables that could affect the outcome, by having both a control group and one or more experimental groups.
Experiment Description and Group Types
In an experiment described, such as investigating the effectiveness of a new math textbook, a pretest is administered to a group of high school students at the beginning of the semester, followed by a posttest at the end of a year. Based on this description, the groups in the study are implied to be matched rather than independent, as students are likely tested before and after the treatment (new textbook) to compare their performance over time.
It is critical during the experiment that the participants are divided into groups through random assignment, ensuring that any differences observed are due to the intervention itself and not other confounding factors. This approach is crucial in test prep and experimental design to test the hypothesis effectively.
Further research and careful consideration are often necessary to refine the experimental design and ensure the validity of the results, as outlined in works by researchers such as Gottfredson and Gresham & Witt.