Which treatment design focuses on an individual client or a single group to evaluate music therapy's effectiveness over time?

The correct choice is case studies, as they are specifically designed to examine the effectiveness of interventions on individual clients or specific groups over time. In case studies, therapists can provide detailed observations and qualitative data about the client's progress, changes in behavior, emotional responses, and overall impact of music therapy. This design allows for a comprehensive understanding of the client's unique needs and the nuanced effects of the music therapy interventions.

By focusing on the individual or a small group, case studies also facilitate an in-depth analysis that can highlight the contextual and personal factors influencing the therapy's effectiveness. This can lead to valuable insights that may not be captured in broader quantitative research methods, where the focus is typically on larger sample sizes and statistical analysis.

Other research methods mentioned may focus on different aspects of therapy effectiveness. Double-blind studies are primarily employed to eliminate bias in experimental research, involving both the participants and the researchers being unaware of who receives the treatment. Group therapy analysis may aim to evaluate group dynamics and outcomes rather than individual progress. Hierarchical evaluations typically refer to structured assessments that prioritize different levels of outcomes and may not focus on the longitudinal evaluation of individual cases. Hence, case studies are the most suitable approach for the described focus on individual treatment effectiveness over time.