Final answer:
The method that involves a detailed and multi-method approach to studying one unit of analysis is the case study. This method enables in-depth exploration using various data collection techniques. Longitudinal research follows participants over time but does not focus on a single unit with multiple methods.
Step-by-step explanation:
The method that involves a detailed and multi-method approach to studying one unit of analysis is the case study. Case studies allow researchers to gain an in-depth understanding of complex issues in real-life contexts. This method can include various data collection techniques such as interviews, observations, and analysis of archival records, enabling a comprehensive exploration of the subject matter. In contrast, survey research is often used to collect large amounts of data from many subjects but usually lacks depth, whereas experimental research focuses on establishing cause and effect through controlled manipulation of variables, which doesn't necessarily provide a detailed examination of a single unit.
Longitudinal research involves following a group of research participants over an extended period, thus providing insights into changes over time. While valuable for understanding dynamics and development, a longitudinal study does not typically focus on an in-depth, multi-method examination of a single unit of analysis.
To elaborate using a historical example, the work of Sigmund Freud on human personality utilized a case study approach. Freud conducted in-depth interviews with a small number of clients over a prolonged period, which is indicative of the qualitative and detailed nature of case study research.