Final answer:
Quincy performed a Factor analysis for his study to identify key variables associated with participation in extracurricular activities, which efficiently finds commonalities or patterns in qualitative data.
Step-by-step explanation:
Identifying the Type of Analysis in Quincy's Study
Quincy conducted a qualitative study to identify the most important variables associated with participation in extracurricular activities. The type of analysis best suited for this purpose is Factor analysis. Factor analysis is a statistical method used to describe variability among observed, correlated variables in terms of a potentially lower number of unobserved variables called factors. Essentially, it helps in understanding which variables have the most impact on the topic of study by reducing the number of variables and identifying the underlying relationships between them.
The data Quincy would have collected could include various demographic and psychographic items that may influence a student's participation in extracurricular activities. For his qualitative study to be informative, this data would be categorized and analyzed through factor analysis to find commonalities or patterns that could reveal the most significant variables. The other options, such as descriptive analysis, correlation analysis, and regression analysis, serve different purposes and would not be as effective in achieving Quincy's goal of identifying key variables.