Which methodology involves identifying, analyzing, and controlling variables in an experimental setup?

The Design of Experiments (DOE) methodology is centered around the systematic approach of identifying, analyzing, and controlling variables in an experimental setup. This methodology allows researchers to design experiments in a manner that optimally investigates the effects of multiple variables simultaneously. By controlling these variables, researchers can isolate their effects on the outcome, leading to more reliable and valid results.

In DOE, the emphasis is on planning the experiment to ensure that enough data is collected to evaluate the relationships between factors, uncover interactions, and make informed decisions based on statistical analysis. This rigorous approach distinguishes it from other methodologies, which may not systematically control for variables. For instance, qualitative research focuses more on understanding subjective experiences and insights rather than on manipulating and controlling variables. A case study analysis investigates specific instances in depth but does not typically involve experimental manipulations. Similarly, control studies often focus on comparing treatment and control groups rather than the systematic variation of multiple factors across various conditions, which is a hallmark of DOE.

Thus, the correct answer is rooted in the unique capability of the Design of Experiments to rigorously identify and manage variables to rigorously test hypotheses and establish causal relationships.