Comparative analysis is the problem of predicting how a system will react to perturbations in its parameters, and why. For example, comparative analysis could be asked to explain why the period of an oscillating spring/block system would increase if the mass of the block were larger. This paper formalizes the problem of comparative analysis and presents a technique, differential qualitative (DQ) analysis, which solves the task, providing explanations suitable for use by design systems, automated diagnosis, intelligent tutoring systems, and explanation-based generalization. DQ analysis uses inference rules to deduce qualitative information about the relative change of system parameters. Multiple perspectives are used to represent relative change values over intervals of time. Differential analysis has been implemented, tested on a dozen examples, and proven sound. Unfortunately, the technique is incomplete; it always terminates, but does not always return an answer.