The method of moments is applied to precisely determine the mean values of three importance measures: risk reduction, partial derivative, and variance reduction. Variance reduction calculations, in particular, are significantly improved by eliminating the imprecision associated with Monte Carlo estimates. The three importance measures are extended to permit analyses of the relative importance of groups of basic and initiating events. The partial derivative importance measure is extended by assessing the contribution of a group of events to the gradient of the top event frequency. The group importance measures are quantified for the overall fuel damage equation and for 14 dominant accident sequences from an independent probabilistic safety assessment of the K Production Reactor. This application demonstrates both the utility and the versatility of the group importance measures.