Sensitivity analysis is an essential part of studying efficiency in data envelopment analysis (DEA). One appealing approach to sensitivity analysis allows simultaneous data perturbation in all DMUs. We present this type of sensitivity analysis for super-efficiency measures when some input relaxation is permissible. We also study sensitivity analysis in the worst-case scenario where the efficiency, based on the relaxed inputs, of an evaluating unit is worsening while the efficiencies of the other DMUs are improving. Necessary and sufficient conditions for preserving a DMU's efficiency classification are developed when various data changes are applied to all DMUs.