Detection and attribution is based on the assumption that the impact of natural and anthropogenic forcings on the climate system can be well approximated by linearly adding the effects of individual forcings. This assumption has been validated for global averages and spatial patterns of (mostly) temperature related variables. Modelling groups in CMIP5 undertook these detection and attribution experiments in various ways, some adding each historical forcing to a preindustrial control, others eliminating certain forcings from a historical all-forcing simulation. Many studies have assumed these methods produce similar results, however the available experiments have not allowed this assumption to be tested until now. Here for the first time we compare these two methods of detection and attribution in ensemble simulations with the CESM1-CAM5 coupled climate model. For example, are the results of a simulation that includes all external forcings but for ozone depletion similar to the results of adding the output of all individual single-forcing experiments but for those driven by ozone changes? Results suggest that similar evolutions of global temperatures and precipitation are found between the two methods, with some notable differences in the response to aerosols. Our experiments enable us to go beyond the global average temperature response and explore different variables at different spatial and temporal scales so to characterize in a systematic fashion where the linearity holds and where it breaks down.