Multivariate pattern analysis (MVPA) methods are now widely used in life-science research. They have great potential but their complexity also bears unexpected pitfalls. In this paper, we explore the possibilities that arise from the high sensitivity of MVPA for stimulus-related differences, which may confound estimations of class differences during decoding of cognitive concepts. We propose a method that takes advantage of concept-unrelated grouping factors, uses blocked permutation tests, and gradually manipulates the proportion of concept-related information in data while the stimulus-related, concept-irrelevant factors are held constant. This results in a concept-response curve, which shows the relative contribution of these two components, i.e. how much of the decoding performance is specific to higher-order category processing and to lower order stimulus processing. It also allows separating stimulus-related from concept-related neuronal processing, which cannot be achieved experimentally. We applied our method to three different EEG data sets with different levels of stimulus-related confound to decode concepts of digits vs. letters, faces vs. houses, and animals vs. fruits based on event-related potentials at the single trial level. We show that exemplar-specific differences between stimuli can drive classification accuracy to above chance levels even in the absence of conceptual information. By looking into time-resolved windows of brain activity, concept-response curves can help characterize the time-course of lower-level and higher-level neural information processing and detect the corresponding temporal and spatial signatures of the corresponding cognitive processes. In particular, our results show that perceptual information is decoded earlier in time than conceptual information specific to processing digits and letters. In addition, compared to the stimulus-level predictive sites, concept-related topographies are spread more widely and, at later time points, reach the frontal cortex. Thus, our proposed method yields insights into cognitive processing as well as corresponding brain responses.