The pursuit of sensitive and dependable biomarkers capable of capturing the neural processes associated with cognition is a prominent area of interest. Event-related potentials (ERPs) hold significant promise for assessing cognitive dysfunction in various neurological disorders. However, existing data analysis techniques often underutilize the available data and may benefit from potential enhancements. In this paper, we investigate biomarker extraction methods based on two ERP experiments. First, we derive average ERPs from the electroencephalography (EEG) recorded during each experiment and store them in third-order tensors with subjects, channels and time samples along the three modes. Then, we extract biomarkers from these datasets via tensor decompositions. We compare single tensor decompositions and joint tensor decompositions that fuse the data from the individual tensors. In a simulated ERP experiment we compare the benefits and limitations of different tensor-based data fusion methods. Finally, we investigate their performance on a real dataset obtained from schizophrenia patients.