In ERP and other large multidimensional neuroscience data sets, researchers often select regions of interest (ROIs) for analysis. The method of ROI selection can critically affect the conclusions of a study by causing the researcher to miss effects in the data or to detect spurious effects. In practice, to avoid inflating Type I error rate (i.e., false positives), ROIs are often based on a priori hypotheses or independent information. However, this can be insensitive to experiment-specific variations in effect location (e.g., latency shifts) reducing power to detect effects. Data-driven ROI selection, in contrast, is nonindependent and uses the data under analysis to determine ROI positions. Therefore, it has potential to select ROIs based on experiment-specific information and increase power for detecting effects. However, data-driven methods have been criticized because they can substantially inflate Type I error rate. Here, we demonstrate, using simulations of simple ERP experiments, that data-driven ROI selection can indeed be more powerful than a priori hypotheses or independent information. Furthermore, we show that data-driven ROI selection using the aggregate grand average from trials (AGAT), despite being based on the data at hand, can be safely used for ROI selection under many circumstances. However, when there is a noise difference between conditions, using the AGAT can inflate Type I error and should be avoided. We identify critical assumptions for use of the AGAT and provide a basis for researchers to use, and reviewers to assess, data-driven methods of ROI localization in ERP and other studies.