A methodology for investigating motor learning is developed using activation distributions rather than the more standard voxel-level interaction tests. The approach uses tests of dimensionality to consider the ensemble of paired changes in voxel activations for an arc-pointing motor task with and without training. The selected method allows for the application of non-focal and non-localized changes. In exchange for increased power to detect learning-based changes in these settings, this complimentary procedure sacrifices the localization information gained via voxel-level interaction testing. The associated framework considers activation distribution, while the specific proposed test investigates linear tests of dimensionality on activation distributions as a starting point. Such approach includes: the development of the framework; a large scale simulation study; and the subsequent application of the methods to a study of motor learning in healthy adults. Complexity results when evaluating the impact of massive numbers of null voxels and varying angles of dimensionality across subjects. However, further analysis found that careful masking addressed the former concern while an angle correction successfully resolved the latter. The simulation results demonstrate that the study of linear dimension reduction using singular value decomposition in a framework similar to Zarahn (2002) is able to capture specific instances of learning effects. The observed data set used to illustrate the method evaluates two similar arc-pointing tasks, each over two sessions with training between the two tasks. The results suggests a marginally significant test in favor of greater activation distribution dimensionality in the untrained arc-pointing task and no evidence of greater dimensionality in the trained task, or in the comparison between the trained and untrained.