Process mining techniques are useful for analyzing and optimizing processes. However, processes often exist in many variants that can differ significantly in their execution. These differences within the data can negatively affect the quality of process mining results and, furthermore, indicate disparities within the process. While several approaches exist that characterize the differences between processes, oftentimes the mere existence of differences can be problematic. To this end, techniques to prove or disprove the existence of such differences are required and should do so in a statistically sound manner. However, the literature on process hypothesis testing is sparse and limited in the considered dimensions of difference. In this paper, we propose a hypothesis testing approach that uses the earth mover’s distance in combination with a permutation test to compare event logs in various dimensions. The evaluation shows that the proposed approach achieves better performance than the existing work in detecting control-flow differences and, moreover, detects differences in further dimensions, demonstrated on the time dimension.