To recapitulate the performance of the five testing methods in situations when LME cannot be applied, ESM provided a more accurate estimation for the HDR curves than ASM, leading to a higher success in detection power. In addition, with the typical sample size in most studies, XUV as an approximate approach had the lowest power loss at the group level compared to other dimensional alternatives as well as the test with the most accurate hypothesis formulation, MVT. However, MVT plus the lesser accurate approximations such as AUC and XMV may play an auxiliary or even irreplaceable role in situations when XUV suffers from power loss (e.g., Table 1 or Voxel 2 in Figure 2).