Among all the testing strategies for ESM (Table 1), MVT and LME maintain an accurate characterization for the hypothesis. In contrast, the dimensional reduction methods AUC, L2D, and EXC (XUV and XMV) project the original space of the alternative hypothesis from ℝm to ℝ1, ℝ1, and ℝm−1, respectively. Any dimensional reduction usually translates to information loss or geometrical distortion. Based on the results from our simulations and real data applications, we believe that the major testing methods for ESM are LME, XUV, MVT, XMV, and AUC, which all have the proper controllability for FPR. If sample size is not an issue in FMRI studies, MVT (e.g., hypothesis 2a or 2b) would be the most accurate approach in terms of hypothesis characterization. However, in practice the number of subjects is usually not large enough for MVT due to resource limitations (e.g., financial cost, time, and manpower), leading to an underpowered performance of MVT as shown in our simulations and real data. Among all the workaround methods through dimensional reduction, XUV has the least hypothesis distortion and the lowest power loss. With one group of subjects and no other explanatory variables present, XUV surpasses MVT, XMV, and AUC in power. However, with an accurate representation of the hypothesis, LME is slightly more efficient than XUV, and should be considered as the first choice (e.g., Alvarez et al., 2008). For all other situations, LME modeling is not feasible due to the constraint of variable parameterization, and we opt for the workaround methods through dimensional reduction, among which AUC is insensitive to subtle shape differences while XMV mostly underperforms unless when the temporal correlation is relatively high (e.g., 0.65 or higher; Chen et al., 2014). XUV achieves the best balance between dimensional reduction and statistical power. However, as XUV tests for parallelism, not exactly the same as the accurate representation characterized in MVT, it may fail in detecting the situation where the HDR profiles are roughly parallel. To compensate for the occasions when XUV fails, other dimensional reduction methods (MVT, AUC, XMV) may offer some complementary detection power.