Distribution-based statistics are often reported as supportive information to anchor-based estimates of responder definition (RD). The purpose of this study is to illustrate the difference among these statistics mathematically in terms of sensitivity and specificity to better facilitate the applications. Five distribution-based statistics (half standard deviation [SD], one standard error of measurement [SEM], 1.96 SEM, reliable change index [i.e., 2.772 SEM], and 4 SEM) were compared in terms of sensitivity and specificity rates under 24 conditions. Specifically, the conditions were generated based on 6 different reliabilities of instruments (i.e., ρ=0.7, 0.75, 0.8, 0.85, 0.9, 0.95) and 4 types of changes from baseline to post-treatment (i.e., no change, small change, moderate change, and large change). Based on the true-score model, the baseline and post-treatment scores were described as Y0=T+e0 and Y1=T+δ+e1, respectively, where T denoted the true score, e denoted the error, and δ denoted a constant change. Assuming normal distribution of baseline and post-treatment scores, the sensitivity and specificity can be calculated using cumulative normal distribution function based on different conditions. The conditions with no change provided the ground for calculating specificity of using different distribution-based statistics as RD. The specificities were 76%, 92%, 98%, and 99.8% for SEM-based statistics, and they were not affected by reliability. The specificities ranged from 74% to 95% for half SD, and the rates decreased with the increase of reliability. The conditions with true changes were used to calculate sensitivity. The sensitivity increased with the increase of change size and reliability in general. Based on the criterion of maximizing the sensitivity and specificity simultaneously, one SEM outperformed other distribution-based statistics. One SEM, derived from the scale characteristics, has methodological advantages when developing and interpreting RD.