In the research area, the criterion to test a hypothesis is frequently the distance of each subject from the mean of the distribution. This concept of distance is constantly used and re-used as a source of evidence in the search for significant contrasts with respect to models of theoretical probability. This paper proposes a number of ideas regarding the use of new distance indicators related to statistics that rely less heavily on parametric assumptions, in particular, the use of median confidence intervals. We have simulated via EXCEL different data samples for a design of two independent groups under 15 different conditions in two different situations: mean equality and mean differences. The results showed the high sensitivity of the comparison of the confidence intervals, especially if a strict decision criterion is used. However, we did not obtain good results for sensitivity. In fact, in some cases, the comparison of the confidence intervals of the mean worked better than those of median.