The problem with "classical" statistics all invoking the mean is that these estimates are notoriously influenced by atypical scores (outliers), partly because the mean itself is differentially influenced by outliers. In theory, "modern" statistics may generate more replicable characterizations of data, because at least in some respects the influence of more extreme scores, which are less likely to be drawn in future samples from the tails of a non-uniform (non-rectangular or non-flat) population distribution, has been minimized. However, "modern" statistics have not been widely employed in contemporary research. The present paper will illustrate various "modern" statistics. Also, a mini-Monte Carlo study will be conducted with a hypothetical population to demonstrate in a concrete fashion that "modern" statistics do tend to yield more replicable characterizations of study results. The present paper explains both trimmed and winsorized statistics, and uses a mini-Monte Carlo demonstration of the robust regression analysis as well as describes other computer-intensive methods such as jackknifing and bootstrapping. (Contains 6 figures and 5 tables.)