Statistical significance is often inappropriately equated with evaluating result importance and evaluating result replicability, even though these are three somewhat different issues. The prudent researcher must separately assess each of these elements of the "research triumvirate" by using different methods. This paper focuses on two types of empirical methods for estimating research result replicability: double cross-validation, and bootstrap procedures. A commonly available statistical computer package, the Statistical Package for the Social Sciences (SPSS-X), is used to carry out the steps required for the double cross-validation procedure, and a recently developed microcomputer program package (developed by C. E. Lunneborg, 1987) is implemented to demonstrate the bootstrap logic. Both methods are applied to a heuristic data set of observed values of three independent variables and one dependent variable for a sample of 25 subjects. It is concluded that although each procedure has some shortcomings, the advantages of using either far outweigh the disadvantages. There are 5 tables of analysis data and a 19-item list of references. (SLD)