Selected methods for evaluating the stability of research results empirically are described, especially with regard to multivariate analysis. It is critically important to evaluate the influences of sampling error on obtained results; statistical significance testing does not inform judgment regarding the probable replicability or the sampling specificity of results. Data provided by K. J. Holzinger and F. Swineford (1939) are used to make the discussion more concrete. As a starting point, an example of a univariate invariance analysis is presented. Other techniques described and illustrated include: (1) multiple regression analysis; (2) factor analysis; and (3) canonical correlation analysis. Ten tables illustrate the data. An appendix contains the Statistical Package for the Social Sciences program used to implement the analyses. A 60-item list of references is included. (SLD)