The purpose of this study was to determine: (1) the extent to which effect sizes vary by chance; (2) the proportion of standardized effect sizes that achieve or exceed commonly used criteria for small, medium, and large effect sizes; (3) whether standardized effect sizes are random or systematic across numbers of groups and sample sizes; and (4) whether it is possible to predict standardized effect sizes using degrees of freedom, number of groups, and sample sizes. Monte Carlo procedures were used to generate standardized effect sizes in a one-way analysis of variance situation with 2 through 10 groups with samples sizes from 5 to 100 in steps of 5. Within each of the 180 configurations, 5,000 replications were done. It was found that standardized effect size variation was systematic rather than random. Numbers of groups and sample sizes were highly predictive of standardized effect size, but error degrees of freedom was not predictive. Equations were developed that could be used to predict standardized effect sizes that could be expected by chance, using number of groups and sample size as the predictor variables. The prediction equations were extremely accurate. This research provides a better alternative for the evaluation of empirical standardized effect sizes than the somewhat arbitrary and fixed criteria often used to classify standardized effect sizes as small, medium, or large. (Contains 3 tables, 10 figures, and 34 references.) (SLD)