Formal empirical assessments of replication have recently become more prominent in several areas of science, including psychology. These assessments have used different statistical approaches to determine if a finding has been replicated. The purpose of this article is to provide several alternative conceptual frameworks that lead to different statistical analyses to test hypotheses about replication. All of these analyses are based on statistical methods used in meta-analysis. The differences among the methods described involve whether the burden of proof is placed on replication or nonreplication, whether replication is exact or allows for a small amount of negligible heterogeneity, and whether the studies observed are assumed to be fixed (constituting the entire body of relevant evidence) or are a sample from a universe of possibly relevant studies. The statistical power of each of these tests is computed and shown to be low in many cases, raising issues of the interpretability of tests for replication.