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In response to concerns about the validity of empirical findings in psychology, some scientists use replication studies as a way to validate good science and to identify poor science. Such efforts are resource intensive and are sometimes controversial (with accusations of researcher incompetence) when a replication fails to show a previous result. An alternative approach is to examine the statistical properties of the reported literature to identify some cases of poor science. This review discusses some details of this process for prominent findings about racial bias, where a set of studies seems too good to be true. This kind of analysis is based on the original studies, so it avoids criticism from the original authors about the validity of replication studies. The analysis is also much easier to perform than a new empirical study. A variation of the analysis can also be used to explore whether it makes sense to run a replication study. As demonstrated here, there are situations where the existing data suggest that a direct replication of a set of studies is not worth the effort. Such a conclusion should motivate scientists to generate alternative experimental designs that better test theoretical ideas.