Failures to reproduce research findings across scientific disciplines from psychology to physics have garnered increasing attention in recent years. External replication of published findings by outside investigators has emerged as a method to detect errors and bias in the published literature. However, some studies influence policy and practice before external replication efforts can confirm or challenge the original contributions. Uncovering and resolving errors before publication would increase the efficiency of the scientific process by increasing the accuracy of published evidence. Here we summarize the rationale and best practices for internal replication, a process in which multiple independent data analysts replicate an analysis and correct errors prior to publication. We explain how internal replication should reduce errors and bias that arise during data analyses and argue that it will be most effective when coupled with pre-specified hypotheses and analysis plans and performed with data analysts masked to experimental group assignments. By improving the reproducibility of published evidence, internal replication should contribute to more rapid scientific advances.