Many issues complicate efforts to replicate studies, including concerns about models. Hundreds of papers published over the last sixty years make it clear that the models underlying the conventional statistical methods that are routinely taught and used can lead to low power, inflated false positive rates and inaccurate confidence intervals. In this chapter, we summarize these issues and how they affect replication assessment. We conclude that instead of trying to replicate poorly characterized effects, our efforts would be better spent on developing and discussing more detailed models.