The purpose of replication is to address the validity of a scientific claim. If I conduct a study and conclude that “X is related to Y”, then others may be encouraged to replicate my study--with independent investigators, data collection, instruments, methods, and analysis--in order to determine whether my claim of “X is related to Y” is in fact true. If many scientists replicate the study and come to the same conclusion, then there’s evidence in favor of the claim’s validity. If other scientists cannot replicate the same finding, then one might conclude that the original claim was false. In either case, this is how science has always worked and how it will continue to work.
Reproducibility, on the other hand, focuses on the validity of the data analysis. In the past, when datasets were small and the analyses were fairly straightforward, the idea of being able to reproduce a data analysis was perhaps not that interesting. But now, with computational science, where data analyses can be extraordinarily complicated, there’s great interest in whether certain data analyses can in fact be reproduced. By this I mean is it possible to take someone’s dataset and come to the same numerical/graphical/whatever output that they came to. While this seems theoretically trivial, in practice it’s very complicated because a given data analysis, which typically will involve a long pipeline of analytic operations, may be difficult to keep track of without proper organization, training, or software. ... If an analysis is reproducible, that says practically nothing about the validity of the conclusion or of the analysis itself. Reproducibility plays a role only in the most downstream aspect of the research process--post-publication. ... At this point it may be difficult to correct any mistakes if they are identified.
... a famous quotation from R. A. Fisher:
To consult the statistician after an experiment is finished is often merely to ask him to conduct a post mortem examination. He can perhaps say what the experiment died of.To summarize, I believe reproducibility of computational research is very important, primarily to increase transparency and to improve knowledge sharing. However, I don’t think reproducibility in and of itself addresses the fundamental question of “Can I trust this analysis?”. Furthermore, reproducibility plays a role at the most downstream part of the research process (post-publication) where it is costliest to fix any mistakes that may be discovered. Ultimately, we need to think beyond reproducibility and to consider developing ways to ensure the quality of data analysis from the start.