Statistics in Service of Metascience: Measuring Replication Distance with Reproducibility Rate

Motivated by the recent putative reproducibility crisis, we discuss the relationship between the replicability of scientific studies, the reproducibility of results obtained in these replications, and the philosophy of statistics. Our approach focuses on challenges in specifying scientific studies for scientific inference via statistical inference and is complementary to classical discussions in the philosophy of statistics. We particularly consider the challenges in replicating studies exactly, using the notion of the idealized experiment. We argue against treating reproducibility as an inherently desirable property of scientific results, and in favor of viewing it as a tool to measure the distance between an original study and its replications. To sensibly study the implications of replicability and results reproducibility on inference, such a measure of replication distance is needed. We present an effort to delineate such a framework here, addressing some challenges in capturing the components of scientific studies while identifying others as ongoing issues. We illustrate our measure of replication distance by simulations using a toy example. Rather than replications, we present purposefully planned modifications as an appropriate tool to inform scientific inquiry. Our ability to measure replication distance serves scientists in their search for replication-ready studies. We believe that likelihood-based and evidential approaches may play a critical role towards building statistics that effectively serve the practical needs of science.