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[Slide talk of this material: https://www.youtube.com/watch?v=xhexCDRKKW4]
Increasing interest in replicability in the social sciences has engendered novel designs for replication projects in which multiple sites replicate an original study. At least 134 such "many-to-one" replications have been completed since 2014 or are currently ongoing. These designs have unique potential to help estimate whether the original study is statistically consistent with the replications and to re-assess the strength of evidence for the scientific effect of interest. However, existing statistical analyses generally focus on single replications; when applied to many-to-one designs, they provide an incomplete view of aggregate evidence and can lead to unduly pessimistic conclusions about replication success. We therefore propose new statistical metrics representing: (1) the probability that the original study's estimated effect size would be as extreme or more extreme than it actually was, if in fact the original study is statistically consistent with the replications; (2) the proportion of true effects agreeing in direction with the original study. Generalized versions of the second metric allow consideration only of true effects of non-negligible size; they estimate the proportion of true effects of scientifically meaningful size in the same direction as the estimate of the original study and, secondly, the proportion of effects of meaningful size in the direction opposite the original study's estimate. We provide an R package ("Replicate").
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