Small Telescopes: Detectability and the Evaluation of Replication Results

Abstract

This paper introduces a new approach for evaluating replication results. It combines effect-size estimation with hypothesis testing, assessing the extent to which the replication results are consistent with an effect size big enough to be detectable by the original study. The approach is demonstrated revisiting replications of three famous findings: the embodiment of morality, the endowment effect, and weather & happiness. Its benefits include: (i) distinguishing p>.05 replications that are simply too-noisy from those that actively indicate the effect is undetectably different from zero, (ii) “protecting” true findings from underpowered replications, and (iii) arriving at intuitively compelling inferences in general and for the revisited replications in particular.

Keywords: Replications, power, p-values, effect size