Employing two vignette studies, we examined how psychology researchers interpret the results of a set of four experiments that all test a given theory. In both studies, we found that participants' belief in the theory increased with the number of statistically significant results, and that the result of a direct replication had a stronger effect on belief in the theory than the result of a conceptual replication. In Study 2, we additionally found that participants' belief in the theory was lower when they assumed the presence of p-hacking, but that belief in the theory did not differ between preregistered and non-preregistered replication studies. In analyses of individual participant data from both studies, we examined the heuristics academics use to interpret the results of four experiments. Only a small proportion (Study 1: 1.6%; Study 2: 2.2%) of participants used the normative method of Bayesian inference, whereas many of the participants' responses were in line with generally dismissed and problematic vote-counting approaches. Our studies demonstrate that many psychology researchers overestimate the evidence in favor of a theory if one or more results from a set of replication studies are statistically significant, highlighting the need for better statistical education.
Keywords: Bayesian inference; Heuristics; Multi-study paper; Replication; Statistical misinterpretation; Vote counting.
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