What type of Type I error? Contrasting the Neyman–Pearson and Fisherian approaches in the context of exact and direct replications

Abstract

The replication crisis has caused researchers to distinguish between exact replications, which duplicate all aspects of a study that could potentially affect the results, and direct replications, which duplicate only those aspects of the study that are thought to be theoretically essential to reproduce the original effect. The replication crisis has also prompted researchers to think more carefully about the possibility of making Type I errors when rejecting null hypotheses. In this context, the present article considers the utility of two types of Type I error probability: the Neyman–Pearson long run Type I error rate and the Fisherian sample-specific Type I error probability. It is argued that the Neyman–Pearson Type I error rate is inapplicable in social science because it refers to a long run of exact replications, and social science deals with irreversible units (people, social groups, and social systems) that make exact replications impossible. Instead, the Fisherian sample-specific Type I error probability is recommended as a more meaningful way to conceptualize false positive results in social science because it can be applied to each sample-specific decision about rejecting the same substantive null hypothesis in a series of direct replications. It is concluded that the replication crisis may be partly (not wholly) due to researchers’ unrealistic expectations about replicability based on their consideration of the Neyman–Pearson Type I error rate across a long run of exact replications. Show more