Extending Reproducibility to Theory: Theoretical Reproducibility and Precision as Foundations of Cumulative Science

The demonstration that many published findings are not replicable has triggered intense methodological debates in psychology and related fields. While substantial efforts have been made to (re)establish methodological norms at the empirical level, comparatively little attention has been paid to reproducibility at the level of theory. This paper examines the interplay between theory and epistemic value of studies and argues that cumulative knowledge development requires extending reproducibility concerns to the theoretical domain. To address the problem of theory ambiguity - situations in which theories are described so vaguely that different theoretical contents or predictions can be inferred - we introduce the concepts of theoretical reproducibility and theoretical precision. Theoretical reproducibility refers to the extent to which a theory is specified such that independent researchers would converge on the same theoretical content and predictions. Theoretical precision captures the degree to which a theory, even if perfectly specified, yields informative predictions. We formally define both concepts and illustrate their role in cumulative knowledge development using a Bayesian framework. The difference between theoretical reproducibility and precision, on the one hand, and the background probability of a hypothesis, on the other hand, determines how much information can be gained from an empirical study. Assessing this difference is essential to ensure that empirical studies can meaningfully contribute to cumulative knowledge development. Strategies for increasing theoretical reproducibility are discussed, highlighting how better-specified theories allow empirical research to be used more efficiently for cumulative science.