A simple model suggesting economically rational sample-size choice drives irreproducibility

TL;DR

This paper presents a simple economic model showing that rational sample-size choices driven by publication incentives lead to low reproducibility in research, especially under certain conditions like low effect probability or small effect size.

Contribution

It formalizes how economic incentives influence sample-size decisions, explaining the prevalence of underpowered studies and irreproducibility, and explores strategies like conditional equivalence testing.

Findings

Small sample sizes are predicted under low effect probability, small effect size, or low publication income.

The model predicts a bimodal distribution of statistical power, matching empirical observations.

Economic incentives are identified as a key driver of irreproducibility.

Abstract

Several systematic studies have suggested that a large fraction of published research is not reproducible. One probable reason for low reproducibility is insufficient sample size, resulting in low power and low positive predictive value. It has been suggested that insufficient sample-size choice is driven by a combination of scientific competition and 'positive publication bias'. Here we formalize this intuition in a simple model, in which scientists choose economically rational sample sizes, balancing the cost of experimentation with income from publication. Specifically, assuming that a scientist's income derives only from 'positive' findings (positive publication bias) and that individual samples cost a fixed amount, allows to leverage basic statistical formulas into an economic optimality prediction. We find that if effects have i) low base probability, ii) small effect size or iii) low grant income per publication, then the rational (economically optimal) sample size is small. Furthermore, for plausible distributions of these parameters we find a robust emergence of a bimodal distribution of obtained statistical power and low overall reproducibility rates, both matching empirical findings. Finally, we explore conditional equivalence testing as a means to align economic incentives with adequate sample sizes. Overall, the model describes a simple mechanism explaining both the prevalence and the persistence of small sample sizes, and is well suited for empirical validation. It proposes economic rationality, or economic pressures, as a principal driver of irreproducibility and suggests strategies to change this.