# Research: Publication bias and the canonization of false facts

## Affiliation details

University of Copenhagen, Denmark; University of Washington, United States; North Carolina State University, United States
Figure 2. A time-directed graph represents the evolution of belief over time.

In panel A, the horizontal axis indicates the number of experiments published and the vertical axis reflects the observer’s belief, quantified as the probability that the claim is true. The process begins at the single point at far left with an initial belief ${q}_{0}$. Each subsequent experiment either supports the claim, moving to the next node up and right, or contradicts the claim, moving to the next node down and right. At yellow nodes, the status of the claim is as yet undecided. At green nodes, it is canonized as fact, and at blue nodes, it is rejected as false. The black horizontal lines show the evidentiary standards (${\tau }_{0}$ and ${\tau }_{1}$). The red path shows one possible trajectory, in which a positive experiment is followed by a negative, then two positives, then a negative, etc., ultimately becoming canonized as fact when it reaches the upper boundary. Panel B shows the same network, but with the vertical axis representing log odds and using color to indicate the probability that the process visits each node. In log-odds space, each published positive result shifts belief by the constant distance ${d}_{1}>0$ and each negative result by a different distance ${d}_{0}<0$. Shown here (in both panel A and B) is a false claim with false positive rate $\alpha =0.2$, false negative rate $\beta =0.4$, publication probabilities ${p}_{0}=0.1$ and ${p}_{1}=1$, and initial belief ${q}_{0}=0.1$. In this case, the claim is likely to be canonized as fact, despite being false.