Choosing alpha post hoc: the danger of multiple standard significance thresholds
A fundamental assumption of classical hypothesis testing is that the significance threshold $α$ is chosen independently from the data. The validity of confidence intervals likewise relies on choosing $α$ beforehand. We point out that the independence of $α$ is guaranteed in practice because, in most fields, there exists one standard $α$ that everyone uses -- so that $α$ is automatically independent of everything. However, there have been recent calls to decrease $α$ from $0.05$ to $0.005$. We note that this may lead to multiple accepted standard thresholds within one scientific field. For example, different journals may require different significance thresholds. As a consequence, some researchers may be tempted to conveniently choose their $α$ based on their p-value. We use examples to illustrate that this severely invalidates hypothesis tests, and mention some potential solutions.