[nextos]

Many articles in e.g. Nature Genetics are cheating by hacking their p-values. These hacks would be much harder to get away with if, as a starter, they were asked to use hierarchical models and continuous explanatory variables, whenever possible.

The article from Andrew Gelman you cited explains this quite well. In general the review articles and books he has co-authored are incredibly helpful to learn how to avoid common issues that plague statistical inference.

We need to shift away from null hypotheses and p-values towards generative models, model selection and effect sizes. It leads to much more robust inference.