With this post I inaugurate the focus on series, where I go much more in depth than usual. I could as well have called it the gory details, but focus on sounds more elegant. You might be in for a shock if you are more into easy reading, so the focus on is also here as a warning sign so that you can skip the post altogether if you are not interested in the detail. For those who are, this way please...

In my previous post I exposed the multiple testing problem. Every null hypothesis, true or false, has at least a 5% chance of being rejected (assuming you work at 95% confidence level). By testing the same hypothesis several times, you increase the chances that it will be rejected at least once, which introduces a bias because this one time is much more likely to be noticed, and then published. However, being aware of the illusion does not dissipate it. For this you need insight and statistical tools.

Fail-safe $(n)$ to measure publication bias

Suppose $(n)$ independent research teams test the same null hypothesis, which happens to be true — so not interesting. This means that the...