This week, a chart with some Bayesian polemic behind it. Alexander Etz put this on Twitter:
He is working on an R package to provide easy Bayesian adjustments for reporting bias with a method by Guan & Vandekerchhove. Imagine a study reporting three p-values, all just under the threshold of significance, and with small-ish sample sizes. Sound suspicious?
Sounds like someone’s been sniffing around after any pattern they could find. Trouble is, if they don’t tell you about the other results they threw away (reporting bias), you don’t know whether to believe them or not. Or there are a thousand similar studies but this is the (un)lucky one and this author didn’t do anything wrong in their own study (publication bias).
Well, you have to make some assumptions to do the adjustment, but at least being Bayesian, you don’t have to assume one number for the bias, you can have a distribution. Here, the orange distribution is the posterior for the true effect once the bias has been added (in this case, p>0.05 has a 0% chance of getting published, which is not unrealistic in some circles!) This is standard probabilistic stuff but it doesn’t get done because the programming seems so daunting to a lot of people. The more easy tools – with nice helpful visualisations – the better.