Ever wondered how the probability of the null hypothesis being true changes given a significant result?

TRIGGER WARNING: These simulations might fundamentally shake your belief system. USE WITH CARE.

In a recently accepted paper in the open access journal Quantitative Methods for Psychology that Daniel Schad led, we discuss how, using Bayes' rule, one can explore the change in the probability of a null hypothesis being true (call it theta) when you get a significant effect. The paper, which was inspired by a short comment in McElreath's book (first edition), shows that theta does not necessarily change much even if you get a significant result. The probability theta can change dramatically under certain conditions, but those conditions are either so stringent or so trivial that it renders many of the significance-based conclusions in psychology and psycholinguistics questionable at the very least.

You can do your own simulations, under assumptions that you consider more appropriate for your own research problem, using this shiny app (below), or play with the source code: here.