Proceedings of the Annual Meeting of the Cognitive Science Society

When researchers carry out a null hypothesis significance test, it is tempting to assume that a statistically significantresult lowers Prob(H0), the probability of the null hypothesis being true. Technically, such a statement is meaningless forvarious reasons: e.g., the null hypothesis does not have a probability associated with it. However, it is possible to relaxcertain assumptions to compute the posterior probability Prob(H0) under repeated sampling. We show that the intuitivelyappealing belief, that Prob(H0) falls when significant results have been obtained under repeated sampling, is in generalincorrect and depends greatly on: (a) the prior probability of the null being true; (b) Type I error, and (c) Type II error.Through simulation we quantify uncertainty and find that uncertainty about the null hypothesis often remains high despitea significant result. To help the reader develop intuitions about this common misconception, we provide a Shiny app(https://danielschad.shinyapps.io/probnull/).