Bayesian Interpretation of the Expression “Significant at .05”: A Discrete Example

Abstract

The Bayesian inference based on the information “significant at .05” depends logically on the sample size, n. If n is sufficiently large, the locution “significant at .05,” taken by itself, implies not strong evidence against the null hypothesis but strong evidence in its favor. More particularly, for large n, a report which says merely “significant at .05,” without further information, should be interpreted as evidence against the null only if for some reason peculiar to the test in question it is considered subjectively that the sample observation x is very probably significant not only at 5% but at 1% or lower. This result holds for any “point” (simple) null hypothesis and is demonstrated here in the context of a simple example. Note that for the purpose of interpreting the expression “significant at .05” per se, it is supposed that the exact value of x is unknown.