Abstract: Statistical significance is often interpreted as providing greater information than non-significance. In this article we show, however, that rejection of a point null often carries very little information, while failure to reject may be highly informative. This is particularly true in empirical contexts that are typical and even prevalent in economics, where data sets are large and there are rarely reasons to put substantial prior probability on a point null. Our results challenge the usual practice of conferring point null rejections a higher level of scientific significance than non-rejections. Therefore, we advocate a visible reporting and discussion of non-significant results.