Statistical significance is often interpreted as providing greater information than nonsignificance. 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 common in economics, where datasets 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 visible reporting and discussion of nonsignificant results.
Abstract:
Statistical significance is often interpreted as providing greater information than nonsignificance. 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 common in economics, where datasets 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 visible reporting and discussion of nonsignificant results.