Significance and nonsignificance

It is a common belief that a statistically significant finding always is practically important and that statistical nonsignificance is a good indication of "no difference". This belief is a major mistake. Statistical significance is a measure of uncertainty, not of importance; practical importance has to be shown by other means than p-values. Equivalence and non-inferiority can only be statistically tested when an equivalence or non-inferiority margin, specifying the practical importance, has been defined.