Standard packages outputs when n is large: when and how should they be adjusted?

In the presence of large sample sizes hypotheses testing procedures often lead to excessive rates of rejection. This is mainly due to the precise null hypothesis formulation usually adopted in statistical packages. We address the fundamental issues of deciding whether commonly reported outputs are misleading and, if this is the case, how to adjust them through suitable calibration procedures. Such procedures are designed to handle different levels of information available on the relevant characteristics of the various applicative contexts.