"It is better to treat p values as nothing more than useful exploratory tools or measures of surprise. In any search for new physics,  a small p value should only be seen as a first step in the interpretation of the data, to be followed by a serious investigation of an alternative hypothesis. Only by showing that the latter provides a better explanation of the observations than the null hypothesis can one make a convincing case for a discovery."

Luc Demortier, "p values and nuisance parameters", CERN-08-001, p.24.