A discussion is presented in which it is considered how properly to evaluate the results of a statistical analysis of the data of physical experiments and how, in particular, to teach statistical methods to students. The case is made that hopes traditionally placed on statistical procedures and methods are often betrayed. Ultimately, the reason is that usual probability model of errors of observation are, as a rule, invalid if considered as physical models. However, if the results of data analysis are evaluated in the frameword of a statistical paradigm, then it is entirely possible that they will be useful for physical applications.