Drawing valid conclusions from statistical tests

One of the more common techniques in answering questions involving statistical inference is to calculate an appropriate test statistic and, based on its value, determine whether some hypothesis should be rejected or otherwise. The thorny issue of one-sided versus two-sided tests has provoked much debate in the literature, particularly with respect to which one may be appropriate and whether the choice is made simply on grounds that a significant result might be obtained. This paper goes a step further and consider precisely what might be concluded if a two-sided test is used with opinions from surveyed experts in the field surprisingly divided. There is also a discussion of constructing confidence intervals for extremely rare events and why conventional theory can be misleading.