ABSTRACT
Broadly speaking, any assumption on the distribution of one or more random
variables observed in an experiment is a statistical hypothesis. The hypothesis
may be based on theoretical considerations, on the analysis of other (similar)
experiments or it may just be an educated guess suggested by reasonableness
or common sense, whatever these terms mean. In any case, it must be checked
by actually performing the experiment and by devising some method which -
in the light of the acquired data - gives us the possibility to decide whether to
accept it or reject it. This, it should be clear from the outset, does not imply
that our decision wil l be right because, as in any procedure of statistical
inference, the best we can do (unless we examine the entire population) is
to reduce the probability of being wrong to an acceptable level, where the
term 'acceptable' generally depends on the problem at hand, the seriousness
of the consequences of being wrong and, last but not least, the cost of the
experiment. Consequently, we wil l not state our conclusions by saying 'our
hypothesis is true (false)' but 'the observed data are in favour (against) our
hypothesis', and we wil l continue our work behaving as if the hypothesis
were true (false).
