Keywords: Bayes' Theorem; Fallacy of the Transposed Conditional; Naked Statistics; Tests of Significance.
A general topic is faced in the first section, which is devoted to Bayes' formula (or theorem): it is a fundamental device which allows the computation of probabilities of possible causes, given related information about certain effects. Strictly connected to this argument is the «fallacy of the transposed conditional», which usually implies an unwarranted assumption of guilt. The third section is devoted to a discussion of some main features of two "causes célèbres", those of Alfred Dreyfus in France and of Nicola Sacco and Bartolomeo Vanzetti in U.S.A. Section 4 discusses the role and significance in trials of so-called naked statistics, which most (but not all) experts exclude from applications in trials. The final section 5 presents two kinds of cases which require a judgment about groups of people; the statistical methods applied in these cases pertain to the so-called tests of significance.