In this chapter, we present an original and synthetical overview of most of the commonly used association rule statistical interestingness measures introduced in previous works. These measures usually relate the confidence of a rule to an independency reference situation. Others relate it to indetermination, or impose a minimum confidence threshold. We propose a systematic generalization of these measures, taking into account a reference point, chosen by an expert, in order to apprehend the confidence of a rule. This generalization introduces new connections between measures. They lead to the enhancement of some measures. We then propose new parameterized possibilities. The behavior of the parameterized measures is illustrated using classical datasets, and these measures are compared to their original counter-parts. This study highlights the different properties of each of them and discusses the advantages of our proposition.