[Examination of some statistical evaluations of independence. Application to drug evaluation]

When two classes of events (E1, E2, ..., Em) on the one hand, (F1, F2, ..., Fn) on the other hand are such that the set of the m x n couples (Ei, Fj) represent all the possible issues of a common random experiment, it is often useful to know whether these two classes must be considered or not as independent of each other. In most cases, the answer to this important question is obtained through a chi 2-test and, less frequently, through various interpretations based upon the value rho of the linear correlation coefficient. A different method is also available to reach a conclusion, after estimating another coefficient mu characterizing the independence. The goal of the present lecture is to compare the possibilities, advantages and inconveniences of the three computational techniques leading to chi 2, rho and mu. Some examples of application to drugs evaluation are exposed.