Data exploration and conditional probability

It is possible to “read” the data of a 2×2 contingency table by interpreting the various proportions as “conditional probabilities”. If we interpret the probability P as degree of belief in the truth of an event E, then P can be looked on as a substitute of our relevant lack of information concerning the truth or falsity of E. In the same way we consider the conditional probability. A suitable interpretation of the concept of conditional event allows one to look at the so-called “Simpson´s paradox”, from a different perspective. We give also a sufficient condition to avoid the paradox