After a brief description of k-anonymity, l-diversity and t-closeness techniques, the paper presents the Discrimination Rate (DR) as a new metric based on information theory for measuring the privacy level of any anonymization technique. As far as we know, the DR is the first approach supporting fine grained privacy measurement down to attribute's values. Increased with the semantic dimension, the resulting semantic DR (SeDR) enables to: (1) tackle anonymity measurements from the attacker's perspective, (2) prove that t-closeness can give lower privacy protection than l-diversity