Several object-oriented cohesion metrics have been proposed in the literature. These metrics aim to measure the relationship between class members, namely, methods and attributes. Different metrics use different models to represent the connectivity pattern of cohesive interactions (CPCI) between class members. Most of these metrics are normalized to allow for easy comparison of the cohesion of different classes. However, in some cases, these metrics obtain the same cohesion values for different classes that have the same number of methods and attributes but different CPCIs. This leads to incorrectly considering the classes to be the same in terms of cohesion, even though their CPCIs clearly indicate that the degrees of cohesion are different. We refer to this as a lack of discrimination anomaly (LDA) problem. In this paper, we list and discuss cases in which the LDA problem exists, as expressed through the use of 16 cohesion metrics. In addition, we empirically study the frequent occurrence of the LDA problem when the considered metrics are applied to classes in five open source Java systems. Finally, we propose a metric and a simulation-based methodology to measure the discriminative power of cohesion metrics. The discrimination metric measures the probability that a cohesion metric will produce distinct cohesion values for classes with the same number of attributes and methods but different CPCIs. A highly discriminating cohesion metric is more desirable because it exhibits a lower chance of incorrectly considering classes to be cohesively equal when they have different CPCIs.