Double dissociations play an important role in neuropsychology, but they are often identified through subjective estimates of "high" versus "low" performance, without considering the probability that such an outcome might have occurred by chance. To determine whether two measures "come apart" in an interesting way in brain-damaged patients, it is important to know the degree to which variance in one measure can be predicted by variance in the other. This study introduces a statistical procedure to determine the probability of a double dissociation when the correlation between measures is taken into account. Different quantitative definitions of dissociations were compared in two large samples of neurological patients, and applied to four pairs of measures (two for language, two for hemispatial neglect) with different degrees of intercorrelation (ranging from +.21 to +.84). If the correlation between measures is not taken into account, large numbers of dissociated cases may be missed, especially for measures that are highly correlated. There are also qualitative differences between methods in the identity of those individuals who meet each definition.