Patterns of can and cannot: Condensing data on success versus failure of several patients at several tasks, and attempting to infer mental structure

Abstract

Many tasks (or tests) have binary outcomes: success or failure. Someone with a persisting injury will succeed in some of a given set of tasks and fail in others. When a group of injured people all attempt the same list of tasks, the resulting dataset will consist of a table of 1’s and 0’s, 1 indicating that a particular person succeeded at a particular task, and 0 indicating failure. In the case of some injuries, there may only be limited knowledge of how the damaged structure is organised in its undamaged state. This may apply, for example, to neuropsychological and psychological injuries. Can patterns of success and failure reveal anything about the organisation of what has been injured, for example, anything about how the brain works? A method of analysing such tables of 1’s and 0’s is described that reveals two (or more) systems or modes of action, if they are needed to explain the data. The approach extends what, in the context of cognitive impairments, is termed double dissociation. In order to be simple and practicable, the approach is deterministic rather than probabilistic. As might be expected, important components of the approach are the concepts of how severely injured is the person, and how difficult is the task. In effect, these are generalised to two characteristics of the person, two characteristics of the task, and a rule such as “the outcome is success if both of two processes are successful”, or “the outcome is success if either process is successful”. A published dataset is discussed (impairments of 39 patients with Alzheimer's disease, on a set of four tests); the patterns of impairment are found to be sufficiently varied that they suggest three characteristics rather than two or one.