How to find multiple systems underlying a two-way table of Os and 1s with applications to cognitive impairments and medical laboratory science

Abstract

Datasets are sometimes encountered that consist of a two-way table of 0’s and 1’s. For example, this might show which patients are impaired on which of a battery of tests, or which compounds are successful at inactivating which of several micro-organisms. The present paper describes a method of analysing such tables, that reveals and specifies two (or more) systems or modes of action, if indeed they are needed to explain the data. The approach is an extension of what, in the context of cognitive impairments, is termed double dissociation. In order to be simple enough to be practicable, the approach is deterministic rather than probabilistic.