In recognition tasks where the stimuli vary along two or more dimensions, the question arises as to what strategy the subject uses in processing the information about the various stimulus attributes. Three strategies are discussed: parallel, serial and integrative processing. It is shown that each of these three strategies implies a relation among the distribution functions of three observable random variables. The problem is then to decide on the basis of three samples, one from each distribution, which one of the relations is most likely. Non‐parametric statistics are defined which can be used to construct test functions for this decision problem, and a suggestion is made concerning the design of experiments which attempt to discriminate between these strategies. 1969 The British Psychological Society