Signed difference analysis: Theory and application

Psychological constructs can only be measured indirectly in terms overt behavior, often by means of changes in the level of performance on tasks they are presumed to affect. However, the exact relationship between constructs and the tasks they are presumed to affect is usually not known, which often requires non-essential auxiliary assumptions to be added to a psychological model to allow it to contact the data. Signed difference analysis is a method of deriving testable consequences from psychological models under the general assumption that the relationship between task performance and the constructs or combinations of constructs postulated by the model is at least monotonic. The predictions derived using signed difference analysis do not depend upon estimation of either model parameters or explicit functional relationships. In the present paper, the mathematical theory of signed difference analysis is presented and applied to illustrative problems drawn from research in memory, spatial attention, and reading. The relationships between signed difference analysis and related inferential procedures such as conjoint measurement, state-trace analysis, and double dissociation are discussed.