Some problems with Bryden and Sprott's "statistical determination of degree of lateralization"

Bryden and Sprott (Neuropsychologia 19, 571-581, 1982) have proposed an index, lambda, of lateralization that has the same range of possible values no matter what the overall level of accuracy obtained in the experiment. It is shown by way of example that changes in lambda over the levels of the independent variable may be predictable from increases in the level of accuracy for the right and left sides. Specifically, if accuracy increases at a constant rate for the two sides, then lambda, except for some highly artificial situations, is constrained to increase or decrease. It is argued that difficulties associated with the difference between correct responses for the two sides as an index of the degree of lateralization may have been exaggerated. It is shown for hypothetical data that the difference measure may have many of the properties of lambda.