A theory of criterion setting: an alternative to the attention band and response ratio hypotheses in magnitude estimation and cross-modality matching.

The attention band and response ratio hypotheses of Green and Luce (1974) and Luce and Green (1974) are discussed and some difficulties are noted. An alternative hypothesis is put forward. This is based on a Thurstonian model for magnitude estimation in which the presented stimulus intensities are subjected to a logarithmic transformation. Response criteria are then applied to the resulting quantities to select corresponding responses. The setting and maintenance of these response criteria are accounted for by a theory of criterion setting previously developed by the senior author (Treisman & Williams, 1984). A similar model is developed for cross-modality matching, and it is shown that these models can predict the V pattern for the coefficient of variation of response ratios, can predict the inverted V pattern for correlations between successive responses, and can account for some of the difficulties found in the literature.