Isobias and alloiobias functions in animal psycophysics

An analogue of the human yes-no detection task was used to train six pigeons to discriminate luminance differences under two different reinforcer-scheduling procedures. When a controlled reinforce-ratio procedure was used, relative stimulus frequency was constant at .5, and relative reinforcer frequency for correct detections was held constant at three different values for each of five luminance differences. When an uncontrolled reinforcer-ratio procedure (the typical detection paradigm) was used, relative reinforcer frequency for correct detections was allowed to covary with changes in relative stimulus frequency for each of five luminance differences. Two measures of bias, response bias (Davison & Tustin, 1978) and the detection-theory likelihood-ratio measure (beta obt), were compared. The controlled reinforcer-ratio procedure generated equal- or iso-response-bias functions, and the uncontrolled reinforcer-ratio procedure gave changing or alloio-response-bias functions. The Davison-Tustin model accounted for 88% and 93% of the data variance in the controlled and uncontrolled reinforcer-ratio procedures, respectively. The best-fitting equal-beta functions accounted for an average of 53% and 69%, respectively, in the two procedures. In addition, neither procedure gave constant measures of beta obt for constant bias manipulations across different discriminability measures.