Zahra Hussain¹ (), Patrick Bennett²; ¹University of Plymouth, ²McMaster University

How do observers integrate information across observations? In detection tasks where the signal is known exactly, or the stimulus is selected randomly from N signals on every observation, d' for an ideal observer improves with the square-root of the observation number. However, if the stimulus is selected randomly on observation 1 and remains constant on subsequent observations, Swets & Birdsall (1978) showed that the initial increase in d' produced by optimal integration exceeds square-root law. We evaluated this prediction by measuring d' in 2IFC detection tasks comprising four observations per trial. The stimuli were band-limited noise textures or 1 cy/deg gratings that varied in orientation. In the no-uncertainty condition, the stimulus was the same in all observations and trials. In the composite condition, the stimulus varied randomly across trials but was the same in all observations within a trial. In the simple uncertainty condition, the stimulus varied randomly across all observations and trials. The effect of observations varied across conditions. In the no-uncertainty condition, d' followed square-root law for gratings but was sub-optimal for textures. In the composite condition, the increase in d’ between observations 1 and 2 exceeded square-root law for gratings but not textures. Hence, Swets & Birdsall’s prediction was supported for gratings but not textures, and is consistent with the absence of stimulus uncertainty effects for textures shown by Hussain et al (VSS 2025). In the simple uncertainty condition, integration was suboptimal for the first two observations and followed square-root law thereafter. These results are consistent with the idea that the effects of uncertainty depend strongly on the visual stimuli and the way that uncertainty is manipulated across observations.