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Zahra Hussain, Patrick Bennett; Integrating information across multiple observations in a visual detection task. Journal of Vision 2020;20(11):570. https://doi.org/10.1167/jov.20.11.570.
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Swets et al (1964) measured auditory sensitivity for narrow-band signals embedded in noise using a 4IFC detection task that contained five observations on each trial. They found that d’ increased with the square-root of observations when the noise varied across observations but not when the noise was the same. This result suggests that observers integrated information nearly optimally across the five observations. We report an experiment designed to test if this result held for visual detection. Ten observers performed a 2IFC detection task using band-limited textures in static white Gaussian noise. Each trial comprised five observations of a texture in variable or constant noise. Variable noise was independently sampled on both intervals of every observation in the trial (no two noise samples were identical). Constant noise was a fixed noise sample used for both intervals of all five observations in a trial. Noise conditions were blocked. Observers performed two sessions over two consecutive days, for a total of 800 trials (4000 observations) across days. Consistent with decision theory, d’ increased at a greater rate across observations in variable noise than in constant noise for the majority of observers. With some exceptions, d’ for each observer followed the square root prediction more closely for variable noise than for constant noise. When sensitivity was averaged across observers, d’ conformed to the square root prediction almost perfectly in variable noise, but levelled off after the second observation in constant noise. In addition, absolute performance in virtually all observers was better in variable noise than in constant noise across all observations. These results provide the first evidence, to our knowledge, of statistically optimal integration of information across observations in a visual detection task.
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