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Human observers can rapidly judge the number of items in a scene. This ability is underpinned by specific mechanisms encoding number or density. We investigated whether judgments of number and density are biased by a change in volume, as they are by a change in area. Stimuli were constructed using nonoverlapping black and white luminance-defined dots. An eight-mirror Wheatstone stereoscope was used to present the dots as though in a volume. Using a temporal two-alternative forced-choice (2AFC) task and the Method of Constant Stimuli (MOCS), we measured the precision and bias (PSE shift) of numerosity and density judgments, separately, for stimuli differing in area or volume. For two-dimensional (2-D) stimuli, consistent with previous literature, perceived density was biased as area increased. However, perceived number was not. For three-dimensional (3-D) stimuli, despite a vivid impression of the dots filling a cylindrical volume, there was no bias in perceived density or number as volume increased. A control experiment showed that all of our observers could easily perceive disparity in our stimuli. Our findings reveal that number and density judgments that are biased by area are not similarly biased by volume changes.

Numerosity and density judgments: Biases for area but not for volume