Abstract
In magnitude discrimination tasks (e.g., which ensemble is more numerous?), differences that are more difficult than the ratio specified as the JND (e.g., 8 vs. 9 dots) are sometimes understood to be completely imperceptible. The Just Noticeable Difference (JND) is often defined as the minimum amount of difference between two values required to be perceivable. Importantly, if analog magnitudes, the most common type of representation in visual perception and cognition, are represented as a series of gaussian tuning curves with linearly increasing variability, as is also often assumed, then there should be no ratio other than 1 at which perception transitions qualitatively from “success” to “chance” performance: More boldly, there should be no JND. To test whether subjects can perform above chance at ratios far more difficult than a typical JND, we asked online subjects (N = 207) to complete a series of trials judging which of two ensembles has more dots, where the trials contained increasingly difficult ratios: between 20 vs. 30 dots (ratio 1.5) up to 50 vs. 51 dots (ratio 1.02). We found that subjects were able to successfully discriminate all tested ratios above chance, all ts > 4.6, all ps < .001. That is, we found that people are sensitive to differences even at a ratio of 1.02, which is far below the point typically thought of as a JND. We anticipate that many scientists may already be familiar with these points (e.g., a JND at 75% correct is not a unique datapoint and subjects will be above chance both above and below this JND). But many (perhaps the majority) of scientists have misunderstood the JND to mark a critical boundary below which differences are imperceptible. Our work shows that, given enough trials, any difference in magnitude, no matter how small, will indeed be perceivable.