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The JND is a statistical, rather than an exact quantity: from trial to trial, the difference that a given person notices will vary somewhat, and it is therefore necessary to conduct many trials in order to determine the threshold. The JND usually reported is the difference that a person notices on 50% of trials.
A difference threshold (or just-noticeable difference, JND) is the magnitude of the smallest difference between two stimuli of differing intensities that a participant can detect a certain proportion of the time, with the specific percentage depending on the task. Several methods are employed to test this threshold.
Weber found that the just noticeable difference (JND) between two weights was approximately proportional to the weights. Thus, if the weight of 105 g can (only just) be distinguished from that of 100 g, the JND (or differential threshold) is 5 g.
The JND does not. The JND is the subjective experience of a difference. 1 and 2 coins are separated by 1 coin (the difference threshold) and 1 JND (I can just tell the difference); 100 and 200 coins are separated by 100 coins (the difference threshold) but just 1 JND (if I can't tell 100 from 199 but can just tell the difference at 100 vs. 200).
If the distance measure is perceptually uniform, then the answer is simply "the set of points whose distance to the reference is less than the just-noticeable-difference (JND) threshold". This requires a perceptually uniform metric in order for the threshold to be constant throughout the gamut (range of colors). Otherwise, the threshold will be ...
This yields several momentary threshold values. In the following step, mean values are calculated for ascending and descending sequences separately. The mean value will be lower for descending sequences. In case of audiometry, the difference of the means in case of ascending vs. descending sequences has a diagnostic importance.
The just-noticeable difference (jnd) (the threshold at which a change is perceived) depends on the tone's frequency content. Below 500 Hz, the jnd is about 3 Hz for sine waves, and 1 Hz for complex tones; above 1000 Hz, the jnd for sine waves is about 0.6% (about 10 cents). [22]
Lindblom found that on average, there was a 27% difference in threshold level between slow and fast mechanical pulses on a participant's finger pad. [21] The threshold for rapid pulses was 5 μm, and 80 μm for slow pulses. Lindblom's study shows that humans are more sensitive to fast stimulation than slow stimulation, at least for touch.