Just noticeable difference

In psychophysics, a just noticeable difference, customarily abbreviated with lowercase letters as jnd, is the smallest difference in a specified modality of sensory input that is detectable by a human being or other animal. It is also known as the difference limen or the differential threshold.

Explanation
For many sensory dimensions, the 'jnd' is an increasing function of the base level of input, and the ratio of the two is roughly constant. Measured in physical units, we have


 * $$\frac {\Delta I} {I} = k,$$

where $$I\!$$ is the original intensity of stimulation, $$\Delta I\!$$ is the addition to it required for the difference to be perceived (the jnd), and k is a constant. This rule was first discovered by Ernst Heinrich Weber, in experiments on the thresholds of perception of lifted weights. A theoretical rationale (not universally accepted) was subsequently provided by Gustav Fechner, so the rule is therefore known either as the Weber Law or as the Weber–Fechner law; the constant k is called the Weber constant. It is true, at least to a good approximation, of many but not all sensory dimensions, for example the brightness of lights, and the intensity and the pitch of sounds. It is not true, however, of the wavelength of light. Stanley Smith Stevens argued that it would hold only for what he called prothetic sensory continua, where change of input takes the form an increase in intensity or something obviously analogous; it would not hold for metathetic continua, where change of input produces a qualitative rather than a quantitative change of the percept.

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. If a different proportion is used, this should be included in the description&#8212;for example one might report the value of the "75% jnd".

Modern approaches to psychophysics, for example signal detection theory, imply that the observed jnd, even in this statistical sense, is not an absolute quantity, but will depend on situational and motivational as well as perceptual factors.

It has also been observed for the distribution of weights on a beam balance (see ).