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In the branch of experimental psychology focused on sense, sensation, and perception, which is called psychophysics, a **just-noticeable difference** (JND) is the amount something must be changed in order for a difference to be noticeable, or detectable at least half the time (absolute threshold). This limen (another word for threshold) is also known as the difference limen, differential threshold, or least perceptible difference.

For many sensory modalities, over a wide range of stimulus magnitudes sufficiently far from the upper and lower limits of perception, the JND is a fixed proportion of the reference sensory level, and so the ratio of the JND/reference is roughly constant (that is the JND is a constant proportion/percentage of the reference level). Measured in physical units, we have:

where *I* is the original intensity of the particular stimulation, Δ*I* is the addition to it required for the change to be perceived (the JND), and *k* is a constant. This rule was first discovered by Ernst Heinrich Weber (1795–1878), an anatomist and physiologist, 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 of 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. Stevens developed his own law, called Stevens’ Power Law, that raises the stimulus to a constant power while, like Weber, also multiplying it by a constant factor in order to achieve the perceived stimulus.

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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. If a different proportion is used, this would be included in the description—for example a study might report the value of the 75 percent JND.

Modern approaches to psychophysics, for example signal detection theory, imply that the observed JND is not an absolute quantity, but will depend on situational and motivational as well as perceptual factors. For example, when a researcher flashes a very dim light, a participant may report seeing it on some trials but not on others.

## Try It Yourself

It is easy to differentiate between a one-pound bag of rice and a two-pound bag of rice. There is a one-pound difference, and one bag is twice as heavy as the other. However, would it be as easy to differentiate between a 20- and a 21-pound bag?

**Question:** What is the smallest detectible weight difference between a one-pound bag of rice and a larger bag? What is the smallest detectible difference between a 20-pound bag and a larger bag? In both cases, at what weights are the differences detected? This smallest detectible difference in stimuli is known as the just-noticeable difference (JND).

**Background:** Research background literature on JND and on Weber’s Law, a description of a proposed mathematical relationship between the overall magnitude of the stimulus and the JND. You will be testing JND of different weights of rice in bags. Choose a convenient increment that is to be stepped through while testing. For example, you could choose 10 percent increments between one and two pounds (1.1, 1.2, 1.3, 1.4, and so on) or 20 percent increments (1.2, 1.4, 1.6, and 1.8).

**Hypothesis:** Develop a hypothesis about JND in terms of percentage of the whole weight being tested (such as “the JND between the two small bags and between the two large bags is proportionally the same,” or “. is not proportionally the same.”) So, for the first hypothesis, if the JND between the one-pound bag and a larger bag is 0.2 pounds (that is, 20 percent; 1.0 pound feels the same as 1.1 pounds, but 1.0 pound feels less than 1.2 pounds), then the JND between the 20-pound bag and a larger bag will also be 20 percent. (So, 20 pounds feels the same as 22 pounds or 23 pounds, but 20 pounds feels less than 24 pounds.)

**Test the hypothesis:** Enlist 24 participants, and split them into two groups of 12. To set up the demonstration, assuming a 10 percent increment was selected, have the first group be the one-pound group. As a counter-balancing measure against a systematic error, however, six of the first group will compare one pound to two pounds, and step down in weight (1.0 to 2.0, 1.0 to 1.9, and so on.), while the other six will step up (1.0 to 1.1, 1.0 to 1.2, and so on). Apply the same principle to the 20-pound group (20 to 40, 20 to 38, and so on, and 20 to 22, 20 to 24, and so on). Given the large difference between 20 and 40 pounds, you may wish to use 30 pounds as your larger weight. In any case, use two weights that are easily detectable as different.

**Record the observations:** Record the data in a table similar to the table below. For the one-pound and 20-pound groups (base weights) record a plus sign (+) for each participant that detects a difference between the base weight and the step weight. Record a minus sign (−) for each participant that finds no difference. If one-tenth steps were not used, then replace the steps in the “Step Weight” columns with the step you are using.

Table 1. Results of JND Testing (+ = difference; − = no difference) | |||
---|---|---|---|

Step Weight | One pound | 20 pounds | Step Weight |

1.1 | 22 | ||

1.2 | 24 | ||

1.3 | 26 | ||

1.4 | 28 | ||

1.5 | 30 | ||

1.6 | 32 | ||

1.7 | 34 | ||

1.8 | 36 | ||

1.9 | 38 | ||

2.0 | 40 |

**Analyze the data/report the results:** What step weight did all participants find to be equal with one-pound base weight? What about the 20-pound group?

**Draw a conclusion:** Did the data support the hypothesis? Are the final weights proportionally the same? If not, why not? Do the findings adhere to Weber’s Law? Weber’s Law states that the concept that a just-noticeable difference in a stimulus is proportional to the magnitude of the original stimulus.

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