Absolute threshold vs difference threshold: the difference, and why neither one is a fixed line

The absolute threshold is the weakest stimulus that you can detect. The difference threshold is the smallest difference between two stimuli that you can detect. For each threshold, the criterion is detection on 50% of trials. The absolute threshold compares one stimulus with no stimulus. The difference threshold compares two stimuli, and it increases when the stimuli become more intense.

• The absolute threshold answers the question "Is anything there?" The difference threshold answers the question "Did it change?"
• The just noticeable difference (JND) is a second name for the difference threshold. The two names refer to one quantity.
• Weber's law is a rule for the difference threshold only. The change that you need is a constant fraction of the original stimulus.
• The two definitions contain the figure 50% because a threshold is not a fixed line. Detection changes from trial to trial.
• Two textbooks say that the eye can detect a candle flame at 30 miles. A 2015 measurement gives approximately 1.6 miles.

What the absolute threshold is

The APA Dictionary of Psychology defines the absolute threshold as "the minimum amount of stimulation required to trigger a reaction or produce a sensation". The dictionary then gives the criterion. The absolute threshold is the weakest level of stimulation "that can be detected on 50% of trials".

The OpenStax psychology textbook explains the same idea with a question. It asks "how dim can a light be or how soft can a sound be and still be detected half of the time". OpenStax also says that absolute thresholds "are generally measured under incredibly controlled conditions in situations that are optimal for sensitivity". Thus an absolute threshold describes the best case. It does not describe your hearing in a noisy street.

A textbook module from Noba gives an everyday example. The absolute threshold "explains why you don't smell the perfume someone is wearing in a classroom unless they are somewhat close to you". At a larger distance, the odour is too weak for detection.

The term has other names. The APA Dictionary lists "absolute limen (AL); detection threshold; sensation threshold". These names refer to the same concept.

What the difference threshold is

The APA Dictionary defines the difference threshold as "the smallest difference between two stimuli that can be consistently and accurately detected on 50% of trials". The same entry lists the other names: "difference limen (DL); just noticeable difference (JND; jnd)". The Noba module adds one more name, the differential threshold. All these names refer to one quantity.

OpenStax gives an example with a phone. You are in a dark cinema, and the screen of a phone becomes bright. Many people notice the change in the light level. In a brightly lit arena during a basketball game, very few people notice the same screen. OpenStax writes: "The cell phone brightness does not change, but its ability to be detected as a change in illumination varies dramatically between the two contexts."

That example shows the most important contrast between the two terms. OpenStax states it in one sentence: "Unlike the absolute threshold, the difference threshold changes depending on the stimulus intensity."

The question that sorts any example

For each example, count the stimuli that the person compares.

If the person compares one stimulus with no stimulus, the example is about the absolute threshold. The question is "Is anything there?" If the person compares two stimuli, the example is about the difference threshold. The question is "Did it change?" One stimulus before and after a change counts as two stimuli.

• You hear the quietest tone in a hearing test. This is the absolute threshold, because you compare a tone with silence.
• You notice that a person increased the volume of the television by one step. This is the difference threshold, because you compare two volume levels.
• You smell perfume only when the person is near you. This is the absolute threshold, because you compare an odour with no odour.
• You cannot feel the difference between a 10 lb bag and an 11 lb bag. This is the difference threshold, because you compare two weights.
• You see a phone screen become bright in a dark cinema. This is the difference threshold, because you compare the light level before and after.

The last example is the most difficult one. A light appears, and that looks like detection. But OpenStax uses this example for the difference threshold. The task is to detect a change in the light level of the room.

John Kihlstrom of the University of California, Berkeley, shows how the two terms are related. In his lecture notes, he uses the name relative threshold for the difference threshold. He writes that "the absolute threshold is a special case of the relative threshold, as it represents the JND between nothing and something".

Weber's law: why the difference threshold increases

The APA Dictionary defines Weber's law as "a mathematical model of the difference threshold". The law states "that the magnitude needed to detect physical change in a stimulus is proportional to the absolute magnitude of that stimulus". The dictionary says that Ernst Heinrich Weber proposed the law in 1834. The ratio between the necessary change and the original magnitude is a constant. The dictionary calls this constant Weber's fraction.

Kihlstrom gives an example with a Weber's fraction of 1/10. For an original intensity of 10 units, you first notice the change at 11 units. For 100 units, you first notice the change at 110 units, "not 101". For 200 units, the figure is 220 units. Thus the necessary change is not a fixed amount. It is a fixed fraction.

The Noba module suggests a test with weights of 1, 2, 10 and 11 lb. A friend holds the 1 lb weight and then the 2 lb weight. Your friend tells you easily which weight is heavier. With 10 lb and 11 lb, it is "much harder for your friend to reliably tell the difference". The difference is 1 lb in each comparison. But 1 lb is 100% of the first weight and only 10% of the 10 lb weight.

Kihlstrom writes that "Weber's Fraction differs for each sensory modality". His lecture slides show four representative fractions from Geldard (1962):

• Visual brightness (white light): 1/60
• Lifted weight: 1/50
• Thermal pain: 1/30
• Auditory loudness: 1/10

With a fraction of 1/50, a 100 g weight needs a change of 2 g. A 1,000 g weight needs a change of 20 g. These fractions are representative values from one source. Use them as an illustration, not as exact constants.

The law also has limits. In 1860, Gustav Fechner called Weber's law "fundamental for psychic measurement". In the same sentence, he wrote that the law is "absolutely or approximately valid" within wide limits. His next sentence starts: "There are, however, limits to its validity as well as complications".

Why both definitions say 50%

A threshold is not a line with the word never on one side and the word always on the other side. The APA Dictionary says this in its definition of the absolute threshold: "Although the name suggests a fixed level at which stimuli effectively elicit sensations, the absolute threshold fluctuates according to alterations in receptors and environmental conditions."

The Noba module gives the same reason for the 50% rule: "Because absolute threshold changes throughout the day and based on what other stimuli you have recently experienced, researchers define absolute threshold as the minimum amount of stimulation needed to detect a stimulus 50% of the time." The module says the same about the difference threshold.

The measurement procedures show how researchers get one number from a response that changes. The APA Dictionary describes two classical procedures.

• The method of limits: the researcher increases or decreases the stimulus "in discrete steps" until the response of the participant changes. The threshold is the average of the stimulus values at which the response changes. The Noba example is a hearing test. The test starts from silence, and the tones become louder.
• The method of constant stimuli: the researcher presents, in random order, "several stimuli known to be close to the threshold". The entry continues: "The threshold is the stimulus value that was detected 50% of the time."

The 50% criterion has a consequence. A stimulus that is a small amount below the threshold is not always missed. The participant detects it on fewer than 50% of the trials. A stimulus that is a small amount above the threshold is not always detected. Two early studies show why a fixed line does not fit the data.

At the limit of vision, the light itself varies

In 1942, Hecht, Shlaer and Pirenne measured the minimum light energy that the eye needs. At the cornea, the threshold was "between 54 and 148 quanta of blue-green light". The authors corrected this figure for reflection and absorption in the eye. The result was "as an upper limit 5 to 14 quanta actually absorbed by the retinal rods".

The number is small. For this reason, the authors could also calculate it from statistics. They compared the intensity of a flash with the frequency with which a person saw the flash. They wrote: "The general assumption has been that the stimulus is constant and the organism variable." Their conclusion was different: "at the threshold it is the stimulus which is variable".

Peirce and Jastrow tested for a fixed difference threshold

In October 1884, Charles Sanders Peirce and Joseph Jastrow presented a paper with the title On Small Differences in Sensation. The paper was printed in 1885. They used the German term Unterschiedsschwelle, which means difference threshold. Their test had a clear logic: "If there be a least perceptible difference, then when two excitations differing by less than this are presented to us, and we are asked to judge which is the greater, we ought to answer wrong as often as right in the long run."

They applied two different pressures to a finger of the observer. The observer said which pressure was larger. The observer also gave a confidence score from 0 to 3. The errors did not stop at a fixed line. They followed the probability curve. In the words of the authors, the results "destroy all presumption in favor of an Unterschiedsschwelle".

One more result is important. In some conditions, the observer gave a confidence score of zero, and the judgments were still "correct three times out of five". The term difference threshold remained in use after this paper. But the modern definitions do not describe a fixed line. They describe the 50% point.

What signal detection theory changed

The classical procedures have a weak point. They treat the answer "yes, I detect it" as a pure measure of the senses. But a participant who is not sure must decide between yes and no.

Signal detection theory separates these two parts. The APA Dictionary has an entry for signal detection theory. The concepts of the theory "were applied during World War II to the detection of radar signals in noise". Researchers applied the concepts to hearing and vision "in the late 1950s". The dictionary names the main contribution: "the separation of sensitivity from criterial, decision-making factors".

In a signal detection experiment, some trials contain the signal and some trials contain only noise. The Noba module names the four possible results:

• A hit: the signal is there, and you say yes.
• A miss: the signal is there, and you say no.
• A false alarm: the signal is not there, and you say yes.
• A correct rejection: the signal is not there, and you say no.

From the rate of hits and the rate of false alarms, the theory calculates two statistics. Kihlstrom names them: d′ is "a measure of sensitivity", and β is "a measure of the observer's bias or decision criterion".

OpenStax gives an example of the decision part. You expect an important phone call. In the shower, you think that you hear the phone, and the phone did not ring. OpenStax explains that "motivation to detect a meaningful stimulus can shift our ability to discriminate between a true sensory stimulus and background noise".

Kihlstrom states the consequence in strong words. Signal detection theory "denies that there is such a thing as absolute sensitivity. Sensitivity varies with expectations and motives." For your exam, the practical point is this: a measured threshold depends on the senses of the person and on the criterion of the person.

Can the eye detect a candle flame at 30 miles?

Two open textbooks give the same figure for the sensitivity of the eye. OpenStax writes: "It has been estimated that on a clear night, the most sensitive sensory cells in the back of the eye can detect a candle flame 30 miles away". OpenStax cites a 2007 paper by Okawa and Sampath for this figure. The Noba module gives the same distance: "the human eye is capable of detecting candlelight from 30 miles away in the dark".

In 2015, Kevin Krisciunas and Don Carona of Texas A&M University tested the distance. They work in the Department of Physics and Astronomy, and they treated the question as a problem of star brightness. They put a candle flame at a distance of 338 m and recorded it with a camera. Then they compared the result with the star Vega.

Their conclusion is "a candle flame situated at ~2.6 km (1.6 miles) is comparable in brightness to a 6th magnitude star". In their paper, stars of magnitude 6 are the practical limit for the unaided eye in a dark sky. The abstract also says: "The human eye cannot detect a candle flame at 10 miles or further". At 10 miles, the flame is as faint as a star of magnitude 10. The authors write that such a star needs binoculars on a tripod.

Two conditions apply to this result. The paper is a preprint from a conference poster, and it is not an experiment with many observers. But it is a direct measurement, and the 30-mile figure is approximately 19 times the distance that the authors calculated. Thus use the textbook figure with care. If your course material contains the figure, you can give it in an exam answer as the textbook estimate.

How to keep the two terms apart when you study

Use the sorting question as your cue. For the absolute threshold, think "Is anything there?" For the difference threshold, think "Did it change?" Then add the two details that exam questions frequently test: the 50% criterion and Weber's fraction.

Do not only read the definitions again. Close the book and write the two definitions from memory. Then sort five new examples. Our guide on how to memorise psychology terminology explains why this type of practice test is effective. Our article on spaced repetition explains how to put time between the sessions.

Psychology World is a psychology dictionary with study games. You save the terms that you confuse to one list, and then you drill that list. The Question game is a multiple-choice test, and it needs a list of at least four words. In the Typing game, you type the answer yourself. You can see the study modes on the home page.