# Stimulus Control: Discrimination, Generalization, Peak Shift, and Errorless Learning

> Stimulus control means a behavior's probability depends on an antecedent. SD vs. S-delta, discrimination, generalization, peak shift, and errorless learning.

- Source: https://operantconditioning.com/stimulus-control/
- Author: Ryan Martinson (https://operantconditioning.com/about/)
- Publisher: Operant Conditioning Inc.
- Published: 2026-09-09 · Updated: 2026-09-10
- License: https://operantconditioning.com/terms/#copyright (quote with attribution and a link; free to reproduce for non-commercial teaching)

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*Antecedents · Core concept*

Consequences decide whether a behavior is learned; antecedents decide when it shows up. Here is how a stimulus comes to govern behavior without forcing it, how far that control spreads, why it can shift in strange directions, and how it is used on everything from pigeons to insomnia.

> **Definition**
>
> A behavior is under **stimulus control** when its probability — how often it occurs, how quickly, or in what form — depends on whether a particular antecedent stimulus is present. The stimulus does not force the behavior; it changes the odds, because in the past the behavior has been reinforced in its presence and not in its absence.
>
> Skinner introduced the analysis, and the symbols S^D and S^Δ, in *The Behavior of Organisms* (1938); the classic experimental review is Terrace (1966).[1][2]

**In brief**

- A behavior is under stimulus control when its probability depends on an antecedent stimulus, because it has been reinforced in that stimulus's presence before.
- A discriminative stimulus (S^D) signals that a response will be reinforced; an S-delta signals that it will not, and discrimination training alternates the two.
- Generalization spreads responding to similar stimuli along a gradient; discrimination training steepens that gradient and can shift its peak away from the S-delta.

## What is stimulus control?

Put a rat in a chamber where lever presses produce food only while a light is on. At first it presses at the same rate light or dark. After a few sessions it presses briskly the moment the light comes on and hardly at all when it goes off. Nothing about the light compels the press — a rat that has just eaten will ignore it — but the light has become the condition under which pressing is worth doing. Pressing is under stimulus control, and the gap between the two rates measures how tightly.[1]

Human life is dense with the same relation. A ringing phone, a green light, a colleague's raised eyebrow, an "Open" sign, the first bars of a song you know: each raises the probability of a specific behavior because that behavior has paid off in its presence before. This is the antecedent term of the [three-term contingency](https://operantconditioning.com/abc-model/) — in the presence of S^D, response R produces reinforcer S^R. Reinforcement builds a behavior; stimulus control decides where and when it appears.[3]

> **Control is not compulsion**
>
> "Control" is a technical word here, closer to the way a thermostat controls a furnace than the way a puppeteer controls a puppet. A stimulus controls an operant by changing its probability, and only because of a history of consequences; change the consequences and the same stimulus stops working. A stimulus that *forces* a response — the puff of air that makes you blink — is eliciting a reflex, a different process. [Operant vs. classical conditioning ›](https://operantconditioning.com/operant-vs-classical-conditioning/)

## S^D and S-delta: how discrimination training works

A **discriminative stimulus**, S^D (pronounced "ess-dee"), is a stimulus in whose presence a response has been reinforced. An **S-delta**, S^Δ, is a stimulus in whose presence the same response has gone unreinforced. In the generalization literature the pair is often written S+ and S−. **Discrimination training** is simply reinforcement in one and extinction in the other, alternated until responding diverges. The organism is said to *discriminate* when it responds differently to the two.[1]

| S^D (respond) | S^Δ (don't) | Behavior | What the S^D signals |
| --- | --- | --- | --- |
| Light on | Light off | Rat presses the lever | Presses will produce food |
| "Sit" | Any other word | Dog sits | A treat is available for sitting now |
| Teacher looking at the class | Teacher writing on the board | Student raises a hand | Hand-raising will get called on |
| Friends at a bar | Grandmother at dinner | Telling a crude joke | Laughter, not a frown |
| Green "Walk" signal | Red hand | Crossing the street | Crossing will be safe and unfined |
| Bed, dark room, 11 p.m. | Desk, daylight | Falling asleep | Sleep will come — unless the bed has also become a cue for scrolling |

Stimulus control is not automatic. A stimulus that is always present, with no difference in consequences attached, may acquire no control at all. Jenkins and Harrison trained pigeons to peck a key with a 1000-hertz tone playing throughout; tested later with tones of other pitches, the birds responded equally at every pitch — a flat gradient. The tone had been there all along, but they had never had a reason to attend to it. Birds trained with the tone on during reinforcement and off during extinction produced a sharply peaked gradient centered on 1000 hertz.[4] A cue has to *predict a difference* to gain control, which is why "sit" said to a dog that will be fed anyway teaches nothing.

## Generalization and the generalization gradient

**Stimulus generalization** is the mirror image of discrimination: responding to stimuli that resemble the S^D without having been trained on them. The more similar the stimulus, the more responding it evokes — a relation that, plotted, is a **generalization gradient**.

The textbook demonstration is Guttman and Kalish's. They reinforced pigeons for pecking a key lit with a single wavelength — separate groups at 530, 550, 580, and 600 nanometers — and then, in extinction so the test itself taught nothing, presented a range of wavelengths on either side. Responding peaked at the training wavelength and fell away smoothly on both sides.[5] The gradient's shape is not fixed: discrimination training steepens it, and what the organism learns is less the stimulus itself than how it differs from what surrounds it.[6]

| Aspect | Discrimination | Generalization |
| --- | --- | --- |
| **What it is** | Responding differently to different stimuli | Responding similarly to similar stimuli |
| **Laboratory sign** | A steep gradient; near-zero responding in S^Δ | A flat, wide gradient |
| **Everyday example** | Answering your own ringtone, not a stranger's | Braking for a stop sign you have never seen before |
| **When it fails you** | A skill that works only in the room it was taught in | A fear of one dog that spreads to every dog |
| **How to get more of it** | Differential reinforcement: pay in S^D, never in S^Δ | Train with many examples in many settings |

Both are adaptive and both can misfire. Generalization lets a toddler call the neighbor's terrier a dog; discrimination stops her calling the cat one. In applied work generalization is usually the scarce commodity: a behavior taught in one place with one person by one method tends to stay there unless generalization is deliberately programmed.[7]

## Peak shift: when discrimination training moves the peak

Discrimination training does something stranger than sharpen the gradient. In 1937 Kenneth Spence proposed that an S+ builds up a gradient of excitation and an S− a gradient of inhibition, and that the two add algebraically. If the S− sits close to the S+ on the same dimension, the sum should peak not at the S+ but a little beyond it, on the side away from the S−.[8] The prediction sat on paper for twenty years.

H. M. Hanson tested it in 1959. He reinforced pigeons for pecking at 550 nm, then extinguished pecking at a slightly yellower 555 nm (other groups had S− at 560, 570, or 590 nm; a control group had no S− at all). In the generalization test, the control birds peaked at 550, as Guttman and Kalish's had. The birds trained against 555 peaked at 540 — a wavelength they had never been reinforced for, displaced away from the S− — and pecked far more overall than the controls. The nearer the S− had been to the S+, the larger the shift.[9] This is **peak shift**: evidence that the S^Δ does not merely switch responding off but exerts an inhibitory gradient of its own, which subtracts most on the side nearest it.

![Peak shift after discrimination training](https://operantconditioning.com/assets/diagrams/peak-shift-after-discrimination-training.svg)

*Schematic of Hanson's result. After discrimination training against a nearby S−, the peak of the gradient moves away from the S− (here from 550 to about 540 nm) and rises above the control gradient.*

## Errorless discrimination learning

In ordinary discrimination training the learner meets the S^Δ at full strength, responds to it, and is extinguished: it learns by making errors. Herbert Terrace showed in 1963 that the errors are optional. He trained pigeons to peck a red key and not a green one, but introduced the green key from the first session so dimly and briefly that the birds never pecked it, then raised its brightness and duration in small steps. Pigeons trained this way acquired the discrimination with few or no errors, where birds trained conventionally made thousands.[10] In a companion study he transferred the discrimination from colors to vertical and horizontal lines by superimposing the lines on the colors and fading the colors out.[11]

The errorless birds differed in more than their error count. They showed none of the agitation that conventionally trained birds displayed during the S−, and in a wavelength test they showed no peak shift: the S− had acquired no inhibitory gradient, because it had never been responded to and extinguished.[10][12] Whether a stimulus becomes aversive depends on how it was learned.

The legacy is everywhere in teaching. **Prompting** — a gesture, a model, a highlighted answer, physical guidance — gets the right response before an error can occur, and **fading** transfers control from the prompt to the natural S^D in graded steps.[13] In neuropsychology, Baddeley and Wilson found that people with amnesia learned word lists better when prevented from guessing than by trial and error: without explicit memory they could not correct their mistakes, so each error was simply practiced.[14] Errorless learning has costs — a learner who never meets the S^Δ may be thrown when it finally appears, and a prompt that is never faded produces a learner who waits for it — but for fragile or fearful learners it is usually the right default. [Prompting and fading in depth ›](https://operantconditioning.com/shaping/)

## Contextual control and renewal

Stimulus control belongs not only to discrete cues but to the background: the room, the time of day, the people present. Contexts acquire control more weakly than a lit key, but reliably, and their influence is sharpest at the moment of extinction. Mark Bouton's research showed that when a behavior is learned in one context and extinguished in another, returning to the first context brings it back — **renewal**. The original learning transfers across contexts; the extinction learning largely does not. Extinction does not erase what was learned but adds a second, inhibitory lesson whose retrieval depends on the context in which it was learned, so that the stimulus becomes ambiguous and the setting decides which meaning wins.[15]

The practical consequences are large. A fear reduced in a therapist's office can return in the parking garage; a tantrum extinguished at the clinic can return at home; a habit dropped on holiday returns on the first morning back at work. The remedies follow directly: extinguish in every context that matters, and teach the replacement behavior where the old one used to pay. [Renewal, resurgence, and spontaneous recovery ›](https://operantconditioning.com/extinction/#renewal)

## Stimulus control in practice

### Stimulus control therapy for insomnia

The most direct clinical use of the concept treats a bed that has stopped working. For a good sleeper, bed, darkness, and bedtime are S^Ds for falling asleep. For a chronic insomniac they have become cues for lying awake, worrying, checking the time, and watching television, because that is what has repeatedly happened there. Richard Bootzin's **stimulus control treatment**, introduced in 1972, re-establishes the bed as a cue for sleep and nothing else.[16]

1. **Go to bed only when sleepy**, not merely tired or because it is late.
2. **Use the bed only for sleep.** No reading, eating, screens, or worrying in bed. (Sex is the conventional exception.)
3. **If you cannot fall asleep within about 10 to 20 minutes, get up**, go to another room, and return only when sleepy. Repeat as needed.
4. **Get up at the same time every morning**, however little you slept.
5. **Do not nap** during the day.

The rules are uncomfortable for a week or two and then, for most people, they work. Stimulus control is a core component of cognitive behavioral therapy for insomnia (CBT-I), which the American College of Physicians recommends as the first-line treatment for chronic insomnia in adults, ahead of medication.[17]

### "Train it everywhere": dog training

A dog that sits perfectly in the kitchen has learned "sit, in the kitchen, facing my owner, treat pouch on." At the park none of those stimuli are present, and neither is the sit. The dog is not stubborn; it is discriminating exactly as its training taught it to. The fix is to program generalization: train with many examples — rooms, people, distances, distractions — until the word alone controls the behavior. Stokes and Baer's "train sufficient exemplars" is the same advice in the language of applied behavior analysis.[7] [Cues and generalization in dog training ›](https://operantconditioning.com/dog-training/)

### Habit design: choose the cue

Habits are behaviors under tight stimulus control: the context evokes the response with little deliberation, and the response survives on the context rather than on intention.[18] That gives you two levers. To build a habit, attach the behavior to a specific, stable cue that already occurs — after the coffee is poured, when the front door closes — and reinforce it there until the cue does the work. To break one, remove or change the cue; a phone charging in the kitchen is not an S^D for scrolling in bed. Skinner listed "changing the stimulus" among the basic techniques of self-control for exactly this reason.[3] [The operant protocol for building habits ›](https://operantconditioning.com/habits/)

### Study in one place

The classic study-skills prescription is Bootzin's rule applied to a desk. Work in one place used for nothing else; when you stop working, leave it. Over a few weeks the desk becomes an S^D for working and stops being one for daydreaming, snacking, and messaging, because those behaviors are never reinforced there. "I'll study on the couch" so rarely produces studying because the couch already controls something else.

## Which is it: discrimination or generalization?

Five scenarios. Decide which process each shows before opening the answer.

**1. A toddler who has learned "doggie" for the family beagle says it to a neighbor's Labrador, then to a goat.**

**Generalization.** The response spreads to stimuli that resemble the training stimulus. The Labrador is a useful generalization; the goat is an overgeneralization that discrimination training — "no, that's a goat" — will correct.

**2. A rat presses the lever rapidly when the light is on and almost never when it is off.**

**Discrimination.** Responding differs sharply between S^D and S^Δ; the behavior is under tight stimulus control.

**3. A dog that sits reliably in the kitchen ignores "sit" at the park.**

**Discrimination — more than the trainer wanted.** The behavior is controlled by the kitchen's stimuli, not by the word. The trainer's job is to build generalization to the cue alone by training across settings.

**4. You reach for your phone whenever you hear a notification chime, including other people's.**

**Generalization.** The response evoked by your own chime spreads to similar chimes. If you later stop reaching for others' phones because only yours has ever paid off, that is discrimination developing.

**5. A student swears freely with friends and never at the dinner table.**

**Discrimination.** The same behavior occurs in one social setting (where it has been reinforced with laughter) and not in another (where it has met disapproval). Friends are the S^D; family dinner is the S^Δ.

## Common confusions

### Discriminative stimulus vs. conditioned stimulus

| Aspect | Discriminative stimulus (S^D) | Conditioned stimulus (CS) |
| --- | --- | --- |
| **What it does** | *Evokes* an operant: raises its probability | *Elicits* a respondent: triggers a reflex |
| **How it got its power** | The behavior was reinforced in its presence | It was paired with an unconditioned stimulus, whatever the organism did |
| **Does the behavior matter?** | Yes: the consequence depends on responding | No: the US arrives regardless |
| **Example** | A lit key: pecking now produces grain | A tone that precedes food: salivation follows the tone |

The two often ride on the same event. The click of the food magazine is a CS (it elicits approach and salivation), a conditioned reinforcer (it strengthens the press it follows), and an S^D for going to the tray. Asking which function a stimulus is serving, rather than what it "is," is the behavior analyst's habit.

### Stimulus control vs. elicitation

An S^D changes probabilities; it never guarantees a response, and a motivating operation can cancel it entirely (the lit key evokes nothing in a stuffed pigeon). Elicitation is closer to a guarantee: the reflex follows the stimulus whether or not the organism is hungry, tired, or busy. When a stimulus seems to "make" someone do something — a craving at the sight of a bar, a flinch at a raised hand — the elicited, Pavlovian component is often doing more of the work than the operant one.

### Three more

- **An S^D is not a motivating operation.** The S^D signals that a reinforcer is *available*; a motivating operation changes how much it is *worth*. [Motivating operations explained ›](https://operantconditioning.com/abc-model/)
- **An S^Δ is not a punisher.** It signals that responding will go unreinforced, not that it will be punished — though, as Terrace's pigeons showed, a stimulus learned through extinction can become mildly aversive in its own right.
- **"Discrimination" here has no social meaning.** It is the technical word for responding differently to different stimuli, as in a discriminating palate.

## Key takeaways

- Stimulus control means an antecedent changes the probability of a behavior; it does not force it. An S^D evokes an operant only because of a history of consequences, and a stimulus that forces a response is eliciting a reflex, a different process.
- Discrimination training is reinforcement in the presence of the S^D and extinction in the presence of the S^Δ, alternated until responding diverges. A cue has to predict a difference in consequences to gain any control at all.
- Generalization is responding to untrained stimuli that resemble the S^D, and the generalization gradient shows how responding falls off with similarity. Discrimination training steepens the gradient and, when the S− is close to the S+, shifts its peak away from the S−: peak shift.
- Errors are optional. Introducing the S^Δ so faintly that it is never responded to, then fading it in, produces a discrimination with few or no errors, no agitation, and no peak shift; prompting and fading apply the same idea in teaching.
- Contexts control behavior too, and extinction learning is more context-bound than the original learning, so an extinguished behavior renews when the setting changes. Stimulus control therapy for insomnia, training a dog in many settings, and choosing a cue for a habit all apply the same principle.

**Explain it to a friend.** Explain why a dog that sits perfectly in the kitchen ignores "sit" at the park, in two sentences a twelve-year-old would follow.

## Frequently asked questions

**What is stimulus control in psychology?**

Stimulus control is the condition in which a behavior occurs more often, faster, or more reliably in the presence of a particular stimulus than in its absence, because the behavior has been reinforced in that stimulus's presence in the past. The stimulus is called a discriminative stimulus. Stimulus control is the antecedent side of operant conditioning: consequences build a behavior, and antecedents decide when it appears.

**What is an example of stimulus control?**

A rat that presses a lever only when a light is on; a driver who brakes at a red light and not a green one; a dog that sits when it hears "sit"; a student who swears with friends but not at the family table. In each case the behavior is possible at any time but is reliably evoked by one stimulus and not by others.

**What is the difference between SD and S-delta?**

An S^D (discriminative stimulus) is a stimulus in whose presence a behavior has been reinforced, so the behavior becomes more likely when it appears. An S^Δ (S-delta) is a stimulus in whose presence the same behavior has not been reinforced, so the behavior becomes less likely. Discrimination training alternates the two — reinforcement in S^D, extinction in S^Δ — until responding diverges.

**What is the difference between discrimination and generalization?**

Discrimination is responding differently to different stimuli: pressing when the light is on but not when it is off. Generalization is responding similarly to similar stimuli: pecking a slightly different color that was never trained. They are two ends of one continuum, and the generalization gradient — how responding falls off as a test stimulus becomes less like the training stimulus — measures where an organism sits on it.

**What is peak shift?**

After discrimination training between an S+ and a nearby S− on the same dimension, the peak of the generalization gradient moves away from the S−. Hanson's pigeons, reinforced at 550 nm and extinguished at 555 nm, responded most to 540 nm, a color they had never been reinforced for. Spence predicted the effect in 1937 from the idea that excitatory and inhibitory gradients add.

**What is stimulus control therapy for insomnia?**

A behavioral treatment, developed by Richard Bootzin in 1972, that makes the bed a cue for sleep and nothing else: go to bed only when sleepy, use the bed only for sleep, get up if you cannot sleep and return only when sleepy, rise at the same time every day, and do not nap. It is a core component of cognitive behavioral therapy for insomnia, the recommended first-line treatment for chronic insomnia.

## References

1. Skinner, B. F. (1938). *The Behavior of Organisms: An Experimental Analysis*. Appleton-Century.
2. Terrace, H. S. (1966). Stimulus control. In W. K. Honig (Ed.), *Operant Behavior: Areas of Research and Application* (pp. 271–344). Appleton-Century-Crofts.
3. Skinner, B. F. (1953). *Science and Human Behavior*. Macmillan.
4. Jenkins, H. M., & Harrison, R. H. (1960). Effect of discrimination training on auditory generalization. *Journal of Experimental Psychology, 59*(4), 246–253.
5. Guttman, N., & Kalish, H. I. (1956). Discriminability and stimulus generalization. *Journal of Experimental Psychology, 51*(1), 79–88.
6. Honig, W. K., & Urcuioli, P. J. (1981). The legacy of Guttman and Kalish (1956): Twenty-five years of research on stimulus generalization. *Journal of the Experimental Analysis of Behavior, 36*(3), 405–445.
7. Stokes, T. F., & Baer, D. M. (1977). An implicit technology of generalization. *Journal of Applied Behavior Analysis, 10*(2), 349–367.
8. Spence, K. W. (1937). The differential response in animals to stimuli varying within a single dimension. *Psychological Review, 44*(5), 430–444.
9. Hanson, H. M. (1959). Effects of discrimination training on stimulus generalization. *Journal of Experimental Psychology, 58*(5), 321–334.
10. Terrace, H. S. (1963). Discrimination learning with and without "errors." *Journal of the Experimental Analysis of Behavior, 6*(1), 1–27.
11. Terrace, H. S. (1963). Errorless transfer of a discrimination across two continua. *Journal of the Experimental Analysis of Behavior, 6*(2), 223–232.
12. Terrace, H. S. (1964). Wavelength generalization after discrimination learning with and without "errors." *Science, 144*(3615), 78–80.
13. Cooper, J. O., Heron, T. E., & Heward, W. L. (2020). *Applied Behavior Analysis* (3rd ed.). Pearson.
14. Baddeley, A., & Wilson, B. A. (1994). When implicit learning fails: Amnesia and the problem of error elimination. *Neuropsychologia, 32*(1), 53–68.
15. Bouton, M. E. (2004). Context and behavioral processes in extinction. *Learning & Memory, 11*(5), 485–494.
16. Bootzin, R. R. (1972). Stimulus control treatment for insomnia. *Proceedings of the 80th Annual Convention of the American Psychological Association, 7*, 395–396.
17. Qaseem, A., Kansagara, D., Forciea, M. A., Cooke, M., & Denberg, T. D. (2016). Management of chronic insomnia disorder in adults: A clinical practice guideline from the American College of Physicians. *Annals of Internal Medicine, 165*(2), 125–133.
18. Wood, W., & Rünger, D. (2016). Psychology of habit. *Annual Review of Psychology, 67*, 289–314.


## About the author

Ryan holds a master's degree from UCLA, where he studied animal behavior in Daniel Blumstein's lab and was part of the university's Evolutionary Medicine Program, which applies findings from evolutionary biology and animal behavior to human health. He founded Operant Conditioning Inc. and built the Operant habit app (https://operantconditioning.com/app/). Every page here is written from the primary literature and cites it. How pages are checked: https://operantconditioning.com/about/#editorial-standards

## Related

- [The ABC model](https://operantconditioning.com/abc-model/): Antecedent, behavior, consequence — the three-term contingency that stimulus control is the front half of.
- [Extinction](https://operantconditioning.com/extinction/): Bursts, spontaneous recovery, resurgence, and the renewal that context brings.
- [Dog training](https://operantconditioning.com/dog-training/): Adding the cue, proofing it everywhere, and why a kitchen "sit" vanishes at the park.