The Variable Interval Schedule: Definition, Examples, and Why It Produces Such Steady Behavior

How a variable interval schedule works

The clock on an interval schedule decides when a reinforcer becomes available, not when it is delivered. On a VI schedule the clock starts when a reinforcer is delivered and runs for an interval drawn from a list: 12 seconds this time, 48 the next, 3 after that. While it runs, responses do nothing. When it runs out, the next response is reinforced, the clock resets, and a new interval begins.^[1][2]

A pigeon on VI 1 min collects close to 60 reinforcers an hour whether it pecks 20 times a minute or 80, because each reinforcer, once set up, waits for the next peck to collect it.^[1] Some procedures add a limited hold, a window (say, two seconds) after which an uncollected reinforcer is cancelled.^[3]

How the intervals are generated

Ferster and Skinner built their VI schedules from an arithmetic series of intervals, evenly spaced lengths from short to long, arranged in an irregular order.^[1] That construction has a flaw: with evenly spaced lengths, the longer an interval has already lasted, the more likely it is to end in the next few seconds, so the probability that a response will be reinforced rises with time since the last reinforcer, and a well-trained animal can learn to speed up as the interval ages.^[5]

Fleshler and Hoffman solved this in 1962 with a formula that generates intervals distributed so that the probability of a reinforcer becoming available in the next moment is the same however long it has been since the last one: a constant-probability VI, the standard laboratory construction since.^[5] Catania and Reynolds later showed that pigeons' moment-to-moment rate tracks the moment-to-moment probability of reinforcement: an arithmetic VI produces a mild acceleration within intervals, a constant-probability VI a roughly flat rate.^[6]

The behavior a variable interval schedule produces

On a cumulative record, VI responding is a nearly straight line of moderate slope, ticked at irregular intervals by reinforcers that leave no visible mark on the rate. There is no post-reinforcement pause worth the name, and no scallop, because nothing about the passage of time predicts the next reinforcer.^[1] Skinner emphasized the stability of VI behavior and its resistance to extinction.^[7]

How fast is "moderate"? Catania and Reynolds answered this in 1968. They ran pigeons on VI schedules spanning a very wide range of reinforcement rates and found that response rate was a negatively accelerated function of reinforcement rate: it rose steeply as the schedule went from very lean to moderately rich and then flattened, so that across the middle and upper range, large changes in reinforcement rate produced comparatively small changes in pecking.^[6] Herrnstein fitted a hyperbola to these data two years later and made it the quantitative form of the law of effect, which is why their study is the empirical foundation of the matching law.^[8]

The steadiness has a second source. On any interval schedule, the longer it has been since the last response, the more likely a reinforcer has become available in the meantime, so a response after a long pause is more likely to be reinforced than one after a short pause. The schedule quietly reinforces moderate spacing, whereas a ratio schedule pays most to whoever responds fastest.^[9] The result is a rate reliably lower than a ratio schedule with the same reinforcement rate would maintain, as Baum showed with pigeons on VR and VI schedules matched for reinforcers per hour.^[4]

Variable interval vs. fixed interval, variable ratio, and fixed ratio

Two questions place any basic schedule: does reinforcement depend on a count of responses or on the passage of time, and is the requirement fixed or variable? VI is time-based and variable. Its nearest neighbors are the fixed interval schedule, which shares its indifference to response rate but adds predictability, and the variable ratio schedule, which shares its unpredictability but pays for every response.

The confusion that matters most is VI with VR, because both are called variable and both are described as unpredictable. The test is what the unpredictability is attached to. On VR an unpredictable number of responses is required, and every response moves the count forward: on a slot machine every pull is another draw at the payout, so more pulls mean more payouts, even though no pull is ever 'due'. On VI an unpredictable amount of time must pass, and responses do not move the clock: checking the mailbox for the twentieth time this morning does not bring the mail. VR produces high rates because effort is rewarded; VI produces moderate rates because only timing is.^[2]

The confusion with FI is the reverse: same clock, different predictability. On FI the interval is always the same, so the organism learns to wait and then accelerate. On VI the interval is different every time, so waiting is never safe and the scallop disappears.^[1]

Why VI is the workhorse of choice experiments

VI schedules appear in a large share of the operant literature because they make such a good baseline. The rate is steady, so any change stands out. The obtained reinforcement rate is nearly independent of the response rate, so an experimenter who programs 60 reinforcers an hour gets about 60 whatever the animal does. And the schedule tolerates interruption: a reinforcer that becomes available while the animal is doing something else is still there when it comes back.^[4][6]

That last property made the modern study of choice possible. In 1961 Richard Herrnstein gave pigeons two keys, each paying on its own VI schedule, a concurrent VI VI schedule, and varied how the total reinforcement was divided between them. Because a reinforcer set up on the unattended key waits to be collected, a bird could work mostly on the richer key and still profit by visiting the other now and then. The result was the matching law: the proportion of pecks on a key equalled the proportion of reinforcers it delivered.^[10] Concurrent VI VI remains the standard procedure for studying choice.^[2]

Ratio schedules cannot do this job. On a concurrent VR VR schedule every response on the poorer key is one that could have advanced the count on the richer one, and pigeons settle on the richer alternative almost exclusively, which leaves little to measure.^[11] Interval schedules keep both alternatives alive and make the division of behavior the thing under study.

Why behavior trained on a VI schedule is so persistent

Behavior maintained on a VI schedule is hard to disrupt. In extinction it keeps going long after continuously reinforced behavior has stopped, the partial reinforcement extinction effect, and the reason is plain from the animal's side: on VI, long unreinforced stretches are normal, so the moment reinforcement is switched off is not a signal that anything has changed.^[2] Skinner made the same point about everyday variable schedules: they build persistence because they never announce that reinforcement has ended.^[7]

John Nevin turned this into a general theory, with VI schedules as the tool. In 1974 he trained pigeons on multiple schedules, two VI components alternating, each with its own signal and its own rate of reinforcement, and then disrupted responding in both at once by presenting free food between components or by extinction. Responding in the richer component fell less, in proportion to its baseline, than responding in the leaner one.^[12] Resistance to change, he argued, is the proper measure of a behavior's strength.

Nevin and Grace's 2000 synthesis, behavioral momentum theory, made the analogy explicit: response rate is like velocity and is governed by the response–reinforcer contingency, while resistance to change is like mass and is governed by the stimulus–reinforcer relation, that is, by how much reinforcement the situation has delivered, whatever response earned it. VI schedules were essential because they let the experimenter set the reinforcement rate without it being hostage to the animal's response rate.^[13] The lesson cuts both ways. Praise on a VI schedule builds classroom behavior that survives a bad day; a problem behavior that has paid off unpredictably in a rich context will survive a good deal of treatment. Momentum and resistance to extinction ›

Variable interval schedules in everyday life

Pure VI schedules are rare outside the laboratory, but the structure is everywhere: something becomes available at unpredictable times, and only the first check after it does is rewarded.

Two rows deserve a note. Fishing is the textbook example of a variable ratio: each cast is a response, and the fish arrive after an unpredictable number of casts. A line left in the water and checked from time to time is a variable interval: the bite comes on the fish's clock, and the angler's responses only collect what time has set up. The manager's walk-through is a VI with a limited hold, which is why it maintains steady work rather than the burst-then-slump of a scheduled inspection.^[3] Skinner observed that much everyday behavior is maintained on intermittent schedules that nobody designed, and that its persistence follows from the schedule rather than from anything in the person.^[7]

How to use a variable interval schedule

Interval schedules are the easiest intermittent schedules to run in a classroom, a home, or a workplace, because they need a timer rather than a count. The teacher does not have to track how many problems each child has finished, only whether the child is working when the timer goes off. Applied behavior analysts use VI to maintain established behavior at a steady rate and to thin reinforcement without the pausing of fixed schedules.^[3]

1. Establish the behavior first. A VI schedule maintains behavior; it does not build it. Start with continuous reinforcement until the behavior is reliable, then thin.
2. Pick an average and write out the intervals. For VI 5 min of praise, list intervals that average five minutes (1, 3, 4, 6, 7, and 9, say) and use them in shuffled order. The learner must not be able to predict the next check.
3. Reinforce the first target response after each interval. When the interval ends, wait for the next instance of the behavior, the child returning to the worksheet or the dog lying quietly, and reinforce that, not whatever happens to be going on when the timer sounds. For a check-in style, add a short limited hold.
4. Thin gradually. Move from VI 1 min to VI 2 min to VI 5 min as the behavior holds up. If the rate drops, go back a step; because VI behavior is steady, a drop is easy to spot.
5. Hand the behavior to natural reinforcers. A VI of praise is a bridge to behavior that continues because the work itself, the peers, or the finished product reinforce it.

Pop quizzes and scheduled tests

The classic classroom application is testing. A midterm on a known date is, loosely, a fixed interval, and it produces the scallop of cramming. Unannounced quizzes make the interval variable: because a quiz could come at any class, the only study pattern that pays is a steady one. The analogy is loose, since a quiz reinforces studying done days earlier and grades are only one consequence of studying, but the direction of the prediction follows from the schedules.

Common mistakes and misconceptions

• Confusing VI with VR. Both are unpredictable, but VR pays per response and VI pays per unit of time. If doing more of the behavior brings the reinforcer sooner, it is a ratio schedule. Slot machines and casting a lure are VR; checking messages and checking a set line are VI.
• Confusing VI with VT. On a variable time (VT) schedule the reinforcer arrives after a variable interval whether or not a response occurs. VT is noncontingent reinforcement, the procedure behind Skinner's "superstition" experiment; a VI requires a response.^[3]
• Expecting VI to produce a high rate. It produces a moderate one. For more of a behavior per hour, use a ratio schedule; for steady and durable, use VI.^[4]
• Calling "giving in every so often" a VI. A parent who gives in to a tantrum now and then is not running a VI. Each tantrum is a response, and giving in after an unpredictable number of them is a variable ratio.
• Delivering the reinforcer when the timer sounds instead of after the next response. That is VT, not VI, and it reinforces whatever the learner happens to be doing at that instant.
• Using a predictable "variable" series. Intervals of 2, 4, 6, and 8 minutes in that order are a pattern, and learners find patterns. Shuffle them.
• Starting on VI. A new behavior on a lean VI is not emitted often enough to contact the reinforcer. Build first, then thin.

What the evidence does not show

The cumulative records are from pigeons and rats, and the everyday examples are classifications by structure, not measurements.

Adult humans often do not produce the textbook patterns. People given interval schedules in the laboratory frequently respond at a very high steady rate or a very low one, depending on what they have been told or have concluded about the rule, and instructions can override the programmed contingency for a long time.^[14] In adults, the description of the schedule is itself a variable, and no one should assume that praise on a VI will produce a pigeon's straight line.

The insensitivity of rate to reinforcement rate is bounded. Catania and Reynolds's curve is flat in the middle and upper range, not everywhere. At very lean schedules, response rate falls steeply and behavior can be lost altogether.^[6] Thinning is safe only within limits found by watching the behavior.

Pop quizzes and steady studying is a prediction, not a finding reported here. Studying is maintained by many consequences at once, and the mapping of response and reinforcer is loose. The same goes for messaging: checking is also reinforced by the content itself and by escape from boredom, and nothing on this page shows that making notifications predictable would reduce it.

VI does not make behavior persistent by itself. Nevin's finding is that persistence tracks the rate of reinforcement in a context. VI was the instrument, not the cause; a lean VI in a lean context produces behavior that is easy to disrupt.^[13]

Key takeaways

• A variable interval schedule reinforces the first response after an unpredictable interval that averages a set value. Responses before the interval ends earn nothing, and responding faster does not shorten the wait.
• VI produces a moderate, very steady rate with no post-reinforcement pause and no scallop, because time since the last reinforcer predicts nothing and speed buys nothing. Laboratory VI schedules use the Fleshler–Hoffman progression to keep the probability of reinforcement constant from moment to moment.
• Response rate on VI rises with reinforcement rate and then flattens, which is why VI behavior is stable across a range of reinforcement rates and why Herrnstein could fit the hyperbola of the matching law to VI data.
• VI is the workhorse of the laboratory because its reinforcement rate is nearly independent of response rate and its reinforcers wait to be collected. Concurrent VI VI produced the matching law, and multiple VI schedules produced behavioral momentum theory.
• VR pays per response and VI pays per unit of time: slot machines are VR, while checking messages and a set fishing line are VI. To use VI, build the behavior first, shuffle the intervals, reinforce the first response after each one, and thin gradually.

Check yourself

A teacher sets a timer to go off at unpredictable times averaging five minutes and, when it sounds, praises whichever students are working at that instant. Is this a variable interval schedule of praise for working?

Nearly. On a true VI the first working response after the interval ends would be reinforced whenever it occurred; here praise is available only at the moment the timer sounds, so it is a VI with a very short limited hold, a momentary check. It still maintains steady work, but a student who looks up at the wrong instant misses the reinforcer, and an off-task student who glances at the worksheet at the right instant may be praised. To make it a VI, wait after the timer for the next instance of working and praise that.

A slot-machine player and a person refreshing an inbox are both being rewarded unpredictably. Which is on a variable ratio and which on a variable interval, and what pattern would you predict for each?

The slot machine pays after an unpredictable number of pulls, so each pull advances the count: variable ratio, and a high, steady rate. The inbox pays only when a message has arrived, and refreshing does not make messages arrive sooner: variable interval, and a moderate, steady rate of checking. Both persist when reinforcement stops; the difference between them is in rate, not persistence.

You switch a dog from a treat every time she lies on her mat to a treat for the first lie-down after intervals averaging three minutes. Within a day she has stopped going to the mat. What went wrong?

You thinned too far too fast. A jump from continuous reinforcement to VI 3 min means long stretches of unreinforced behavior before the dog has learned that the mat still pays, so the behavior never contacted the new schedule. Go back to continuous reinforcement, then thin in steps, VI 20 s, then VI 45 s, then VI 90 s, watching the rate at each step and backing up if it falls.

Want more? The 20-question quiz covers every page on the site with instant explanations.