Schedules of reinforcement: the four schedules, in Ferster and Skinner's own definitions

A schedule of reinforcement is the rule that decides which responses are reinforced. Under continuous reinforcement every response that meets the requirement is reinforced; under an intermittent schedule only some responses are, either after a number of responses have been made (a ratio schedule) or after a stretch of time has passed and a response is then made (an interval schedule). The number or the time can be fixed, or it can vary around an average.

Five points this article keeps returning to:

• The four intermittent schedules are built from two pairs of words: ratio or interval, fixed or variable.
• On an interval schedule, the passage of time alone earns nothing. The first response after the interval is what gets reinforced.
• Ferster and Skinner's shorthand describes the arrangement, not the reinforcer: FR 100 means the hundredth response, FI 5 the first response five minutes or more after the last one reinforced.
• Most exam scenarios can be classified with two questions: count or clock? fixed or variable?
• The definitions and the notation come from Schedules of Reinforcement (1957); the response patterns textbooks add on top are later summaries.

If you want the wider picture first, our article on classical and operant conditioning sets out where operant conditioning sits and how it differs from Pavlov's kind.

Continuous reinforcement and extinction are the two non-intermittent cases

In Ferster and Skinner's plan of analysis, the two non-intermittent schedules come first: continuous reinforcement (crf), "in which every response emitted is reinforced", and extinction (ext), "in which no responses are reinforced". The rest of the book is built on not reinforcing every response.

Continuous reinforcement is the arrangement for building a new behaviour, because the link between the response and its consequence is immediate and unambiguous. OpenStax's Psychology 2e calls it the quickest way to teach one, and the arrangement to use until the behaviour is established. Extinction is the schedule that reinforces nothing at all, which is why the 1957 book lists it among the schedules rather than treating it as the absence of one.

Schedules are a separate question from the four consequences of behaviour. Reinforcement and punishment describe what a consequence does to the behaviour; a schedule describes when a consequence follows a response.

The four schedules of reinforcement, in Ferster and Skinner's own words

The four intermittent schedules are fixed ratio (FR), variable ratio (VR), fixed interval (FI) and variable interval (VI), and their names come from two independent questions. What is counted before reinforcement can be earned: responses (a ratio) or elapsed time (an interval)? And is the amount constant or does it vary around an average — fixed or variable?

Ferster and Skinner define each in a sentence or two, and the Skinner Foundation's reprint has the book's full text. The fixed-interval definition is the one to read slowly:

The words behind the abbreviations are the definitions. In a fixed-ratio schedule, "a response is reinforced upon completion of a fixed number of responses counted from the preceding reinforcement" — under FR 100, the hundredth response after the last reinforcer — and the word ratio refers to the ratio of responses to reinforcements. A variable-ratio schedule keeps the arrangement and draws the ratios from a random series with a given mean: VR 100 averages one reinforcer per hundred responses, with individual runs longer or shorter.

The two interval schedules read the same way with time in place of a counted number of responses. A variable-interval schedule reinforces the first response after intervals drawn from a random series with a given mean, as in VI 3, an average of three minutes. The response requirement never goes away, and that is where the next section comes in.

The patterns in the last column are the textbook summaries, not part of the definitions: they describe what cumulative records tend to look like under each arrangement. OpenStax's Psychology 2e, for instance, gives the fixed-interval pattern as a moderate response rate with significant pauses after reinforcement. The book itself describes fifteen schedules in all; the remaining ones are compound arrangements, such as alternative, conjunctive and interlocking schedules, that combine two or more of the basic four and belong to a later course.

On an interval schedule, time alone earns nothing

On an interval schedule, the clock does not deliver the reinforcer; it only makes one available. FI 5 is not a reward every five minutes. It is the first response occurring five minutes or more after the preceding reinforcement that is reinforced, and if nothing is emitted once the interval has passed, nothing is reinforced.

The same clause sits in the variable-interval definition, with the intervals varying and the response requirement unchanged. An interval schedule is never a delivery on a timer. It is a response that is finally worth making, after a wait.

The shorthand is where the mistake comes from: "every five minutes" is a shorter way to say fixed interval than the definition is, and it leaves out the half that decides exam questions. A two-question test puts it back:

1. 1.Count or clock? If reinforcement depends on a number of responses, the schedule is a ratio. If it depends on elapsed time, it is an interval — and a response is still required.
2. 2.Fixed or variable? If the number or the time is the same every time, it is fixed. If it varies around an average, it is variable.

Two answers put a scenario in one of the four boxes, and the reasoning follows from the pair of words rather than from a memorised example. One more connection is worth making here: a schedule is a relation between responses and outcomes, and learned helplessness is the other side of that relation — what happens to behaviour when experience suggests that responses do not control the outcome.

Classifying exam scenarios

The two questions classify most scenarios on sight, and the table below works through the examples textbook writers keep reaching for. The middle column is the answer a multiple-choice question wants; the right column is the reasoning that gets you there.

Why intermittent reinforcement resists extinction

When reinforcement stops, an intermittent schedule makes the behaviour harder to lose than continuous reinforcement does. The Dorsch Lexikon der Psychologie states the finding in one line: if reinforcement is withheld, intermittent schedules prove more resistant to extinction than other schedules.

OpenStax's textbook ranks the four: "Among the reinforcement schedules, variable ratio is the most productive and the most resistant to extinction", and names fixed interval the least productive and the easiest to extinguish. Treat that as a textbook generalisation rather than a measured law. What the sources state firmly is that extinction is slower after intermittent reinforcement than after continuous reinforcement, and that under a variable ratio the point of extinction "comes very slowly".

Where the everyday examples go wrong

Textbooks and other educational material often describe certain everyday patterns of behaviour as fixed-interval scalloping, a term borrowed from the shape a laboratory record takes as the end of an interval approaches. Poppen (1982) called that a misleading use of the term: it implies that the behaviour "is accounted for by the schedule, when, in fact, many other variables are operating", and his paper works through eleven of them. The point is not that schedules never shape everyday behaviour; it is that naming the everyday shape after the laboratory pattern claims an explanation the evidence does not carry, and turns attention away from the variables that provide the more adequate account.

Where the schedules of reinforcement came from

The schedules began with a supply problem. Skinner's own account, A Case History in Scientific Method (1956), describes running short of the food pellets he made himself on a Saturday afternoon, and asking why he should have to reinforce every bar press; the reprint's foreword retells the episode. Instead of a pellet after every response, he arranged a pellet after the first response that followed a minute without one — the first fixed-interval schedule, FI 1 — and reported being amazed that the number of responses increased. Fixed-ratio schedules and the rest of the family grew out of the long sessions that followed.

Ferster and Skinner's book reports fifteen schedules, more than 900 figures, and, in the foreword's summary, over 70,000 recorded hours of experiment and approximately one-quarter billion responses. The four names that end up on an exam are the survivors of a much larger programme.

The five abbreviations as one list

The five abbreviations differ by one word each, and exam questions ask for the right one in a fresh scenario. In Psychology World you can save CRF, FR, VR, FI and VI to one list and drill them as flashcards, as multiple-choice questions once the list holds four or more words, or by typing the answer out, which accepts no half-remembered answer. Our guide to memorising psychology terms covers why near-synonyms need the strictest mode, and what each study mode does is set out on the home page.