Innovative Learning

Stimulus Sampling Theory (William Estes)

Stimulus sampling theory (SST), first proposed by Estes in 1950, was an attempt to develop a statistical explanation for learning phenomena. The theory suggested that a particular stimulus-response association is learned on a single trial; however, the overall learning process is a continuous one consisting of the accumulation of discrete S-R pairings. On any given learning trial, a number of different responses can be made but only the portion that are effective (i.e., rewarded) form associations. Thus, learned responses are a sample of all possible stimulus elements experienced. Variations (random or systematic) in stimulus elements are due to environmental factors or changes in the organism.

A key feature of SST was the probability of a certain stimulus occurring in any trial and of being paired with a given response. SST resulted in many forms of mathematical models, principally linear equations, that predicted learning curves. Indeed, SST was able to account for a wide variety of learning paradigms including: free recall, paired-associates, stimulus generalization, concept identification, preferential choice, and operant conditioning. SST also formed the basis for mathematical models of memory (e.g., Norman, 1970) and instruction (e.g., Atkinson).


Most of the research on SST was conducted using probability or verbal learning experiments, limiting its application to other types of learning. Furthermore, SST did not really take into account cognitive strategies used by participants in these experiments (such as hypothesis testing or the "gamblers fallacy") which could affect the results.


The SST explanation of forgetting (as well as spontaneous recovery) is as follows. Over time, different stimulus elements become available or unavailable for sampling due to external or internal variations. Hence, some of the stimuli that have been conditioned in S-R pairs (i.e., memory traces) may not be available at a given time we wish to make use of the pairing. On the other hand, something we have temporarily forgetten may be remembered when the relevant stimuli happen to be included in the sample. The stronger the memory (i.e., the more pairings created), the higher the likelihood that relevant stimuli are included in the current sampling.


  1. While learning of a particular instance is all or none, the overall learning process is gradual and cumulative.
  2. Fluctuations in environmental and internal factors will cause variability in learning progress.


Estes, W.K. (1950). Toward a statistical theory of learning. Psychological Review, 57, 94-107.

Estes, W.K. (1970). Learning Theory and Mental Development. New York: Academic Press.

Norman, D. (1970). Models of Memory. New York: Academic Press.

Niemark, E.D. & Estes, W.K. (1967). Stimulus Sampling Theory. San Francisco: Holden-Day.