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Stimulus Sampling Theory (SST) makes use of ideas that we should all be familiar with from our introductory statistics courses.  In particular, the idea of a population and samples randomly selected from the population.  In the case of SST the population is the set of all stimulus elements that MIGHT confront a learner/subject in a learning situation/experiment (including transitory elements like a brief noise or bodily states of the subject).  Estes doesn’t specify what a stimulus element is; he is just assuming that we can divide the learning subject’s perception of its environment into numerous small bits. We might denote the overall population of stimulus elements-- including transitory external and internal stimulus elements-- as S^* and the population of stimulus elements consistently available for an experimental session as S.  S^* includes, therefore, all the elements of S.  It is the overall set of stimulus elements.

            Suppose that you are a cat in a puzzle box on the first trial of day 1 of an experiment.  The set of all sights and sounds and smells, etc. of the puzzle box on that first trial is a sample, s, of S (the set of sights and sounds consistently available in the experiment).  Our text denotes s with the symbol θ.  So, you are experiencing s as you find yourself in that puzzle box for the first time.  If you stumble across the correct response R (the text calls this A₁), then you can escape from the puzzle box.  To Estes that means all the elements of s become connected to the response R.  An important point:  following Guthrie, Estes believes that each element of s becomes connected to R in an All-or-None way.  There is no partial element-response connection.  On trial 2, a different sample of S, say, s’, is observed as the cat is put back in the puzzle box.  If the cat hits upon R again, each element of s’ becomes connected to R.  And so on.  Thereby, increasing the number of elements in S that are connected to R on each trial.  Important to note that at the outset of the experiment none of the elements of S are connected to R.  All elements at the start of the experiment are connected to not-R (the text calls this response A₂).  For mathematical reasons, Estes divided up all possible responses into the correct response (R) and a set of all other responses (not-R).

            The probability of a correct response R at the start of a trial is the percentage of elements in S that are connected to R.  Since the sample s is randomly selected from S, the percentages of S should carry over to that s on average.  If we denote the probability of R with the letter p, then the probability of an incorrect response is 1-p (since there are only two possibilities, R and not-R, the probabilities p and 1-p have to add up to 1).  After n trials the probability of an element not yet being connected to R is (1-p)ⁿ.  Why?  Because in order to not be connected to R after n trials means it would have to be connected to not-R for n trials.  The probability that an element will be connected to R after n trials is 1 minus that quantity or 1-(1-p)ⁿ.  If you plot out the different p’s for different trial numbers (p_n’s) then you get a so-called negatively accelerated learning curve (figure 6-1 in your text) that is the shape of the classic learning curve found by many researchers.  Note that Estes derived the shape of the curve, not by looking at his data and saying this is what the growth of learning must look like, but by mathematically deriving the shape from his theoretical ideas.

            The above explains the course of simple response learning.  But Estes can also explain other common learning phenomena with his theory.  For example, Estes can easily explain extinction. An extinction trial is one where the response that ends the trial is a response other than R--- in other words, a non-R response.  When that happens all the elements of s (from population S) become connected to not-R.  The next extinction trial begins with another sample s’ and ends with a not-R response.  Therefore, all the elements of s’ become connected to not-R.  And so on.  Until response R is extinguished. 

            After extinction, we take the subject back to its home cage and let it hang out for a few days.  When we decide to conduct another experiment, something interesting happens.  The behavior R re-appears.  This is the phenomenon of spontaneous recovery (discovered by Pavlov).  Why does this happen?  Well remember our discussion of the difference between S and S^*.  S is the consistent set of stimulus elements available throughout an experiment.  But, on any particular trial, some of the transitory elements of S^* might get conditioned to R, then they might wander off and not re-appear for the rest of the experiment.  On the next trial other transitory element of S^* might make an appearance and be conditioned to R.  Then not re-appear for the rest of the experiment.  However, after a couple of days away from the lab those elements of S^* might still be connected to R and wander into the set S for this new experiment.  In that case we might witness the spontaneous recovery of R.