An Introduction to
THEORIES of LEARNING
Ninth Edition
CHAPTER
9
William Kaye Estes
An Introduction to Theories of Learning, Ninth Edition
Matthew H. Olson | B. R. Hergenhahn
Copyright © 2014 by Pearson Education, Inc.
All Rights Reserved
William Kaye Estes (1919—2011)
An Introduction to Theories of Learning, Ninth Edition
Matthew H. Olson | B. R. Hergenhahn
Copyright © 2014 by Pearson Education, Inc.
All Rights Reserved
Stimulus Sampling Theory (SST)
• Statistical learning theory differs from
other theories.
• An attempt to describe the
“composition” of learning, but it does
not provide tools for the classroom or
for behavior therapy.
An Introduction to Theories of Learning, Ninth Edition
Matthew H. Olson | B. R. Hergenhahn
Copyright © 2014 by Pearson Education, Inc.
All Rights Reserved
Major Theoretical Concepts
• The learning situation involves a large
but finite number of stimulus elements
called S.
• Includes experimental events, such as
a light, a lever…
• Also includes changeable or transitory
stimuli, such as extraneous noises
inside the room, and the condition of
the experimental participant.
An Introduction to Theories of Learning, Ninth Edition
Matthew H. Olson | B. R. Hergenhahn
Copyright © 2014 by Pearson Education, Inc.
All Rights Reserved
Major Theoretical Concepts
• All responses are in one of two
categories.
• Correct responses are labeled A1
• Incorrect responses are labeled A2
An Introduction to Theories of Learning, Ninth Edition
Matthew H. Olson | B. R. Hergenhahn
Copyright © 2014 by Pearson Education, Inc.
All Rights Reserved
Major Theoretical Concepts
• Elements in the environment (S) are
attached either to correct responses
(A1) or to incorrect responses (A2)
An Introduction to Theories of Learning, Ninth Edition
Matthew H. Olson | B. R. Hergenhahn
Copyright © 2014 by Pearson Education, Inc.
All Rights Reserved
Major Theoretical Concepts
• The learner experiences or samples
only a small proportion of the stimuli
available on any learning trial.
• The size of the sample is constant
throughout the experiment.
An Introduction to Theories of Learning, Ninth Edition
Matthew H. Olson | B. R. Hergenhahn
Copyright © 2014 by Pearson Education, Inc.
All Rights Reserved
Major Theoretical Concepts
• The constant proportion of S
experienced at the beginning of each
learning trial is designated by Θ
(theta).
• After each trial, the elements in Θ are
returned to S.
An Introduction to Theories of Learning, Ninth Edition
Matthew H. Olson | B. R. Hergenhahn
Copyright © 2014 by Pearson Education, Inc.
All Rights Reserved
Major Theoretical Concepts
• A learning trial ends when a response
occurs.
• If an A1 response terminates a trial, the
stimulus elements in Θ are conditioned
to the A1 response.
An Introduction to Theories of Learning, Ninth Edition
Matthew H. Olson | B. R. Hergenhahn
Copyright © 2014 by Pearson Education, Inc.
All Rights Reserved
Major Theoretical Concepts
• Elements in Θ are returned to S at the
conclusion of a trial.
• Because Θ sampled at the beginning of
a learning trial is essentially random,
the proportion of elements conditioned
to A1 in S will be reflected in the
elements in Θ at the beginning of every
new trial.
An Introduction to Theories of Learning, Ninth Edition
Matthew H. Olson | B. R. Hergenhahn
Copyright © 2014 by Pearson Education, Inc.
All Rights Reserved
MAJOR THEORETICAL CONCEPTS
An Introduction to Theories of Learning, Ninth Edition
Matthew H. Olson | B. R. Hergenhahn
Copyright © 2014 by Pearson Education, Inc.
All Rights Reserved
Major Theoretical Concepts
• The probability of response A1 on any
trial n (Pn) is equal to the proportion of
elements conditioned to A1 on that trial
(pn).
• Pn =pn
An Introduction to Theories of Learning, Ninth Edition
Matthew H. Olson | B. R. Hergenhahn
Copyright © 2014 by Pearson Education, Inc.
All Rights Reserved
Major Theoretical Concepts
• All elements are either A1 elements
(with probability p) or A2 elements
(with probability q). And these
constitute 100 percent of the elements
in the situation.
• p + q = 1.00 and
p = 1.00 – q
An Introduction to Theories of Learning, Ninth Edition
Matthew H. Olson | B. R. Hergenhahn
Copyright © 2014 by Pearson Education, Inc.
All Rights Reserved
Major Theoretical Concepts
• The A2 elements (with probability q)
must be elements that were not
preconditioned to A1 prior to the first
trial and that were not conditioned to
A1 on any previous trial.
• Therefore
q = (1 - P1) (1 - Θ)n-1
An Introduction to Theories of Learning, Ninth Edition
Matthew H. Olson | B. R. Hergenhahn
Copyright © 2014 by Pearson Education, Inc.
All Rights Reserved
Major Theoretical Concepts
• Substituting for q in p = 1 – q, for the
nth trial, we get the SST equation:
• pn = 1 - (1 - P1) (1 - Θ)n-1
• This is the essence of Stimulus
Sampling Theory.
An Introduction to Theories of Learning, Ninth Edition
Matthew H. Olson | B. R. Hergenhahn
Copyright © 2014 by Pearson Education, Inc.
All Rights Reserved
SST Equation Produces
• The negatively accelerated learning
curve
An Introduction to Theories of Learning, Ninth Edition
Matthew H. Olson | B. R. Hergenhahn
Copyright © 2014 by Pearson Education, Inc.
All Rights Reserved
SST equation produces the negatively accelerated learning curve.
An Introduction to Theories of Learning, Ninth Edition
Matthew H. Olson | B. R. Hergenhahn
Copyright © 2014 by Pearson Education, Inc.
All Rights Reserved
Probability Matching
• For example, left light comes on 75%
of the time while right light comes on
25% of the time.
• Experimental participant has to guess
which light will come next.
• Participant guesses 75% left/25%
right.
An Introduction to Theories of Learning, Ninth Edition
Matthew H. Olson | B. R. Hergenhahn
Copyright © 2014 by Pearson Education, Inc.
All Rights Reserved
Probability Matching
• Note that matching is irrational. If
participant wanted to do well, guess left
100% of the time.
• According to SST, matching occurs
because
 Pn= π - (π - P1) (1 - Θ)n-1
• Where π = probability of the event– for
example 75% left.
An Introduction to Theories of Learning, Ninth Edition
Matthew H. Olson | B. R. Hergenhahn
Copyright © 2014 by Pearson Education, Inc.
All Rights Reserved
Estes' Markov Model of Learning
• Markov process: Characterized by an
abrupt, step-wise change in response
probabilities rather than a relatively
slow, gradual change from trial to trial.
• Contradicts Thorndike and Hull
An Introduction to Theories of Learning, Ninth Edition
Matthew H. Olson | B. R. Hergenhahn
Copyright © 2014 by Pearson Education, Inc.
All Rights Reserved
Why a Negatively Accelerated
Learning Curve?
• After correct response, the person
would be correct on 100 percent of the
subsequent trials, but people attained
the correct response at different times.
• The negatively accelerated learning
curve results from averaging.
An Introduction to Theories of Learning, Ninth Edition
Matthew H. Olson | B. R. Hergenhahn
Copyright © 2014 by Pearson Education, Inc.
All Rights Reserved
Why a Negatively Accelerated Learning Curve?
An Introduction to Theories of Learning, Ninth Edition
Matthew H. Olson | B. R. Hergenhahn
Copyright © 2014 by Pearson Education, Inc.
All Rights Reserved
The Results from Averaging
An Introduction to Theories of Learning, Ninth Edition
Matthew H. Olson | B. R. Hergenhahn
Copyright © 2014 by Pearson Education, Inc.
All Rights Reserved
The Cognitive Array Model—
Classifying and Categorizing
• Examining a creature, noting that it has
feathers, that it flies, and that it lays
eggs, and then calling it “bird.”
• Physicians gather data and diagnose a
common cold, rather than pneumonia,
An Introduction to Theories of Learning, Ninth Edition
Matthew H. Olson | B. R. Hergenhahn
Copyright © 2014 by Pearson Education, Inc.
All Rights Reserved
Array Model versus SST
• SST focuses on stimulus-response
associations formed in the past and the
way in which those associations were
accumulated.
• Array model focuses on the
classification of events that are
encountered in the present or that will
be encountered in the future.
An Introduction to Theories of Learning, Ninth Edition
Matthew H. Olson | B. R. Hergenhahn
Copyright © 2014 by Pearson Education, Inc.
All Rights Reserved
SST Assumes Additive Stimulus Relationships
An Introduction to Theories of Learning, Ninth Edition
Matthew H. Olson | B. R. Hergenhahn
Copyright © 2014 by Pearson Education, Inc.
All Rights Reserved
The Array Model Assumes
Multiplicative Stimulus Relationships
• A factor called s, the similarity
coefficient, describes the degree of
similarity between pairs of stimulus
attributes.
• Apply a similarity coefficient of unity
(1.00) if the features match and a
coefficient with some smaller value s, if
they differ.
An Introduction to Theories of Learning, Ninth Edition
Matthew H. Olson | B. R. Hergenhahn
Copyright © 2014 by Pearson Education, Inc.
All Rights Reserved
Items within a Category Are Similar to Each Other
An Introduction to Theories of Learning, Ninth Edition
Matthew H. Olson | B. R. Hergenhahn
Copyright © 2014 by Pearson Education, Inc.
All Rights Reserved
Stimulus Items Represent a Whole Category: A items with Category A
An Introduction to Theories of Learning, Ninth Edition
Matthew H. Olson | B. R. Hergenhahn
Copyright © 2014 by Pearson Education, Inc.
All Rights Reserved
Stimulus Items Represent a Whole Category: A items with Category B
An Introduction to Theories of Learning, Ninth Edition
Matthew H. Olson | B. R. Hergenhahn
Copyright © 2014 by Pearson Education, Inc.
All Rights Reserved
How Do We Recognize 2A as Part
of the A Category?
• The probability of correctly recognizing
stimulus 2A as a member of A is
(1+s)
__________
(1+s) +(s2 +s3)
An Introduction to Theories of Learning, Ninth Edition
Matthew H. Olson | B. R. Hergenhahn
Copyright © 2014 by Pearson Education, Inc.
All Rights Reserved
Estes on Reinforcement
• Following Guthrie, Estes believed that
reinforcement prevented the unlearning
of an association.
• Estes’s more recent view of the role of
reinforcement stressed the
information that it provided to the
organism.
An Introduction to Theories of Learning, Ninth Edition
Matthew H. Olson | B. R. Hergenhahn
Copyright © 2014 by Pearson Education, Inc.
All Rights Reserved