Rescorla's Correlation
*Experiments
* Note that Rescorla referred to his experiments as
contingency experiments, however since a true contingency
(cause-effect relationship) does not exist between the CS &
UCS in classical conditioning experiments, they are more
properly described as correlation experiments.
CS-UCS relations (correlation)
Contiguity is necessary but NOT sufficient
for classical conditioning to occur
 There must also be a consistent relationship
or correlation between the CS and the UCS.
 To experience a reliable correlation between
the CS and the UCS the subjects must be
exposed to numerous instances of the CS
and UCS, thus many trials are typically
necessary for conditioning.

Types of correlations between
the CS and the UCS - #1

CS
UCS
If the CS is a reliable predictor of the
presence of the UCS, then the CS and UCS
are positively correlated.
Types of correlations between
the CS and the UCS - #2

CS
UCS
If the CS is an unreliable predictor of the
UCS, then the CS and UCS are not
correlated.
Types of correlations between
the CS and the UCS -#3

CS
UCS
If the CS reliably predicts the absence of the
UCS, then the CS and UCS are negatively
correlated.
Rescorla’s Equations
It is inconvenient to draw time lines for
experiments with large number of trials.
 We will use equations which describe the
type of correlation that a subject
experiences in a classical conditioning
experiment.

Rescorla’s Equation describing a
positive correlation between the
CS & UCS
p (UCS / CS) > p (UCS / No CS)









the probability (p)
of a UCS
given that (/)
a CS is present
*** is GREATER THAN***
the probability (p)
of a UCS
given that (/)
NO CS is present
Rescorla’s Equation describing a
positive correlation between the
CS & UCS
p (UCS / CS) > p (UCS / No CS)
The left side of the equation simply notes the
percentage of CSs that are temporally
contiguous (paired) with a UCS.
•If p = 1.0 then 100% of CSs are paired with UCSs
•If p = 0.5 then 50% CSs are paired with UCSs and 50%
of CSs are presented alone.
•If p = 0.0 then all the CSs are presented alone, there are
no CS-UCS pairings.
Rescorla’s Equation describing a
positive correlation between the
CS & UCS
p (UCS / CS) > p (UCS / No CS)
The right side of the equation simply notes the percentage
of time intervals without a CS in which a UCS occurs.
•If p = 1.0 then UCSs are presented on 100% of the
time intervals with No CS present.
•If p = 0.5 then UCSs are presented on 50% of the time
intervals with No CS present.
•If p = 0.0 then UCSs are never presented when No CS
is present.
Rescorla’s Equation describing
positive correlations between
the CS & UCS
p (UCS / CS) p (UCS / No CS)
1.0
>
0
.5
>
0
When these correlations are used in
classical conditioning experiments
the subjects show evidence of
.4
>
.1
excitatory conditioning
.3
>
.2
Notice that the percentage of contiguous CS-UCS pairings
decrease from the top example to the bottom example
Rescorla’s Equation describing no
correlation between the CS & UCS
p (UCS / CS) = p (UCS / No CS)
the
probability (p)

of a UCS

given that (/)

a CS is present

*** is EQUAL to ***
the probability (p)

of a UCS

given that

NO CS is present
Rescorla’s Equation describing
no correlation between
the CS & UCS
p (UCS / CS) p (UCS / No CS)
.8
=
.8
.5
=
.5
.4
=
.4
.3
=
.3
.2
=
.2
When these correlations are used in classical
conditioning experiments the subjects show
no evidence of conditioning
Rescorla’s Equation describing
negative correlations between
the CS & UCS
p (UCS / CS) < p (UCS / No CS)
p (UCS / CS) p (UCS / No CS)
0
<
.5
.2
<
.5
.3
<
.5
.4
<
.5
When these correlations are used in
classical conditioning experiments
the subjects show evidence of
inhibitory conditioning
Calculate Rescorla’s equation
using the time lines below
CS
UCS
First take notice that time line is divided into 12 equal
Next we will calculate the left side of the equation
intervals
ofare
time.
There
time intervals
with
a CS
A UCS 4occurs
in all 4 CS
intervals
Therefore the probability of a UCS
given the presence of a CS is 1.0
p (UCS / CS) ? p (UCS / No CS)
4 / 4
= 1.0
Calculate Rescorla’s equation
using the time lines below
CS
UCS
Next we will calculate the right side of the equation
There
are 8occurs
time intervals
withNo-CS
No CSintervals
A UCS
in 0 of these
Therefore the probability of a UCS
given the absence of a CS is 0
p (UCS / CS) ?> p (UCS / No CS)
4 / 4
0 / 8
= 1.0
= 0.0
CS
Calculate Rescorla’s equation
using the time lines below
UCS
First take notice that time line is divided into 12 equal
Next we will calculate the left side of the equation
intervals
ofare
time.
There
time intervals
a CS
A UCS 4occurs
in only 1with
of the
CS intervals
Therefore the probability of a UCS
given the presence of a CS is 0.25
p (UCS / CS) ? p (UCS / No CS)
1 / 4
= 0.25
CS
Calculate Rescorla’s equation
using the time lines below
UCS
Next we will calculate the right side of the equation
There
are 8occurs
time intervals
withNo-CS
No CSintervals
A UCS
in 2 of these
Therefore the probability of a UCS
given the absence of a CS is 0.25
p (UCS / CS) ?= p (UCS / No CS)
1 / 4
2 / 8
= 0.25
= 0.25
Calculate Rescorla’s equation
using the time lines below
CS
UCS
First take notice that time line is divided into 12 equal
Next we will calculate the left side of the equation
intervals
ofare
time.
There
time intervals
with
CSintervals
A UCS 4occurs
in none of
theaCS
Therefore the probability of a UCS
given the presence of a CS is 0.0
p (UCS / CS) ? p (UCS / No CS)
0 / 4
= 0.0
Calculate Rescorla’s equation
using the time lines below
CS
UCS
Next we will calculate the right side of the equation
There
are 8occurs
time intervals
withNo-CS
No CSintervals
A UCS
in 3 of these
Therefore the probability of a UCS
given the absence of a CS is 0.38
p (UCS / CS) ?< p (UCS / No CS)
0 / 4
3 / 8
= 0.0
= 0.38
Summary
When subjects experience CSs and UCSs
that are positively correlated they acquire a
conditioned response to the CS; this is
called excitatory conditioning.
 When subjects experience CSs and UCSs
that are negatively correlated responses are
inhibited (not performed) when the CS is present;
this is called inhibitory conditioning or
conditioned inhibition.

Summary continued
When
subjects experience CSs and UCSs that
are NOT correlated they show no evidence of
conditioning.
Vocabulary
positive correlation
 negative correlation
 excitatory conditioning
 inhibitory conditioning or conditioned
inhibition

Using Rescorla’s equations to show differences in
conditioning despite fixed contiguity between groups
p (UCS / CS) p (UCS / No CS)
.4
.4
.4
>
>
>
=
0
.1
.2
.4
Suppression Ratio
.4
0.5
0.4
0.3
0.2
0.1
0
0
0.1
0.2
0.4
p (UCS | no CS)
CS - Alone Trials after Acquisition
Contiguity as necessary but not sufficient

The results of the previous experiment, as
well as the results of the blocking studies
and other experiments, suggest that
although contiguity is necessary for
classical conditioning to occur it is not
enough (not sufficient), the CS and the UCS
must be correlated either positively or
negatively.
Explanations of Rescorla’s
Correlation Experiments

COGNITIVE BEHAVIORIST: a correlation
is also necessary because the CS must be
predictive or informative.
1. When a CS is positively correlated with a UCS
the subjects learn that the CS predicts the presence
of a UCS.
2. When a CS is negatively correlated with a UCS
the subjects learn that the CS predicts the absence
of a UCS.
This is a highly cognitive explanation of classical
conditioning.
Explanations of Rescorla’s
Correlation Experiments

RADICAL BEHAVIORIST: positive and
negative correlations affect the acquisition of
conditioned responding because several basic,
mechanistic principles are at work. For example,
when several UCSs are presented alone to degrade
the CS-UCS correlation the context becomes
excitatory and blocks conditioning to the CS.