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) l Contiguity is necessary but NOT sufficient for classical conditioning to occur l There must also be a consistent relationship or correlation between the CS and the UCS. l 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 l If the CS is a reliable predictor of the presence of the UCS, then the CS and UCS are positively correlated. CS UCS

Types of correlations between the CS and the UCS - #2 l If the CS is an unreliable predictor of the UCS, then the CS and UCS are not correlated. CS UCS

Types of correlations between the CS and the UCS -#3 l If the CS reliably predicts the absence of the UCS, then the CS and UCS are negatively correlated. CS UCS

Rescorla’s Equations l It is inconvenient to draw time lines for experiments with large number of trials. l 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 l the probability (p) l of a UCS l given that (/) l a CS is present l *** is GREATER THAN*** l the probability (p) l of a UCS l given that (/) l NO CS is present p (UCS / CS) > p (UCS / No CS)

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) When these correlations are used in classical conditioning experiments the subjects show evidence of excitatory conditioning 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) l the probability (p) l of a UCS l given that (/) l a CS is present l *** is EQUAL to *** l the probability (p) l of a UCS l given that l NO CS is present

Rescorla’s Equation describing no correlation between the CS & UCS p (UCS / CS)p (UCS / No CS) 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) 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 intervals of time. Next we will calculate the left side of the equation p (UCS / CS) ? p (UCS / No CS) There are 4 time intervals with a CS / 4 A UCS occurs in all 4 CS intervals 4 = 1.0 Therefore the probability of a UCS given the presence of a CS is 1.0

Calculate Rescorla’s equation using the time lines below CS UCS Next we will calculate the right side of the equation p (UCS / CS) ? p (UCS / No CS) There are 8 time intervals with No CS / 4 A UCS occurs in 0 of these No-CS intervals 4 = 1.0 Therefore the probability of a UCS given the absence of a CS is 0 = 0.0 / 80 >

Calculate Rescorla’s equation using the time lines below First take notice that time line is divided into 12 equal intervals of time. Next we will calculate the left side of the equation p (UCS / CS) ? p (UCS / No CS) There are 4 time intervals with a CS / 4 A UCS occurs in only 1 of the CS intervals 1 = 0.25 Therefore the probability of a UCS given the presence of a CS is 0.25 CS UCS

Calculate Rescorla’s equation using the time lines below Next we will calculate the right side of the equation p (UCS / CS) ? p (UCS / No CS) There are 8 time intervals with No CS / 4 A UCS occurs in 2 of these No-CS intervals 1 = 0.25 Therefore the probability of a UCS given the absence of a CS is 0.25 = 0.25 / 82 = CS UCS

Calculate Rescorla’s equation using the time lines below First take notice that time line is divided into 12 equal intervals of time. Next we will calculate the left side of the equation p (UCS / CS) ? p (UCS / No CS) There are 4 time intervals with a CS / 4 A UCS occurs in none of the CS intervals 0 = 0.0 Therefore the probability of a UCS given the presence of a CS is 0.0 CS UCS

Calculate Rescorla’s equation using the time lines below Next we will calculate the right side of the equation p (UCS / CS) ? p (UCS / No CS) There are 8 time intervals with No CS / 4 A UCS occurs in 3 of these No-CS intervals 0 = 0.0 Therefore the probability of a UCS given the absence of a CS is 0.38 = 0.38 / 83 < CS UCS

Summary l When subjects experience CSs and UCSs that are positively correlated they acquire a conditioned response to the CS; this is called excitatory conditioning. l 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 l When subjects experience CSs and UCSs that are NOT correlated they show no evidence of conditioning.

Vocabulary l positive correlation l negative correlation l excitatory conditioning l 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) CS - Alone Trials after Acquisition

Contiguity as necessary but not sufficient l 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 l 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 l 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.