A Mathematical Model for Type II Instrumental Discriminations
Abstract
Using the same assumptions found in the Trabasso & Bower (1968) mathematical model for type I and relevant redundant cue (RRC) discriminations, a mathematical model was proposed for type II discriminations. A type I discrimination has one relevant cue. An RRC discrimination has two relevant cues, either of which could be used, independently, to solve the discrimination problem. A type II discrimination has two relevant cues, both of which must be used before the discrimination problem can be solved.
In the Trabasso & Bower (1968) model, the difficulty of a type I discrimination problem was defined in terms of the salience of the relevant cue, where salience was represented as a measure of the probability of S attending to a particular cue in a stimulus complex. The difficulty of an RRC discrimination problem was defined as the sum of the two relevant saliences. Since a type II discrimination requires attention and usage of both relevant cues in the problem, the difficulty of the discrimination problem was assumed to be a multiplicative function of the two relevant cue saliences.
This hypothesis was tested and supported. The mathematical model could predict the mean errors for a type II discrimination. However, the experiment also produced data which conflicted with Trabasso & Bower's (1968) assumptions. For example, Ss were capable of learning a new solution to a discrimination problem, even though a previously learned solution was still correct. It was concluded that changes in the underlying assumptions of the Trabasso & Bower (1968) model may necessitate a change in the mathematical model itself.
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