Psychology Learning Resources
Murray Sidman and Stimulus Equivalence

Concept Definition: Equivalence Test

Important characteristics of an equivalence test:

  • An untrained relation between two physically dissimilar stimuli (A and C).
  • Based on the properties of (1) reversible order and (2) when two ordered stimulus pairs (AB and BC) share a common element (B), such that the second element of the first pair is the first element of the second pair, this determines a third ordered pair (AC).
  • Training and testing occurs in a match-to-sample paradigm.
  • The learner is taught two prerequisite relations, both sharing a common stimulus; that stimulus functions as the comparison in the first relation (AB) and as the sample in the second relation (BC).
  • A learner is said to have demonstrated stimulus equivalence when he or she reliably matches the sample stimulus from the first trained relation to the comparison stimulus from the second trained relation (CA).
  • Rationale is that performance indicative of a CA relation encompasses both symmetry and transitivity (with reflexivity assumed). Specifically, the combination of the AB and BC relations yields the AC relation via transitivity, and its symmetrical counterpart is the CA relation.
  • Summarized by the equation If A = B and B = C, then C = A.

Illustrative Example/Nonexample Pair

Nonexample

A young child, Lois, is learning how to read. On some learning trials, her teacher first says the name of an object (e.g., "radio"), and then he lays three picture cards on the table. Lois is told to choose the picture (e.g., radio illustration) that goes with the spoken word. On other learning trials, her teacher first shows her one of the picture cards and then he puts three word cards on the table. Lois is told to choose the printed word (e.g., radio) that goes with the picture. All correct responses on these learning trials are praised by her teacher. Later, after the first two tasks are mastered, Lois is tested on another task. Her teacher shows her one of the word cards (e.g., radio illustration) and then he reads three names out loud; Lois is told to choose the name that goes with the word card (e.g., "correct" choice would be teacher saying "radio"). Lois performs accurately on about 33% of the test trials, even though her teacher did not prompt or praise her correct answers.

Example

A young child, Lois, is learning how to read. On some learning trials, her teacher first says the name of an object (e.g., "radio"), and then he lays three picture cards on the table. Lois is told to choose the picture (e.g., radio illustration) that goes with the spoken word. On other learning trials, her teacher first shows her one of the picture cards and then he puts three word cards on the table. Lois is told to choose the printed word (e.g., radio) that goes with the picture. All correct responses on these learning trials are praised by her teacher. Later, after the first two tasks are mastered, Lois is tested on another task. Her teacher shows her one of the word cards (e.g., radio) and then he reads three names out loud; Lois is told to choose the spoken word that goes with the printed word (e.g., "correct" choice would be teacher saying "radio"). Lois performs perfectly on this third task, even though her teacher did not prompt or praise her correct answers.

Analysis

The first item is not an example of stimulus equivalence. As noted above, Lois was taught a AB relation, A being the spoken word (e.g., "radio") and B being the picture (e.g., radio illustration). She was also taught a BC relation, B being the picture (e.g., radio illustration) and C being the printed word (e.g., radio). On the test, Lois sometimes matched the sample stimulus from the first trained relation (e.g., "radio") to the comparison stimulus from the second trained relation. This test assesses the CA relation, an indicator of stimulus equivalence. However, because Lois was unable to do no better than chance, stimulus equivalence did not occur. This could be due to the absence of any one or more of the defining properties of equivalence: reflexivity, symmetry, and transitivity.

The second item is an example of stimulus equivalence. The rationale is the same as above, except that for this item Lois' test performance was perfectly consistent with the CA relation. Here, we assume that this test simultaneously evaluates both transitivity (AC) and symmetry (CA) and that Lois is capable of demonstrating reflexivity.