Psychology Learning Resources
Murray Sidman and Stimulus Equivalence

Concept Definition: Equivalence Class

Defining characteristic of an equivalence class:

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 spoken. 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 first shows her one of the word cards (e.g., radio); then, he places the three picture cards on the table, and tells Lois to choose the one that goes with it (e.g., "correct" choice would be the radio illustration). Lois performs perfectly on this third task, even though her teacher did not prompt or praise her correct answers. (We'll assume that Laura, given the opportunity, would be able to match all training stimuli to themselves on the basis of their sameness without extra training.)

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 given a number of different test trials. Sometimes her teacher shows her one of the picture cards (e.g., radio illustration) and then he reads three names out loud; Lois is told to choose the spoken word that goes with the picture (e.g., "correct" choice would be teacher saying "radio"). Sometimes her teacher first shows her one of the word cards (e.g., radio), places the three picture cards on the table, and tells Lois to choose the one that goes with it (e.g., "correct" choice would be the radio illustration). And sometimes her teacher first shows her one of the word cards (e.g., radio), places the three picture cards on the table, and tells Lois to choose the one that goes with it (e.g., "correct" choice would be the radio illustration). Lois performs perfectly on all test trials, even though her teacher did not prompt or praise her correct answers. (We'll assume that Laura, given the opportunity, would be able to match all training stimuli to themselves on the basis of their sameness without extra training.)

Analysis

In the first item there is not enough information provided to conclude that an equivalence class has formed. The rationale is as follows. First, because it is assumed that Laura, given the opportunity, would be able to match these training stimuli to themselves on the basis of their sameness without extra training, we are in effect assuming reflexivity.

Second, we note that Lois was taught a AB relation, A being the spoken word (e.g., "radio") and B being the picture (e.g., radio illustration); that is, she learned to match the picture to the spoken word. And, she was taught a BC relation, B being the picture (e.g., radio illustration) and C being the printed word (e.g., radio); that is, she learned to match the printed word to the picture. During testing, she reliably matched the comparison stimulus from the second trained relation (e.g., radio) to the sample stimulus from the first trained relation (e.g., "radio"), an AC relation. Because she was able to do this without training, the AC relation is considered to have emerged as a consequence of learning the AB and BC relations, an indication of transitivity between the A and C stimuli.

Thus, there is evidence of both reflexivity and transitivity in the first item. What about symmetry? We do not know if symmetry exists without testing for it. Will Lois match the spoken word to the picture (BA) and the picture to the printed word (CB)? We cannot assume symmetry even though there is evidence of transitivity (D'Amato, Salmon, Loukas, Tomie, 1985). One of the three defining properties of stimulus equivalence is missing from the first item.

In the second item we can conclude that an equivalence class has formed. As described above, reflexivity and transitivity are both present. Symmetry is also present. Lois was taught a AB relation, A being the spoken word (e.g., "radio") and B being the picture (e.g., radio illustration). In other words, she learned to match the picture to the spoken word. On one test trial type, she performed perfectly in accordance with the reversal of this task, that is, she matched the spoken word to the picture, a BA relation. Because she was able to do this without training, the BA relation is considered to have emerged as a consequence of learning the AB relation, an indication of symmetry between the A and B stimuli. Also, Lois was taught a BC relation, B being the picture (e.g., radio illustration) and C being the printed word (e.g., radio). In other words, she learned to match the printed word to the picture. On another test type, she performed perfectly in accordance with the reversal this task, that is, she matched the picture to the printed word, a CB relation. Because she was able to do this without training, the CB relation is considered to have emerged as a consequence of learning the BC relation, an indication of symmetry between the B and C stimuli.

So, only in the second item was it determined that the training stimuli (e.g., spoken word "radio," radio illustration, printed word radio) contained all three defining properties of an equivalence class: reflexivity, symmetry, and transitivity.