Stimulus equivalence

Three relational properties define the conventional test

Reflexivity is untrained matching of a stimulus to itself. Symmetry is reversal of a taught relation. If A-to-B is trained, B-to-A emerges. Transitivity combines relations. After A-to-B and B-to-C training, A-to-C emerges.

A C-to-A probe can provide a combined symmetry-and-transitivity test. Sidman and Tailby formalized the distinction between conditional-discrimination training and equivalence testing.

Matching-to-sample is a procedure

Equivalence studies often use matching-to-sample. A sample appears with comparison options, and the sample changes which selection is correct.

Identity matching, arbitrary matching, and directly taught conditional relations may all be accurate without a complete equivalence pattern. Sidman’s introductory tutorial reviews the paradigm and its early educational roots.

Baseline must remain stable during probes

Suppose A is a clinic symbol, B is its printed name, and C is its spoken name. Teaching A-to-B and B-to-C creates baseline relations. Tests then ask whether untrained reversals and combinations emerge.

Check baseline trials during the probe phase. If trained relations deteriorate, failed emergent probes are hard to interpret. Record probe order, feedback, repetition, retraining, and any exposure that changes an “untrained” relation.

A fictional equivalence record

Imani completes 12 of 12 final baseline trials for symbol-to-word and word-to-spoken-name relations. The team then presents 12 predeclared, unreinforced probes across symmetry and combined relations. She responds correctly on 10 of 12.

The 83.3% aggregate is insufficient by itself. Results need review by relation and proposed class. If both errors occur in one required C-to-A relation, the full class criterion may not be met. The record should report every relation rather than converting the total into a broad equivalence claim.

Function transfer is an additional outcome

Once stimuli participate in a class, a function taught to one member may appear with others under some conditions. That possibility can support efficient instruction, but transfer needs its own test.

Define the function, response, context, and baseline. If a safety response follows a novel class member, report the eligible probes and errors. Avoid assuming that demonstrated equivalence guarantees every function will transfer.

Test design can create apparent classes

Position patterns, common colors, names, experimenter cues, and repeated feedback can support accurate selections without the intended relations. Balance arrays and vary irrelevant features. Ensure that the person can perceive the samples and comparisons.

Testing itself can teach. The first unreinforced probe and a later repeated probe have different histories. Preserve that distinction.

Applied value depends on the person’s goal

Potential uses include reading, symbol comprehension, vocabulary, and concept instruction. Choose relations that improve meaningful access. Speech and eye contact are never required when another reliable response form works.

Preserve AAC, interpreters, visual access, breaks, mobility, and ordinary support. A laboratory-efficient class may still be burdensome or irrelevant in daily life.

Mechanism claims remain contested

Lionello-DeNolf’s review documents the complex history of symmetry research across procedures and species. Naming, common reinforcement, verbal history, contextual control, and other accounts remain part of the literature.

A clinician can describe the demonstrated relations without claiming that one explanatory mechanism has been proven. The BACB BCBA Test Content Outline, 6th edition includes equivalence concepts as examination content, not a clinical protocol.

Measure every class and relation

Report correct responses divided by eligible trials for baseline, reflexivity, symmetry, transitivity, and combined tests. Include class size, comparison number, prompts, feedback, invalid trials, latency, and retention.

Keep maintenance and generalization separate. Adding a new class member requires fresh evidence that it participates in the planned relations.

Expanding a class changes the test set

Adding D to an established A-B-C class requires a planned baseline link and new emergent tests. Teaching C-to-D may support predictions about D-to-C, A-to-D, and D-to-A, but every required relation needs defined evidence under the chosen criterion.

Keep old-class maintenance trials in the expansion phase. New teaching can disrupt earlier relations or create position and sequence patterns. Report failures rather than averaging them into the larger set.

Efficiency should be calculated from actual teaching and testing. Count directly taught relations, instructional trials, retraining, probe trials, and time. A smaller direct-training set is valuable only when the resulting relations are accurate, retained, useful, and acceptable to the person.

When the class supports communication or safety, verify use outside the matching task. Tabletop selection and everyday application are distinct outcomes.