Arbitrary matching

The sample changes which comparison is correct

In matching to sample, a sample appears with two or more comparison options. Selection of one comparison is reinforced in the presence of one sample, while another comparison is correct for another sample.

That sample-comparison dependency makes the task conditional. A learner who always chooses the left comparison, the brightest card, or one favorite picture has not demonstrated the intended relation.

“Arbitrary” refers to physical dissimilarity

The related stimuli need no formal resemblance. The printed word “cup” looks different from a cup, and a spoken word has a different sensory form from a photograph.

The relation can be culturally established, explicitly taught, or derived from other learning. Arbitrary does not mean random, meaningless, or selected without a rule.

Identity matching uses physical sameness

In identity matching, the correct comparison is physically identical to the sample, such as matching one blue circle to another blue circle. Arbitrary matching instead depends on a learned relation between different forms.

Both tasks can use matching-to-sample procedures. The clinician should name the relation being assessed rather than treating the procedure name as the skill.

Build a trial that isolates the relation

Define the sample, comparison array, correct relation, response, response window, prompts, reinforcement, error procedure, and trial order. Rotate comparison positions and balance them across samples.

Use enough comparison options to distinguish relation-based performance from chance while respecting visual, motor, attention, and communication needs. Track omissions and invalid trials separately from incorrect selections.

A fictional example

Leena is learning three community symbols that she selected as useful. On each trial, she hears one place name and chooses among three symbol cards. Each place name appears six times, and comparison positions are balanced.

Leena responds correctly on 15 of 18 independent trials, or 83.3%. Errors occur twice when one symbol is in the right position and once when it is in the center. That pattern prompts a position-bias check rather than a claim that one relation is missing.

On six later trials with new exemplars of the same places, she responds correctly on 4 of 6. Keep acquisition and generalization denominators separate.

Control for unintended cues

An instructor can accidentally signal the answer through gaze, card placement, tone, timing, or a consistent sequence. Materials may contain irrelevant cues such as color, size, wear marks, or background.

Randomize within planned constraints, use balanced arrays, and sample procedural integrity. Video review requires appropriate consent, privacy controls, secure systems, and defined retention.

Directly taught and derived relations differ

A directly taught arbitrary relation has a reinforcement history for the trained sample-comparison pair. A derived relation appears without direct teaching of that exact relation after other relations were learned.

A review of derived stimulus relations describes untrained matching that can emerge from a smaller trained network. One correct novel trial provides weak evidence. Use planned probes, adequate opportunities, and a clear history of what was trained.

The BACB outline provides a broad boundary

The BACB BCBA Test Content Outline covers stimulus control, discrimination, conditional discrimination procedures, and emergent relations. It is entry-level examination content, not an implementation standard or authority to practice.

Clinical interpretation belongs to a qualified professional working within competence, law, supervision, payer, and organizational requirements.

A useful record includes

• samples, comparisons, modality, and relation
• eligible-trial and response definitions
• array size and position-balancing rule
• prompted, independent, incorrect, omitted, and invalid trials
• teaching versus novel-probe status
• accessibility supports kept constant
• procedural-integrity and observer-agreement checks
• the person's preferences and practical outcome

Report raw counts beside percentages. A score can look strong while hiding a small denominator or one untested relation.

Analyze errors by relation and array

Build an error table with one row per sample and columns for each selected comparison and position. A cluster within one sample can suggest that relation needs teaching. Errors following one location can suggest position control. Confusion between two comparisons can reveal a feature or naming overlap. Keep this descriptive until a planned test supports the interpretation.

Review latency and self-correction alongside accuracy. A learner may select correctly after long scanning because the array is visually crowded. Another may answer quickly from a repeated trial sequence. Adjust access or trial design while preserving the arbitrary relation being taught.

Plan maintenance without drilling one set

After acquisition, reduce contrived feedback as appropriate and sample natural consequences. Rotate trained exemplars, partners, devices, and settings that the person actually encounters. Keep a few untrained exemplars for later checks. If performance drops, identify the failing relation or context before returning every pair to intensive teaching.