Arbitrary matching to sample serves as a foundational experimental paradigm in behavior analysis, unlocking the behavioral mechanisms that give rise to human symbolic thought, semantic categorization, and complex verbal repertoires. By systematically training organisms to link physically disparate stimuli through conditional reinforcement contingencies, this method demonstrates how abstract relational networks emerge without direct instruction. Understanding this procedure illuminates the boundary between basic associative conditioning and generative linguistic capability.
Arbitrary Matching to Sample
1. Concise Definition
Arbitrary matching to sample (AMTS), frequently termed symbolic matching to sample, is an experimental and clinical procedure in behavior analysis wherein an organism is presented with a sample stimulus and must subsequently select one of two or more comparison stimuli based on a non-physical, socially defined, or experimentally stipulated relationship rather than physical resemblance. The reinforced selection depends entirely upon the specific sample presented, establishing a conditional discrimination between stimuli that share no formal sensory or morphological properties.
Unlike identity matching, in which the correct choice shares exact physical dimensions with the sample (such as matching a red square to another red square), arbitrary matching establishes an abstract functional linkage. When an organism consistently chooses stimulus B1 in the presence of stimulus A1, and stimulus B2 in the presence of stimulus A2, under reinforcement schedules that extinguish alternative combinations, conditional relations are formed. This methodology serves as the fundamental engine for investigating stimulus equivalence, derived relational responding, and the behavioral prerequisites of verbal behavior and symbolic reasoning.
2. Etymology & Linguistic Origin
The phrase “arbitrary matching to sample” derives from three distinct linguistic and methodological roots. The adjective “arbitrary” traces to the Latin arbitrarius, signifying that which depends upon the will, judgment, or discretion of an arbiter (arbiter) rather than on natural or inherent necessity. In psychophysics and operant psychology, it denotes the deliberate lack of intrinsic physical correlation between the paired stimuli. The verb “matching” originates from Middle English macche and Old English gemæcca, denoting a companion, equal, or suitable pairing. The term “sample” stems from the Old French essample, evolved from the Latin exemplum, meaning something taken out of a larger quantity to serve as an illustration, specimen, or model.
The composite paradigm emerged within the mid-twentieth-century operant conditioning laboratories founded upon the conceptual lineage of B. F. Skinner. When Murray Sidman and his contemporaries formally distinguished physical identity matching from non-identity tasks in the early 1970s, the descriptor “arbitrary” was adopted to accentuate that the experimental contingency—and not structural similarity—determines the correctness of the relational pairing.
3. Pronunciation & Grammatical Form
The term is pronounced phonetically as /ˈɑːrbɪtrɛri ˈmætʃɪŋ tuː ˈsæmpəl/ in Standard American English, and /ˈɑːbɪtrəri ˈmætʃɪŋ tuː ˈsɑːmpəl/ in Received Pronunciation. Grammatically, it operates as a compound noun phrase designating an experimental procedure or learning protocol. It can function syntactically as a subject, direct object, or adjectival modifier (e.g., “arbitrary matching-to-sample training”).
In standard academic literature, the term is frequently abbreviated as AMTS or MTS, sometimes interchangeably described as symbolic matching-to-sample (SMTS) or non-identity conditional discrimination. When used attributively before a noun, hyphenation is standard practice (e.g., “an arbitrary matching-to-sample task”). The gerund “matching” retains its dynamic process-oriented usage, while “sample” acts as the object of the preposition “to.”
4. Detailed Conceptual Explanation
To fully comprehend arbitrary matching to sample, one must examine the architecture of the operant contingency. Basic operant learning operates within a three-term contingency: discriminative stimulus ($S^D$), response ($R$), and reinforcing stimulus ($S^R$). Arbitrary matching expands this architecture into a four-term contingency, commonly designated as a conditional discrimination. In this higher-order framework, a prior event—the conditional stimulus or sample ($S_1$)—determines which of several subsequent discriminative stimuli ($S^D$ versus $S^\Delta$) will set the occasion for reinforcement upon the emission of a selection response.
In a standard discrete trial of AMTS, the sequence unfolds through strictly timed stages. First, a sample stimulus is presented to the participant (e.g., an arbitrary visual icon, a printed word, or an auditory vocalization). Often, an “observing response,” such as pressing a button or pointing to the sample, is required to guarantee active sensory registration. Once the observing response occurs, an array of two or more comparison stimuli is displayed either simultaneously with the sample or following a programmed temporal delay (delayed matching to sample, or DMTS). The participant chooses one comparison stimulus. If the participant selects the designated comparison ($S+$) corresponding conditionally to that sample, reinforcement is delivered; selections of incorrect comparisons ($S-$) yield brief timeouts or extinction.
The defining boundary of the arbitrary variant is that the sample and its corresponding comparison stimulus share zero formal, topographical, acoustic, or visual overlap. For instance, pairing the printed word “CANIS” with a pictorial representation of a dog constitutes an arbitrary match; no perceptual feature of the ink arrangement “C-A-N-I-S” resembles the physical anatomy, fur, or four legs of a canine. The link is entirely functional, maintained solely by the history of reinforcement arranged by the social or experimental environment.
Through iterative exposures across diverse stimulus sets, AMTS establishes complex relational repertoires. When multiple arbitrary relations are taught systematically (e.g., training A $\rightarrow$ B and B $\rightarrow$ C), subjects often display generative performances without explicit training, such as spontaneously matching B to A, C to B, A to C, and C to A. Consequently, AMTS is not merely a tool for training rote associations; it is the premier laboratory engine for generating and analyzing the emergent symbolic networks that characterize human cognition and verbal behavior.
5. Historical Development
The trajectory of matching to sample originated within comparative psychology during the first half of the twentieth century. Early comparative researchers, including Karl Lashley and later comparative primatologists, utilized identity matching apparatuses to evaluate visual discrimination, perceptual acuity, and short-term memory in non-human animals. These classic configurations were limited primarily to testing whether an animal could recognize physical sameness or difference across visual targets.
The turning point for the modern arbitrary paradigm occurred in 1971 through the groundbreaking investigations of behavioral scientist Murray Sidman. Working at the Massachusetts General Hospital and the E.K. Shriver Center, Sidman sought behavioral techniques to teach reading comprehension to an individual with severe intellectual and developmental disabilities. Sidman configured an automated AMTS paradigm linking spoken words (stimulus class A), printed words (stimulus class B), and pictorial representations of objects (stimulus class C).
After directly training only spoken-to-picture (A $\rightarrow$ C) and spoken-to-printed-word (A $\rightarrow$ B) conditional relations, Sidman observed an unexpected, monumental behavioral phenomenon: the participant could instantly and accurately match the printed words to their corresponding pictures (B $\rightarrow$ C) and the pictures to the printed words (C $\rightarrow$ B) without a single trial of direct reinforcement. This finding catalyzed the formalization of the stimulus equivalence paradigm in 1982 by Sidman and Tailby, who operationalized mathematical equivalence relations (reflexivity, symmetry, and transitivity) within an operant conditioning framework, permanently establishing AMTS as the primary method for investigating emergent cognition.
6. Theoretical Foundations
Arbitrary matching to sample is rooted in behavior-analytic theories of conditional discrimination and stimulus control. Radical behaviorism posits that complex intellectual behavior, including language and reasoning, does not necessitate invoking unobservable mental mechanisms; instead, it can be accounted for by identifying the environmental contingencies that establish conditional control over human action. Within this tradition, AMTS is conceptualized as an environmental arrangement that builds functional response classes across disparate physical stimuli.
The dominant theoretical paradigm stemming from AMTS is Stimulus Equivalence Theory. Murray Sidman posited that conditional discrimination training possesses the inherent capacity to establish equivalence classes among stimuli. When arbitrary stimuli become members of an equivalence class, they become functionally interchangeable in specific contexts. This framework demonstrates that complex emergent cognitive structures are natural outcomes of reinforcement contingencies acting upon conditional relations, providing an empirical, non-mentalistic model of referential meaning.
In contemporary contextual behavioral science, Relational Frame Theory (RFT), developed by Steven C. Hayes, Dermot Barnes-Holmes, and colleagues, expanded upon Sidman’s foundations. RFT conceptualizes matching to sample as an instance of arbitrarily applicable relational responding (AARR). According to RFT, AMTS performance is an operant behavior learned early in life through extensive social reinforcement. Once learned, humans can relate arbitrary stimuli not only through equivalence or coordination, but also through comparative, hierarchical, spatial, temporal, and perspective-taking relations based on arbitrary contextual cues (e.g., “is bigger than,” “is opposite of,” “comes before”).
7. Key Components, Types & Dimensions
The structural and operational dimensions of arbitrary matching to sample can be classified across several operational parameters:
- The Sample Stimulus: The initial conditional stimulus presented to the participant at the onset of a trial, setting the occasion for the valid conditional discrimination (e.g., an abstract glyph, auditory phoneme, or olfactory marker).
- The Comparison Array: The set of two or more alternative stimuli simultaneously or sequentially presented from which the subject must select. This array contains exactly one correct comparison ($S+$) and one or more non-reinforced incorrect comparisons ($S-$).
- The Observing Response: An operational requirement ensuring that the subject attends to the sample stimulus (such as a touchscreen press or sustained gaze) before the comparison array appears.
- Simultaneous vs. Delayed Presentation: In simultaneous AMTS, the sample remains visible while comparisons are evaluated. In delayed matching to sample (DMTS), a programmed interval (ranging from milliseconds to minutes) elapses between the termination of the sample and the onset of the comparisons, tapping working memory and stimulus persistence.
- Training Structures: The organizational topology used to interconnect stimulus classes, including:
- One-to-Many (Sample-as-Node): A single central sample is trained to multiple comparisons (e.g., A $\rightarrow$ B and A $\rightarrow$ C).
- Many-to-One (Comparison-as-Node): Multiple samples are trained to a single comparison (e.g., B $\rightarrow$ A and C $\rightarrow$ A).
- Linear Series: Stimuli are trained sequentially end-to-end (e.g., A $\rightarrow$ B $\rightarrow$ C $\rightarrow$ D).
8. Examples & Illustrative Cases
To see AMTS in practice, consider an educational application designed to teach written vocabulary to a child with an autism spectrum disorder. The instructor initiates a computer-delivered trial presenting an auditory vocalization: the spoken word “triangle” (Sample A1). The child touches the speaker icon to confirm observation. Instantly, three printed words appear on the screen: “TRIANGLE” (Comparison B1), “CIRCLE” (Comparison B2), and “SQUARE” (Comparison B3). Touching “TRIANGLE” activates an animated chime and grants access to a preferred token, while selecting either alternate text produces a three-second blank screen. Crucially, the spoken auditory frequency pattern of the word “triangle” shares zero physical properties with the geometric visual typography of the printed word “TRIANGLE”; the relationship is arbitrary.
In a laboratory setting evaluating emergent mathematical logic, an experimenter trains an adult human subject using meaningless Greek characters and fabricated nonsense syllables. The participant is trained to match the Greek letter $Theta$ (A1) to the syllable “VEK” (B1), and $Psi$ (A2) to “PAF” (B2). In a second phase, the participant is trained to match “VEK” (B1) to a designated geometric fractal (C1), and “PAF” (B2) to an alternate fractal (C2). When subsequently presented with $Theta$ (A1) as a sample and asked to choose between fractal C1 and C2 without any feedback or direct instruction, neurotypical humans reliably select C1. The subject demonstrates derived transitivity, validating the emergence of unified symbolic equivalence classes without direct trial-by-trial conditioning.
9. Measurement & Assessment
Evaluating AMTS performance requires rigorous behavioral metrics to distinguish genuine conditional discrimination from idiosyncratic response biases, position preferences, or chance guessing. The primary quantitative indices include:
- Accuracy Percentage: The proportion of correct comparison selections ($S+$) divided by total trial exposures across baseline training blocks, typically requiring a criterion of 90% to 100% across consecutive blocks before introducing novel test probes.
- Equivalence Test Probes: Unreinforced test trials distributed among baseline trials to evaluate derived responding:
- Symmetry Probes: Reversing the direction of trained conditional relations (e.g., testing B $\rightarrow$ A after training A $\rightarrow$ B).
- Transitivity Probes: Testing combined untrained forward connections (e.g., testing A $\rightarrow$ C after training A $\rightarrow$ B and B $\rightarrow$ C).
- Equivalence Probes: Testing combined untrained symmetrical and transitive relations (e.g., testing C $\rightarrow$ A).
- Response Latency: The time elapsed from the onset of comparison stimuli to the execution of the selection response, which systematically reflects cognitive processing load, task difficulty, and nodal distance across relational networks.
- Nodal Distance Effects: Measurement of drop-offs in accuracy or increases in latency as the number of intermediate stimulus links (“nodes”) between tested stimuli increases within a derived network.
10. Applications & Practical Significance
The practical implementations of AMTS span education, cognitive rehabilitation, and neuropsychology. Within applied behavior analysis, AMTS is the premier operational technology for teaching functional communication, reading comprehension, spelling, and numerical calculation to children with developmental delays, intellectual disabilities, and autism. By strategically designing one-to-many or many-to-one training curricula, clinicians can instruct a minimal baseline of relations and foster an exponential emergence of untaught verbal repertoires, dramatically increasing instructional efficiency.
In adult neurorehabilitation, speech-language pathologists apply AMTS protocols to treat individuals recovering from severe stroke or traumatic brain injury experiencing receptive and expressive aphasia. By systematically re-establishing conditional discriminations between auditory phrases, environmental sounds, printed text, and tactile objects, patients can reconstruct damaged semantic networks.
Beyond clinical intervention, AMTS paradigms are utilized in corporate and industrial safety training. Workers are trained to match arbitrary hazardous chemical symbols to categorical risk profiles and designated emergency responses. Furthermore, cognitive psychologists employ AMTS software to assess prefrontal cortex functionality, working memory degradation in neurodegenerative disorders such as Alzheimer’s disease, and implicit social attitudes via relational reaction-time tests.
11. Research & Empirical Evidence
Decades of empirical literature substantiate the robustness of arbitrary matching to sample. Seminal research by Sidman and Tailby (1982) demonstrated that when children were taught eight conditional relations among three three-member stimulus classes, all children demonstrated sixteen derived symmetrical, transitive, and equivalence relations without further training. These findings established that equivalence relations are systematically derived outcomes of conditional discrimination training in humans.
Extensive investigations by researchers such as Carol Pilgrim, Richard Smeets, and Dermot Barnes-Holmes have illuminated the conditions that facilitate or impede equivalence formation. Studies comparing training structures have demonstrated that the One-to-Many and Many-to-One training topologies yield significantly faster emergence and higher stability of equivalence classes compared to Linear Series training. Neuroimaging studies utilizing functional magnetic resonance imaging (fMRI) during AMTS tasks show increased activation within the prefrontal cortex, anterior cingulate, and left parahippocampal gyrus during the derived emergence of unreinforced symmetry and transitivity trials, highlighting the distinct neural signatures of derived relational responding.
12. Cultural & Cross-Cultural Considerations
The functional dynamics of AMTS operate universally across human populations, yet the specific content and pre-experimental learning histories of participants introduce cross-cultural variations. Because arbitrary matching relies upon stimuli lacking natural physical linkages, cultural artifacts, written orthographies, and semiotic conventions fundamentally shape baseline performance. An abstract graphic that appears completely arbitrary to a Western participant may carry pre-existing symbolic or religious connotations for an individual from another cultural background, inadvertently biasing stimulus selection.
Cross-cultural cognitive research confirms that humans from literate, highly schooled environments typically acquire AMTS tasks and display derived equivalence classes more rapidly than individuals from non-literate societies. This variation does not stem from intrinsic biological differences, but rather from extensive lifelong histories with formal educational frameworks that heavily reinforce arbitrary symbolic substitutions (such as relating abstract numbers to physical quantities or letters to spoken sounds). When AMTS experiments employ culturally neutral, tactile, or non-representational geometric stimuli, individuals across diverse cultures establish conditional equivalence classes with comparable proficiency.
13. Criticisms, Debates & Limitations
Despite its widespread utility, AMTS has ignited prominent theoretical controversies within psychology. A long-standing debate centers on the “Naming Hypothesis,” championed by Pauline Horne and C. Fergus Lowe (1996). Horne and Lowe argued that stimulus equivalence in AMTS is not a direct product of reinforcement contingencies alone; rather, it requires that participants tacitly generate internal or overt verbal labels (names) for the stimuli. According to this view, an individual matches stimulus A to B because both have been assigned the identical intraverbal or tacted name (e.g., “that’s a cat”). While Sidman and others countered this claim by showing emergent equivalence in participants who lacked functional expressive naming repertoires, the degree to which covert verbal mediation facilitates AMTS performance remains actively debated.
Another profound point of contention concerns the phylogenetic continuity of AMTS and stimulus equivalence. While non-human animals, such as pigeons, sea lions, and chimpanzees, readily master basic AMTS tasks (matching A to B for food reinforcement), decades of experimentation have revealed that non-humans overwhelmingly fail to demonstrate emergent symmetry (spontaneously matching B to A) or transitivity without extensive explicit training. While some comparative researchers claim to have demonstrated rudimentary equivalence in non-humans, most behavior analysts argue that derived arbitrary relational responding represents an exclusively or predominantly human behavioral adaptation tied to the evolutionary development of verbal language.
14. Related Terms & Distinctions
To prevent conceptual confusion, arbitrary matching to sample must be carefully delineated from related procedures and behavioral constructs:
- Identity Matching to Sample (IMTS): A matching task where the comparison stimulus is physically identical to the sample stimulus (e.g., matching a circle to a circle). AMTS, by contrast, involves comparison stimuli that bear no physical resemblance to the sample.
- Oddity from Sample: A matching procedure in which selection of the comparison that is physically or arbitrarily distinct from or opposite to the sample is reinforced (e.g., selecting “dark” when presented with “bright”).
- Stimulus Equivalence: The emergent behavioral phenomenon wherein trained arbitrary conditional relations give rise to untrained reflexive, symmetric, and transitive relations. AMTS is the experimental vehicle used to establish and verify stimulus equivalence.
- Paired-Associate Learning: A cognitive memory protocol where pairs of items (e.g., word-word) are memorized. Unlike AMTS, paired-associate tasks typically assess rote recall rather than the conditional discriminative control of comparison selections within multi-choice arrays, nor do they formally assess systematic derived equivalence networks.
- Relational Framing: A broader behavioral process conceptualized by Relational Frame Theory wherein organisms relate stimuli arbitrarily under contextual cues across numerous relational types (e.g., opposition, comparison, hierarchy), of which AMTS represents the prototypical coordination/equivalence frame.
15. Summary / Key Takeaways
Arbitrary matching to sample is a central paradigm in contemporary behavioral science. It converts a basic operant discrimination into a four-term conditional arrangement, enabling organisms to associate stimuli that share no physical or perceptual overlap. The paradigm provides the empirical bridge linking simple operant conditioning to higher-order cognitive faculties, including symbolic reference, receptive and expressive language, reading comprehension, and abstract mathematics. Decades of clinical evidence demonstrate its exceptional utility in special education and neurorehabilitation, while basic research continues to explore its boundaries across human development, neurobiology, and comparative animal behavior.
References
- Barnes-Holmes, D., Finn, M., McEnteggart, C., & Barnes-Holmes, Y. (2018). Derived stimulus relations and relational frame theory: New directions for creating effective educational and clinical interventions. European Journal of Behavior Analysis, 19(1), 5–28. https://doi.org/10.1080/15021149.2017.1422826
- Hayes, S. C., Barnes-Holmes, D., & Roche, B. (Eds.). (2001). Relational Frame Theory: A Post-Skinnerian Account of Human Language and Cognition. Kluwer Academic/Plenum Publishers. https://doi.org/10.1007/b108413
- Horne, P. J., & Lowe, C. F. (1996). On the origins of naming and other symbolic behavior. Journal of the Experimental Analysis of Behavior, 65(1), 185–241. https://doi.org/10.1901/jeab.1996.65-185
- Sidman, M. (1971). Reading and auditory-visual equivalences. Journal of Speech and Hearing Research, 14(1), 5–13. https://doi.org/10.1044/jshr.1401.05
- Sidman, M., & Tailby, W. (1982). Conditional discrimination vs. matching to sample: An expansion of the testing paradigm. Journal of the Experimental Analysis of Behavior, 37(1), 5–22. https://doi.org/10.1901/jeab.1982.37-5