Matching Law in ABA Therapy: Explained

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The ABA therapy is a type of treatment that uses the principle to teach children with autism how to use language, socialize and interact. With the help of this program, many autistic people have found success in their learning journey.

The “matching law example aba” is a therapy technique that involves matching the client’s behavior to a specific rule, which can be found in the ABA Therapy Manual.


The matching law explains mathematical equations that are used to analyze the link between one person’s behavior and external or internal reinforcers. The rate of response is the frequency with which a person chooses a given behavior in response to the presence of certain reinforcers.

Reinforcers may be positive, such as preferring to spend time with a particular buddy because they make you happy. When applied behavior analysis (ABA) therapists use the phrase, they almost invariably refer to negative reinforcers, which are acts that inadvertently reinforce a maladaptive habit that the therapist is trying to alter.

ABA Treatment

Applied behavior analysis (ABA) is a kind of behavioral treatment that focuses on enhancing certain behaviors such as communication, learning, socialization, and academics. Behavioral change and management techniques may be used to a variety of activities in everyday life, from personal cleanliness to job abilities.

ABA Treatment is the most used evidence-based approach for treating symptoms of autism. Therapists certified in this practice can work in specialized clinics, schools, community centers, and clients’ homes.

The Matching Law: Using Math to Explain Behavior in Support of Evidence-Based Practices

ABA Treatment is an evidence-based therapy practice, meaning therapists are trained to make observations of their clients’ behaviors and determine whether the treatment plan is effective at leading to positive (or adaptive) behavioral change or if the client is not benefitting from the therapist’s approach. One way that ABA therapists may determine that is through a mathematical formula called the matching law.

The matching law outlines the relationship between the rate of reinforcement and the rate of replies. When someone is given a choice between two actions that are equally likely to occur, the person will often allocate their responses to the conduct that has historically resulted in greater positive reinforcement or “feeling better.”

Someone may equate feeling good with eating ice cream, but they are gaining weight and should avoid eating ice cream. Despite this, if given the option between a piece of fruit and ice cream, they would choose the latter since they have previously felt better after eating it.

The conduct of youngsters on a playground is another common illustration. A researcher may obtain disseminated information on where the children travel with their playmates, what equipment they pick, and if they prefer more or less physically intense activities by observing their behavior. Aggregating answers may reveal the children’s pReferences based on their patterns, implying that they respond to the playground environment reinforcement at a given pace.

Strict matching refers to a one-to-one relationship between the rate of response and the rate of reward. While the notion is beneficial, it is no longer regarded feasible. Because the matching equation has systematic deviations from exact matching, an extended version is more often employed in current behavioral analysis to characterize gathered data.

What is the Law of Matching?

The matching law allows behavioral therapists or researchers to utilize a behavior formula, make observations, collect data, and predict what a person will do using a methodical methodology. Equations derived from the matching law result in two graph types.

  1. When the reinforcer is internal, generalized matching is a linear function between two or more behavior-reinforcement possibilities.

  2. Single-alternative matching resembles a hyperbolic function that describes one goal behavior in response to external reinforcement.

The matching law’s fundamental formula is:

B1/B1 + R1/R1 + R2 =

The response rates for two behaviors are Behavior 1 and Behavior 2. The reinforcement rates for the two actions are R1 and R2.

These ways of graphing behavior give ABA therapists with valuable visual information about their clients, allowing them to enhance treatment results. The data’s correlations aid therapists in assessing behaviors that their clients have been rewarded, either positively or negatively, and determining how to promote adaptive behaviors by altering negative reinforcement and increasing positive reinforcement. These modifications may be adopted across the child’s family, classroom, or larger school setting, depending on where the behavior analyst works.

The Study of the Matching Law

Two articles on the matching law are often cited as part of ABA Treatment, justifying the use of the equation to understand the relationships between a behavior from a client, like a child with autism, and a reinforcer, like the negative reaction of the parent.

A paper published in 1981, for example, cited a case study of a boy with autism who had self-injuring behaviors, which are maladaptive. The boy’s family verbally reprimanded him when he injured himself, but using the matching equation, his injurious behavior was correlated with the verbal reprimands as reinforcing that behavior. When there were more reprimands, the boy was more likely, rather than less likely, to continue injuring himself. This study showed that the matching law functions as a theory in ABA Treatment.

Positive reinforcement is most often used in ABA Treatment. It’s important for both the therapist and the child with autism to understand how negative reinforcers creep in and cause stagnation or regression in efforts to create adaptive behaviors.

The matching law was utilized in a 2002 research to learn how four adults with developmental impairments were rewarded for certain actions in a clinical environment with their therapist and at home with their carers. Potential reinforcers, suitable behaviors, and problematic behaviors were all documented by the researchers. The researchers used functional analysis to identify the reinforcers in these contexts that kept the harmful behaviors going. The researchers found that the proportionate rate of suitable to problem behaviors learnt by the subjects seemed to connect with the rate of issue behavior reinforcement after analyzing the data.

Another research collected data on parent-child interactions from ten dyads of a woman and her socially aggressive kid. The research discovered that the mother’s response to her son’s conduct was often an accidental reinforcer of the child’s behavior. The researchers looked at both good and negative verbal exchanges between the boys and their moms.

The Matching Law: Practical but Not Infallible

In most cases, the response rate and the reinforcement rate do not have a one-to-one relationship. When two options are equivalent, an organism will pick the option that is connected with immediate reinforcement, according to the matching law. The link between the organism’s affiliation and its decision seems evident when presented this way.

However, neither people nor animals make decisions with such clarity very frequently. The artificial simplification of a research on the supposed tautology of the matching rule when applied to consumer behavior, monitoring amount spent with quantity bought, was artificial. The consumer behavior analysis’ independent and dependent variables were constructed and assessed in a manner that was controlled, rather than being indicative of the customers’ “natural” environment.


ABA stands for Applied Behavior Analysis. Today’s Psychology

A Practitioner’s Guide to the Matching Law (2011). International Association for Behavioral Analysis (ABAI).

Visualization Tool for Law Matching (May 2015). ScholarWorks at KU.

The Matching Law is a mathematical equation that explains why people make decisions. July 15, 2015. Central Psychiatry.

A Study of Severe Problem Behavior Using the Matching Law (2002). The Journal of Applied Behavior Analysis is a publication dedicated to the study of human behavior.

A Social Dynamics Application of the Matching Law (2007). The Journal of Applied Behavior Analysis is a publication dedicated to the study of human behavior.

In Consumer Behavior Analysis, on the Tautology of the Matching Law. (Apr. 2010). Processes of Behaviour.

“Matching law psychology examples” is a term that is often used in the field of ABA therapy. It refers to the process by which teachers and therapists use their knowledge of the individual’s preferences, interests, and skills to create an environment that is both stimulating and meaningful. Reference: matching law psychology examples.

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