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The matching law is a descriptive mathematical model thatconceptualizes an organism’s response rates as a function of rela-tive rates of reinforcement (Herrnstein 1961). This relation isexpressed by equation (1):B1=B2 ¼ R1=R2 (1)where Bs represent rates of behaviour and Rs represent reinforcerrates. However, extensive research has confirmed that organisms’behaviour systematically deviates from predictions of equation (1)(Baum 1974, 1979 , 1983; Wearden & Burgess 1982; Davison M McDowell 2012). The power function version,known as the generalized matching law (Baum 1974), providesbetter descriptions of animals’ and humans’ choices in concurrentschedules and is represented logarithmically by equation (2):log ðB1=B2Þ¼a log ðR1=R2Þþlog c (2)where Bs and Rs are the same as in equation (1), a is referred to assensitivity and represents the organism’s adjustment to the con-tingencies, and c is called the bias parameter and represents theorganism’s preference when choice is asymmetrical. Note thatequation (2) reduces to equation (1) when a ¼ c ¼ 1, and is usuallycalled strict matching. Furthermore, most studies have found thatthe sensitivity value varies around 0.8, which is referred to asundermatching.Herrnstein (1961) developed the matching law to describe in-dividual choices. A misunderstanding of this fundamentalassumption has led several authors (i.e. Schroeder & Holland 1969;Conger & Killeen 1974; Schmitt 1974; Vollmer & Bourret 2000;Borrero & Vollmer 2002; Alferink et al. 2009; McDowell & Caron2010a, b) to conduct their analyses incorrectly. For instance, theyused a small number of levels of the independent variable andpooled their subjects’ data, which combined idiosyncraticdependent variables into a single analysis and did not account forwithin-subject and within-level variances. At best, between-subject data will estimate an inaccurate model with erroneousparameter values and, at worst, will violate several statistical as-sumptions and lead to uninterpretable results. The purpose of thecurrent study is to prevent future misunderstanding by clarifyingthese errors.Pooling Different VariablesStatistically, the dependent variable must be the same throughall levels of the independent variable. Applied to the matching law,this means that the response ratio must remain the same at alllevels of the reinforcer ratios. Therefore, between-subject analysesmust rely on the same responses for every subject. However, if thesubjects had different target behaviours, then their log response

Please check the original document before citing this paper.; International audience; The matching law, regardless of the version, is a mathematical model that accounts for an organism's response rate as a function of the reinforcer rate. McDowell (2012) investigated to which extent a combined version of the quantitative law of effect (Herrnstein, 1970) and the generalized matching law (Baum, 1974) accounts for a substantial amount of the variance through several data sets. Even if I agree with most points raised by McDowell, there are two important issues within his reanalysis. Two out of six studies relied on pooled-subject data that are inappropriate for an investigation of the matching law (Caron, 2013). Moreover, the combined equation was not systemically investigated through all data sets. The current study casts some doubt on the empirical status of modern matching equations and thus shows they still deserve extensive attention.

International audience; Perfectionism is a multidimensional construct conceptualized as an excessive need in meeting high standards, striving for flawlessness and harsh self-criticism. Past studies have shown that positive perfectionism is related to a better school performance whereas negative perfectionism is often associated with social and emotional difficulties such as anxiety, depression and lower self-esteem. The current study investigated the associations between negative perfectionism and the performance in reading, mathematics and IQ performance in children from regular classroom who are applying to an international schooling program. Correlation analyses show that a high score on the negative perfectionism scale is related to a lower performance in mathematics, reading and on three IQ subscale tests. These results are important since negative perfectionism seem to affect negatively the performance in mathematics and in reading and thus may lead to negative long term outcomes such as drop out. These findings highlight the significance of developing the research on perfectionism and the importance of prevention and intervention among children.

International audience; Increasing the appropriate response rate of a target student without producing major drawbacks in the classrooms is a major concern for teachers. Several behavioral interventions have been developed to answer this issue. They often require, however, professional supports and may have the disadvantage to focus only on specific and/or isolated problem behaviors. One way to improve teacher skills in managing student behaviors is through the assessment of their social sensitivity [1]. Social sensitivity quantifies the behavioral adjustment of a subject to contingencies of social reinforcement by means of the generalized matching law [2]. It hypothesizes that social attention has an operant function on student behavior and that their adjustment follow the matching law predictions. The purpose of the current study is to illustrate social sensitivity as an analytical tool for identifying different possible treatments in a school context. Two primary school students and their teachers were directly observed in their usual classroom. The students had no diagnosis nor exhibited any problem behavior. They were chosen because, according to their teachers, they showed poor attention to the task. A behavior analyst recorded the naturally occurring rates of appropriate and inappropriate behaviors of the children and the rate of attention given by their teacher. Behaviors and reinforcers were recorded according to an interval sampling method (five seconds of observing followed by five seconds of recording). Social sensitivity accounted for 58 % and 82 % of the variance. Both subjects demonstrated undermatching and a small preference (bias) toward inappropriate behaviors. Subject 1’s sensitivity was .73 (moderate undermatching) whereas subject 2’s was .29 (strong undermatching). Biases for both subject were respectively –log(.026) and –log(.08), favouring inappropriate behavior and confirming teachers’ perception that children had low attention to the task. Results are similar to other experimental and descriptive studies in humans. High explained variance suggests that social sensitivity can be applied in the classroom to direct interventions. Based on the obtained matching relations of each subject, two treatments are discussed. Given the results of subject 1, the teacher should be careful in choosing the behavior to reinforce, because the subject has a strong tendency to behave inappropriately. The teacher does not have to increase the absolute number of reinforcers, but rather should distribute them according to a ratio favoring appropriate behaviors. Assuring that reinforcers were contingent to appropriate behavior was also emphasized. According to subject 2's results, the teacher should extinguish, as much as possible, reinforcers to inappropriate behavior and increase social attention to appropriate ones. Given a lower sensitivity to social attention, the teacher should expect a modest modification of behavior. Other types of treatment, such as token economy or based on tangible reinforcers, could be considered in this case. Some limits should be considered. First, the number of subject and the sample size were low. Since social sensitivity relies on a within-subject and molar conceptualisation of behavior, they do not appear as essential factors. Second, the treatments proposed herein were not tested. Effects of the intervention could not have been empirically investigated. It would have brought better support to the model and its efficiency in classrooms. The current study suggests that social sensitivity can be used in school context in order to influence and fine tune behavioral interventions. It seems easier to introduce reluctant teachers to behavioral and cognitive therapies. They require less professional support and would provide autonomy to teachers towards classroom management. Finally, more studies are necessary to assess the therapeutic contribution of social sensitivity; nevertheless, the current results are promising and indicate the need for further examination of the model.; Comment améliorer les comportements d’un élève sans nuire à la gestion globale de la salle de classe ? En fait, la sensibilité sociale constitue un concept privilégié afin d’améliorer les habiletés des enseignants à gérer les comportements difficiles de leurs élèves [1]. La sensibilité sociale est un concept décrivant la relation entre les comportements d’un individu et l’attention sociale prodiguée par son entourage [2]. L’objectif de la présente étude est de présenter ce concept et d’illustrer deux études de cas réalisées selon les résultats obtenus à la suite d’une analyse comportementale de la sensibilité sociale de l’élève. L’observation directe est utilisée afin de noter les comportements sociaux des élèves en salle de classe. Un observateur note la fréquence d’apparition des comportements appropriés et inappropriés en contingence avec les renforçateurs prodigués par leur enseignant. Les résultats montrent que la sensibilité sociale décrit 58 % et 82 % de la variance du comportement des élèves. La présente étude illustre la pertinence de ce concept dans l’élaboration d’interventions comportementales en salle de classe.

International audience; Increasing the appropriate response rate of a target student without producing major drawbacks in the classrooms is a major concern for teachers. Several behavioral interventions have been developed to answer this issue. They often require, however, professional supports and may have the disadvantage to focus only on specific and/or isolated problem behaviors. One way to improve teacher skills in managing student behaviors is through the assessment of their social sensitivity [1]. Social sensitivity quantifies the behavioral adjustment of a subject to contingencies of social reinforcement by means of the generalized matching law [2]. It hypothesizes that social attention has an operant function on student behavior and that their adjustment follow the matching law predictions. The purpose of the current study is to illustrate social sensitivity as an analytical tool for identifying different possible treatments in a school context. Two primary school students and their teachers were directly observed in their usual classroom. The students had no diagnosis nor exhibited any problem behavior. They were chosen because, according to their teachers, they showed poor attention to the task. A behavior analyst recorded the naturally occurring rates of appropriate and inappropriate behaviors of the children and the rate of attention given by their teacher. Behaviors and reinforcers were recorded according to an interval sampling method (five seconds of observing followed by five seconds of recording). Social sensitivity accounted for 58 % and 82 % of the variance. Both subjects demonstrated undermatching and a small preference (bias) toward inappropriate behaviors. Subject 1’s sensitivity was .73 (moderate undermatching) whereas subject 2’s was .29 (strong undermatching). Biases for both subject were respectively –log(.026) and –log(.08), favouring inappropriate behavior and confirming teachers’ perception that children had low attention to the task. Results are similar to other experimental and descriptive studies in humans. High explained variance suggests that social sensitivity can be applied in the classroom to direct interventions. Based on the obtained matching relations of each subject, two treatments are discussed. Given the results of subject 1, the teacher should be careful in choosing the behavior to reinforce, because the subject has a strong tendency to behave inappropriately. The teacher does not have to increase the absolute number of reinforcers, but rather should distribute them according to a ratio favoring appropriate behaviors. Assuring that reinforcers were contingent to appropriate behavior was also emphasized. According to subject 2's results, the teacher should extinguish, as much as possible, reinforcers to inappropriate behavior and increase social attention to appropriate ones. Given a lower sensitivity to social attention, the teacher should expect a modest modification of behavior. Other types of treatment, such as token economy or based on tangible reinforcers, could be considered in this case. Some limits should be considered. First, the number of subject and the sample size were low. Since social sensitivity relies on a within-subject and molar conceptualisation of behavior, they do not appear as essential factors. Second, the treatments proposed herein were not tested. Effects of the intervention could not have been empirically investigated. It would have brought better support to the model and its efficiency in classrooms. The current study suggests that social sensitivity can be used in school context in order to influence and fine tune behavioral interventions. It seems easier to introduce reluctant teachers to behavioral and cognitive therapies. They require less professional support and would provide autonomy to teachers towards classroom management. Finally, more studies are necessary to assess the therapeutic contribution of social sensitivity; nevertheless, the current results are promising and indicate the need for further examination of the model.; Comment améliorer les comportements d’un élève sans nuire à la gestion globale de la salle de classe ? En fait, la sensibilité sociale constitue un concept privilégié afin d’améliorer les habiletés des enseignants à gérer les comportements difficiles de leurs élèves [1]. La sensibilité sociale est un concept décrivant la relation entre les comportements d’un individu et l’attention sociale prodiguée par son entourage [2]. L’objectif de la présente étude est de présenter ce concept et d’illustrer deux études de cas réalisées selon les résultats obtenus à la suite d’une analyse comportementale de la sensibilité sociale de l’élève. L’observation directe est utilisée afin de noter les comportements sociaux des élèves en salle de classe. Un observateur note la fréquence d’apparition des comportements appropriés et inappropriés en contingence avec les renforçateurs prodigués par leur enseignant. Les résultats montrent que la sensibilité sociale décrit 58 % et 82 % de la variance du comportement des élèves. La présente étude illustre la pertinence de ce concept dans l’élaboration d’interventions comportementales en salle de classe.

The generalized matching law (GML) is a descriptive mathematical model that conceptualizes an organism's response ratios as a function of associated reinforcer ratios (Baum 1974). The matching equation has been used in several experimental and natural studies and results frequently showed explained variances (r2) over 80% and sensitivity of 0.80 (Davison & McCarthy 2010). This high level of r2 might suggest that constraints within operant conditioning procedures may inflate GML parameters. For instance, in most operant procedures, such as a concurrent variable-interval schedule of reinforcement, the amount of reinforcers obtained is always lower or equal to the amount of responses, which can be seen as an emergent property of feedback functions. The purpose of the current study is to apply the GML to pseudorandomly sampled data in which this constraint has been computed. A Monte Carlo simulation shows that the generalized matching law explained on average 47 % of the variance, with sensitivity around a value of 0.60 and bias of log c = 0.00. Results found in the current study could be used as an alternative null hypothesis for future studies in natural settings. For instance, explained variances of 0.62, 0.80, and 0.97 could be qualify, respectively, as small, medium and large differences compared to 0.47. The current study is finally compared to McDowell's (2004) simulations. McDowell computed behavioral processes, such as the selection by consequences (Skinner, 1981), within the organism whereas the current study investigates environmental and observational constraints on the regressions estimates. Current results suggest further investigations of underlying environmental constraints when studying the GML. Futures studies are necessary to assess what to expect from the GML when such constraints occur in the operant conditioning procedure., La loi généralisée de l'appariement (LGA) est un modèle descriptif conceptualisant le ratio des réponses en fonction du ratio des renforçateurs (Baum, 1974). Les résultats des études montrent généralement une sensibilité autour de 0,80 et des variances expliquées (r2) supérieures à 0,80 (Davison & McCarthy, 1988). Les r2 très élevés de la LGA suggèrent la présence de contraintes inhérentes à la plupart des situations opérantes. Dans un programme de renforcement concurrent à intervalle variable, par exemple, la quantité de renforçateurs ne peut surpasser la quantité de comportements émis. L'objectif de la présente étude est de simuler les résultats de la LGA lorsque cette contrainte est implantée à des échantillons pseudoaléatoires. Au total, seize conditions sont répliquées 1 500 fois, représentant 24 000 essais. Les résultats montrent que la LGA obtient en moyenne un r2 de 47 %, une sensibilité de 0,60 et un biais nul. Les résultats suggèrent que des r2 de 0,62, 0,80 et 0,97 sont qualifiables, respectivement, de petite, moyenne et forte différence comparativement à 0,47. La perspective de la présente étude est comparée aux simulations de McDowell (2004) et des pistes de recherche futures sont présentées.

Picoeconomic (Ainslie, 1992) and the molar maximisation theory (Kagel, Battalio & Green, 1995) have risen from the integration of microeconomics within the experimental analysis of behavior. In both models, the relationship between a subject's responses and obtained reinforcers are said to respect the law of demand. The current study illustrates the integration of picoeconomic in the classroom by focusing on descriptive analyses of the relationship between the attention to the task rate of three students and different forms of interactions they received from their teachers. The purpose of the current study is to analyze these relationships according to three schedules of reinforcement that are the variable-ratio schedule, the variable-interval schedule and the concurrent schedule. Each schedule is also analyzed according to a molecular, local or molar perspective. Results indicate that at the molecular level, the generalized matching law is the best descriptor of children's behavior according to their teacher attention. The variable-interval schedule and the variable-ratio schedule were also statistically significant for one student each. At the molar level, the results show that attention rate is primarily a function of the relative rates of attention from the teacher. To conclude, relationships between subjects' behaviors and the associated reinforcers from their teachers were well pictured by economic concepts, and that the classical notion of program of reinforcement is neglected by authors interesting by descriptive and functional analysis of behavior., Dans le cadre de la picoéconomie, la contrainte exercée par un programme de renforcement est considérée comme le prix nécessaire à l'obtention d'un bien (Ainslie, 1992). L'allocation des réponses d'un sujet respecte alors la loi de la demande (Green & Kagel, 1987). La présente étude vise à illustrer l'intégration de la picoéconomie dans un contexte scolaire de salle de classe. Elle porte sur une analyse descriptive des relations entre le taux d'attention de trois écoliers d'une école primaire et différentes formes d'attention qu'ils obtiennent de leur enseignant. Ces relations sont analysées suivant trois programmes de renforcement, soit un programme à proportion variable, un programme à intervalle variable et un programme concurrent. L'étude vise à établir le type de contingences qui prédit le mieux le taux d'attention des écoliers en fonction d'une perspective moléculaire (séquences comportement-conséquence de 5 minutes), locale (séquences de 10 minutes) ou molaire (moyenne quotidienne). Les résultats de cette étude de cas suggèrent qu'une analyse moléculaire permet une meilleure prédiction des comportements des enfants. En revanche, la loi de l'appariement est le meilleur prédicteur du taux d'attention des écoliers autant sur le plan moléculaire que molaire. Ces résultats sont abordés selon le modèle picoéconomique d'Ainslie (1992). Enfin, il est relevé que l'analyse quantitative des relations entre comportement et conséquence en termes de programme de renforcement telle que réalisée dans la présente étude est totalement négligée par les auteurs qui s'intéressent à l'analyse descriptive et fonctionnelle du comportement.

Social sensitivity is defined by the adjustment of an organism to the contingencies of social reinforcement (Forget & Rivard, 2010) and relies on the generalized matching law (Baum, 1974) and the operant function of social attention (Sajwaj & Dillon, 1977) such as verbal and non-verbal approvals, staring, proximity (Forget & Otis, 1984). The current article assesses the actual state of knowledge on social sensitivity that has been carried over the last 30 years of research. Studies were identified through a search in PsycInfo regardless of the year of publication. The keywords were matching law, social sensitivity, social attention. The reference section of each article was further examined to identify additional studies on social sensitivity. Inclusion criteria were the use of single-subject designs with social reinforcers and single-subject statistical analyses relying on the generalized matching law. Other studies were rejected because of statistical issues arising from between-subject analyses (Caron, 2013). The current review identified 15 published articles and 4 theses. Results reveal that social sensitivity has been mostly studied on children with Autism Spectrum Disorder and within classroom. Most studies showed that the generalized matching law describes well participants' response allocation according to social reinforcers. Among the 83 identified participants, 57 % conformed to matching law predictions. Results suggest a continuum of social sensitivity. For instance, typical participants' response allocations were generally closer to matching law predictions whereas participants with Asperger syndrome appeared to be insensitive to social reinforcers. Response allocations of the latter population showed low explained variances and a single participant showed a high sensitivity parameter. Participants with Austism Spectrum Disorders ranged between these two groups and showed higher bias value. This result agrees with the idea that this population presents and prefers stereotypic behavior. However, the review shows that 78 % of the identified studies did not use experimental designs. Most studies relied on descriptive observations, that is unconstrained reinforcers ratios, that may lead to relevant issues (St. Peter al., 2005), incorrect outcomes (Thompson & Iwata, 2007) and does not allow definitive conclusions (Bijou, Peterson & Ault, 1968). Considering only experimental designs, a single study showed results in favor of the generalized matching law, another one shows mixed results and the last two cast doubt on the capacity of the generalized matching law to describe social interaction. These ambiguous conclusions clearly point out that more experimental studies are needed. Despite that the flight from natural fields to the laboratory may represent a challenge, it is the next necessary step forward a robust and relevant theory of social sensitivity., La sensibilité sociale se définit comme l'ajustement d'un organisme aux contingences de renforcement social de son environnement (Forget et Rivard, 2010). Ce concept repose sur la loi généralisée de l'appariement (Baum. 1974) et sur l'hypothèse selon laquelle l'attention sociale présente généralement une fonction de renforcement (Sajwaj & Dillon, 1977). La présente recension des écrits empiriques expose les résultats des trente dernières années de recherche sur cette notion de sensibilité. Parmi 83 sujets provenant de 19 études, la fréquence relative des comportements étudiés correspond majoritairement bien aux prédictions de la loi généralisée de l'appariement. Les résultats suggèrent un continuum de sensibilité d'une personne à l'autre, ou d'un type de personnes à l'autre. Ainsi, le comportement des populations tout-venant correspond davantage aux prédictions du modèle tandis que les personnes ayant un syndrome d'Asperger sembleraient insensibles aux renforçateurs sociaux. Par ailleurs, la sensibilité sociale des personnes ayant un trouble du spectre de l'autisme présente une plus grande variabilité, à mi-chemin entre ces deux premiers groupes. Toutefois, 78 % des études n'impliquent aucun contrôle expérimental du taux de renforcement prodigué par l'adulte. Si la loi généralisée de l'appariement semble avoir une valeur heuristique pour déterminer le degré de sensibilité d'une personne à son environnement social, l'établissement de la validité empirique et expérimentale du concept reste à démontrer.

Please check the original document before citing this paper.; International audience; The matching law, regardless of the version, is a mathematical model that accounts for an organism's response rate as a function of the reinforcer rate. McDowell (2012) investigated to which extent a combined version of the quantitative law of effect (Herrnstein, 1970) and the generalized matching law (Baum, 1974) accounts for a substantial amount of the variance through several data sets. Even if I agree with most points raised by McDowell, there are two important issues within his reanalysis. Two out of six studies relied on pooled-subject data that are inappropriate for an investigation of the matching law (Caron, 2013). Moreover, the combined equation was not systemically investigated through all data sets. The current study casts some doubt on the empirical status of modern matching equations and thus shows they still deserve extensive attention.