Des outils pour évaluer la sensibilité au renforcement sous Excel, R et Matlab

C’est dans les années 1990s que l’on note un accroissement important des études sur les applications en milieux naturels et en contextes appliqués de la loi de l’appariement. Le problème est cependant qu’il n’existe que des règles arbitraires non soutenues empiriquement et théoriquement pour évaluer si, effectivement, les comportements d’un agent respectent les prédictions de loi de l’appariement (si le modèle s’applique bien aux données comportementales). Depuis des travaux récents, une avenue intéressante se basant sur les propriétés statistiques inhérentes aux situations opérantes et utilisant ces dernières comme modèle nul répond à ce problème. Cette conceptualisation possède plusieurs avantages : elle s’accorde avec une perspective molaire-moléculaire du comportement, elle repose sur des mathématiques formelles et elle est flexible par rapport aux probabilités comportementales et de renforcement. Cependant, il n’existe aucune façon simple de réaliser ces calculs. Dans l’optique de démocratiser son utilisation et d’améliorer la qualité des études publiées sur la loi de l’appariement, l’objectif du présent article est de présenter trois logiciels implémentant les calculs du modèle et du test d’hypothèse pour évaluer la sensibilité au renforcement. Un exemple est présenté en guise de conclusion afin d’illustrer la procédure.

In the 1990s, there is an increase in the number of paper published on the matching law in natural and applied settings. In these transactional studies, the matching law is used as a tool to evaluate whether subjects’ behavior is sensitive to contingencies of reinforcement. The problem however is that there is only arbitrary rules of thumb, neither supported empirically nor theoretically, to evaluate whether a subject's behavior is sensitive to reinforcement or not (i.e., if the subject's behavior follows the matching law). Recent works on the statistical properties in operant settings address this problem. The model proposed is that a subjects’ behavior should be significantly different from random noise (randomly generated behavior). It is based on the following conjectures: response and reinforce rate follow a binomial distribution; reinforcer rates are conditional to response rates; response rates are correlated to each other. This leads to compute an expected correlation representing random variation in behavior-reinforcer contingencies to which the matching relation can be compared. This approach has numerous advantages such as being consistent with an molar-molecular perspectives, as being derived from formal mathematics, and as being flexible in accounting for different probabilities of reinforcement and responses. Unfortunately, there is no simple way to carry out the computation implied by this model. The current paper presents a software (in Microsoft Office Excel) and two scripts (in R and Matlab) implementing the works on the statistical properties in operant settings. They are all available online. Researchers and practitioners can enter the reinforcer and response probabilities in the top left corner. Choice of Type I error, unilateral or bilateral testing is implemented. The output is in the middle left of the spreadsheet and shows the hypothetical correlation (null hypothesis), the z-score and the P-value relevant to the hypothesis testing. Finally, he paper illustrate the procedure with an example. The results show a subject’ behavior sensitivity to reinforcement with explained variance of 82% (r = .90). Based on the empirical data, response and reinforcer rates are then computed. Probabilities of responses to option 1 or 2 are .67 and .34 respectively and the unconditional (independent of response rate) probabilities of reinforcers are .66 and .59, which are relatively high. Given the observation sampling a correlation of −1 is added to the hypothesis model (correlation between response rate). Following the R and Matlab scripts or the Excel spreadsheet, the results shows that the hypothetical correlation is .78, z = 1.87, P = .032, which is significant with a unilateral test with a threshold of .05. Thus, the subjects’ behaviors are likely to follows the matching law rather than being due to a random process. It is finally worth to note the flexibility of the null model. For instance, if reinforcer probabilities would have been lower, such as .20 and .30, then, in this case, the results would have been an hypothetical correlation of .50, z = .87, P < 0.001, suggesting a more important difference between the null model and the data. To conclude, the current work is an attempt to promote the use of quantitative analysis as well as a more rigorous approach in testing the matching law.