An example of social interaction: Spatial contagion effect in exams

In the last decades the study of collective phenomena has produced a great interest in the field of Statistical Physics within the framework of Complex Systems, being a paradigmatic example flocking, the collective motion of self-propelled organisms. Such studies have been more recently extended to collective human behavior, where social interactions are important and concepts such as ’social force’ have arisen. In this work we want to explore the possible existence of a ’social field’ in a very controlled human environment: a classroom where the students take an exam. Since the students are seated in individual tables while working in their corresponding exams, the only possible interaction occurs when the students finish the exam and deliver it to the teacher. We conjecture that the existence of social interactions could lead to a contagion effect among the students, so that a given student who delivers the exam may influence another close student to do the same, and as a result the exams are not randomly delivered in the space. In this sense, each classroom can be seen as a complex system, where there exist interactions between the different elements, the students. To show the existence of this contagion effect, we use experimental data registered in 10 high-school classrooms during different exams, and for each student we record the exam delivery time and the spatial location of the student in the classroom while taking the exam. We use the distances between students who finish the exam consecutively and compare these distances with the random expectation in the corresponding classroom using Monte Carlo simulations. We observe a significant nonrandom behavior of the experimental data, and show the existence of a clustering effect in space, supporting the existence of a contagion effect as a consequence of an underlying ’social field’. Finally, to quantify this contagion effect, we propose a probabilistic distance-driven contagion model, according to which a given student who delivers the exam may influence another student closer than a given distance to do the same with certain contagion probability. By comparing the results of the model with the experimental data, we obtain a global contagion probability of around 1/6.