Complex decision-making problems such as the privacy policy selection when sharing content in online social networks can significantly benefit from artificial intelligence systems. With the use of Computational Argumentation, it is possible to persuade human users to modify their initial decisions to avoid potential privacy threats and violations. In this paper, we present a study performed over 186 teenage users aimed at analysing their behaviour when we try to persuade them to modify the publication of sensitive content in Online Social Networks (OSN) with different arguments. The results of the study revealed that the personality traits and the social interaction data (e.g., number of comments, friends, and likes) of our participants were significantly correlated with the persuasive power of the arguments. Therefore, these sets of features can be used to model OSN users, and to estimate the persuasive power of different arguments when used in human-computer interactions. The findings presented in this paper are helpful for personalising decision support systems aimed at educating and preventing privacy violations in OSNs using arguments.