A polynomial regression and surface response analysis of the (in)congruence of enjoyment and anxiety in online EFL learning

Despite a bulk of research focusing on how foreign language enjoyment and anxiety influence engagement, such endeavors have been predominantly conducted using linear statistical methods and in traditional offline learning. Given that learners often experience multiple emotions simultaneously and computer-mediated language learning is becoming increasingly prevalent, it is essential to investigate how levels of enjoyment and anxiety—two extensively studied emotions in foreign language learning—align with each other, and how their congruence and incongruence impact learners' online learning engagement and interactions. The current study aimed to contribute to the literature by exploring both linear and curvilinear relationships between the (in)congruence of foreign language enjoyment and anxiety and their effects on online English learning engagement and interactions. Questionnaire responses from a total of 348 Chinese English-as-a-Foreign-Language (EFL) undergraduates from two universities were obtained. Polynomial regression with response surface analysis revealed that 1) the congruence between foreign language enjoyment and anxiety had a significantly positive linear relationship with emotional and cognitive engagement, as well as learner-learner, learner-instructor, and learner-content interactions; 2) the incongruence between enjoyment and anxiety had positive linear relationships with all the outcomes and positive curvilinear relationships with learner-learner and learner-instructor interactions; 3) along the line of congruence, the outcomes were higher when both enjoyment and anxiety were high; along the line of incongruence, the outcomes were higher when enjoyment was higher than anxiety. Theoretical and practical implications were also discussed.