This study discusses the mediating role of statistics anxiety and motivation in the relationship comprising academic dishonesty, personality traits, and previous academic achievements in three different learning environments (Face to Face-F2F, Planned Online Environment -- POE, and Emergency Remote Teaching -- ERT). Self-determination theory (SDT) provides a broad psychological framework for these phenomena. Data were collected from 649 bachelor-degree students in the Social Sciences in five Israeli academic institutions. Structural equation modelling was employed to investigate the research variables' relationships. Findings indicate that statistics anxiety mediates the relationship between personality traits and academic dishonesty in the POE and the ERT learning environments. Findings also indicate the relationship between students' achievements and academic dishonesty, but only in the ERT learning environment. In contrast, motivation mediates the relationship between students' achievements and statistics anxiety only in the POE learning environment. This study unveils that learning environments determine the mediating role of statistical anxiety. In digital learning environments (POE, ERT), mediation has been found between students' personality traits and academic dishonesty. No similar parallel mediation could be established in the physical learning environment, F2F. Thus, we conclude that online courses should be designed according to student-centred approaches.