This study examines the impact of anonymity on students’ social-affective processes, as well as their perceptions and preferences regarding peer assessment and grading for both formative and summative purposes. 177 higher education students participated in this quasi-experimental study. They participated in two peer assessment activities after receiving training on the provision of effective feedback. The first peer assessment activity was formative in nature, while the second was summative. The study had two conditions: anonymous peer assessment and non-anonymous peer assessment. Results indicate that although 73.6 % of all students (90.5 % in the anonymous condition and 56.5 % in the non-anonymous condition) preferred anonymous peer assessment, this preference did not significantly impact perceptions of fairness or peer pressure. This challenges assumptions around the effects of anonymity. Interestingly, non-anonymous settings were still favourably viewed, with the open-ended responses indicating the value of face-to-face dialogue. This suggests that non-anonymous, highly formative peer assessment requiring more interaction may lead to better social and interpersonal outcomes.