The fairness and precision of peer assessment have been questioned by educators and academics. Of particular interest, yet poorly understood, are the factors underlying the biases that cause unfair and imprecise peer assessments. To shed light on this issue, I investigated gender and academic major biases in peer assessments of oral presentations. The study sample comprised 66 science students enrolled in a formative assessment-based communication module at an Asian university. Each student presented an oral presentation in English and also evaluated 10-14 of their classmates' oral presentations. The students' evaluations were anchored by the instructor's evaluation of each oral presentation. I performed many-facet Rasch measurement (MFRM) for two purposes: (a) to examine the effect of multiple facets on the student and teacher ratings of oral presentations and (b) to adjust the ratings on oral presentations according to gender and academic major biases. The scores assigned by student raters had good fit to MFRM; however, when students evaluated oral presentations by peers of the opposite sex, the scores were overestimated. An academic major bias was also observed, where students consistently underestimated the scores of same-major peers. After adjusting for biases, it was concluded that peer assessments can be a reliable and useful form of formative assessment.