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Construct validity of peer assessment (PA) is important for PA application, yet difficult to achieve. The present study investigated the impact of an assessment rubric and friendship between the assessor and assessee on construct validity of PA. Two-hundred nine bachelor students participated: half of them assessed a peer's concept map with a rubric whereas the other half did not use a rubric. The results revealed a substantial reliability and construct validity for PA. All students over-score their peers’ performance, but students using a rubric were more valid. Moreover, when using a rubric a high level of friendship between assessor and assessee resulted in more over-scoring. Use of a rubric resulted in higher quality concept maps for peer and expert ratings.