Justifications play a central role in argumentation, which is a core topic in school science education. This paper contributes to this field of research by presenting two studies in which we assess students' justifications for supporting or rejecting hypotheses in the physics lab based on self-collected, anomalous experimental data, which are defined as data that contradict a prior belief, hypothesis, or concept. Study 1 analyzes the spectrum of possible justifications students give in semi-structured interviews and categorizes these into ten types: "appeal to an authority," "data as evidence," "experimental competence (technical/skills)," "experimental competence (self-concept)," "ignorance," "intuition," "measurement uncertainties (explicit)," "measurement uncertainties (implicit)," "suitability of the experimental setup," and "use of theoretical concepts." Study 2 presents a questionnaire suitable for medium- and large-scale assessments that probes students' use of four of these types of justifications: "appeal to an authority," "data as evidence," "intuition," and "measurement uncertainties (explicit)." The questionnaire can be administered in 5-10 minutes and is designed for students in the eighth and ninth grades. We outline the development and quality of the assessment tools of both studies, reporting on the content validity, factorial validity, discriminant validity, convergent validity, and reliability of the questionnaire. The two studies shed light on the various justifications students use when evaluating anomalous data at a fine-grained level.