The Survey of Physics Reasoning on Uncertainty Concepts in Experiments (SPRUCE) was designed to measure students' proficiency with measurement uncertainty concepts and practices across ten different assessment objectives to help facilitate the improvement of laboratory instruction focused on this important topic. To ensure the reliability and validity of this assessment, we conducted a comprehensive statistical analysis using classical test theory. This analysis includes an evaluation of the test as a whole, as well as an in-depth examination of individual items and assessment objectives. We make use of a previously reported on scoring scheme involving pairing items with assessment objectives, creating a new unit for statistical analysis referred to as a "couplet." The findings from our analysis provide evidence for the reliability and validity of SPRUCE as an assessment tool for undergraduate physics labs. This increases both instructors' and researchers' confidence in using SPRUCE for measuring students' proficiency with measurement uncertainty concepts and practices to ultimately improve laboratory instruction. Additionally, our results using couplets and assessment objectives demonstrate how these can be used with traditional classic test theory analysis.