Traditional analyses of psychometric data typically focus on the means or sums of individual item responses. In contrast, our new compositional data approach allows us to analyze psychometric data in a novel way, providing more concise results and fresh perspectives. The data we examined were originally published by Murphy et al. (2021) and pertain to personality traits, conspiracy beliefs, and the willingness to receive a COVID-19 vaccination in the United Kingdom and Ireland. Compared to traditional statistical methods, the compositional data approach reveals additional significant findings that enhance our understanding of human behavior and attitudes in the context of the COVID-19 pandemic. We emphasize that interpreting bipolar psychometric scale data through a compositional lens improves subsequent statistical analyses and yields more insightful results than conventional methods. The results affect data science approaches in health psychology, behavioral psychology and social psychology, e.g., regression and correlation based machine learning.