Instructors and researchers often use research-based assessments to identify the impact of instructional activities. These investigations often focus on issues of diversity, equity, and inclusions by comparing outcomes across social identity groups (e.g., gender, race, and class). Comparisons across groups assume the assessments measure the same factors in the same way across social identity groups. Very few research-based assessments, however, have validation evidence to support this assumption. Measurement invariance testing provides validity evidence that an assessment measures latent factors (e.g., Newtonian thinking or physics identity) equivalently across groups. We examined the measurement invariance of the Eaton and Willoughby five (EW5) factor model on the Force Concept Inventory. We found evidence for measurement invariance across the intersections of gender (men and women) and race or ethnicity (Asian, Black, Hispanic, White, and White Hispanic). These results indicate that performance differences across the five factors can further understanding of equity in physics courses. Without measurement invariance, such work could produce misleading results that undermine efforts to support equity in physics courses.