Background: Many engineering education researchers acknowledge that their positionality impacts their research. Practices for reporting positionality vary widely and rarely incorporate a nuanced discussion of the impact of demographic identities on research. Researchers holding marginalized or relatively hidden identities must navigate additional layers regarding transparency of their positionality. Purpose: We identify ways in which positionality impacts research, with a particular emphasis on demographic identity dimensions. We note that whether identities are relatively marginalized, privileged, hidden, or apparent in a research context creates complexities for conceptualizing, practicing, and disclosing one's positionality. Method: In a collaborative inquiry informed by autoethnography, we assemble positionality reflections of current engineering education researchers to demonstrate the primary ways in which positionality impacts research. Results: We find that positionality impacts six fundamental aspects of research: research topic, epistemology, ontology, methodology, relation to participants, and communication. These aspects of research delve deeper than conceptions of positionality as a methodological limitation, a measure to prevent bias, or a requirement for research quality. Conclusion: The impact of positionality on research is complex, particularly when researchers occupy minoritized identities and for research topics that interrogate power relations between identity groups. By demonstrating the practices of interrogating and representing positionality, we hope to encourage more researchers to represent positionality transparently, thus making researchers' transparency safer for all. We argue that positionality is an important tool for reflecting on and dislocating privilege, particularly when working on equity research.