Invariant relationships in the internal mechanisms of estimating achievement scores on educational tests serve as the basis for concluding that a particular test is fair with respect to statistical bias concerns. Equating invariance and differential item functioning are both concerned with invariant relationships yet are treated separately in the psychometric literature. Connecting these two facets of statistical invariance is critical for developing a holistic definition of fairness in educational measurement, for fostering a deeper understanding of the nature and causes of equating invariance and a lack thereof, and for providing practitioners with guidelines for addressing reported score-level equity concerns. This study hypothesizes that differential item functioning manifested in anchor items of an assessment will have an effect on equating dependence. Findings show that when anchor item differential item functioning varies across forms in a differential manner across subpopulations, population invariance of equating can be compromised.