Most equivalence scales that are applied in research on inequality do not depend on income, even though there is strong empirical evidence that equivalence scales are actually income-dependent. This paper explores the consistency of results derived from income-independent and income-dependent scales. We show that applying income-independent scales when income-dependent scales would be appropriate leads to violations of the transfer principle. Surprisingly, there are some exceptions, but these require unrealistic and strong assumptions. Thus, the use of income-dependent equivalence scales almost always leads to different assessments of inequality than the use of income-independent equivalence scales. Two examples illustrate our findings.