Most colleges and universities offering institutional scholarship funds use some variation of Institutional Methodology (established by the College Board) to calculate a family’s Expected Family Contribution (EFC). The EFC is used to determine the student’s level of demonstrated need and overall eligibility for aid; this will appear on your offer letter from the University.
Data provided on the Free Application for Federal Student Aid (FAFSA) calculates the Student Aid Index (SAI), which is used only to determine eligibility for all federal aid, such as Pell Grants, Direct Loans, Federal Work-Study, and most State Scholarship Aid. Your federal Student Aid Index (SAI) and the Family Responsibility listed on your Brown aid offer will likely not be the same.